Tables of polyhedra vertices, faces, and edges. More...

Collaboration diagram for Polyhedra:

Files
file	polyhedra_all.scad
	Polyhedra data table: `polyhedra_all`.

file	anti_prisms.scad
	Polyhedra data table: `anti_prisms`.

file	archimedean_duals.scad
	Polyhedra data table: `archimedean_duals`.

file	archimedean.scad
	Polyhedra data table: `archimedean`.

file	cupolas.scad
	Polyhedra data table: `cupolas`.

file	dipyramids.scad
	Polyhedra data table: `dipyramids`.

file	johnson.scad
	Polyhedra data table: `johnson`.

file	platonic.scad
	Polyhedra data table: `platonic`.

file	prisms.scad
	Polyhedra data table: `prisms`.

file	pyramids.scad
	Polyhedra data table: `pyramids`.

file	trapezohedron.scad
	Polyhedra data table: `trapezohedron`.

Detailed Description

Tables of polyhedra vertices, faces, and edges.

Database of polyhedra vertices, faces, and edges. Classes of polyhedra are grouped into separate files. The file polyhedra_all.scad contains all polyhedra from all files. Each table uses the following column data structure.

field	description
id	identifier
n	name
o	other name
g	group
d	data source
c	cartesian vertices
s	spherical vertices
f	faces
e	edges

Use the functions table_get_value() to retrieve field data as show in the following example. To see a list of table identifiers consider the function table_get_row_ids(), table_get_column_ids(), or module table_dump(). See datatypes/table.scad for other available table functions. For a general introduction to this topic, see Wikipedia on Polyhedron.

Example

include <omdl-base.scad>;
include <units/coordinate.scad>;
include <tools/polytope.scad>;
include <database/geometry/polyhedra/platonic.scad>;
 
tc = dtc_polyhedra_platonic;
tr = dtr_polyhedra_platonic;
 
id = "dodecahedron";
 
pv = table_get_value(tr, tc, id, "c");
pf = table_get_value(tr, tc, id, "f");
 
sv = coordinate_scale3d_csc(pv, 100);
 
polytope_number(sv, pf, to=[0,0,5]);
polytope_frame(sv, pf) {circle(r=2); color("grey") sphere(r=4);}
polyhedron(sv, pf);

Autotests

ECHO: "checking table: "
ECHO: "colums = dtc_polyhedra_polyhedra_all"
ECHO: "  rows = dtr_polyhedra_polyhedra_all"
ECHO: "[ INFO ] table_check(); begin table check"
ECHO: "[ INFO ] table_check(); row identifier found at column zero."
ECHO: "[ INFO ] table_check(); checking row column counts."
ECHO: "[ INFO ] table_check(); checking for repeat column identifiers."
ECHO: "[ INFO ] table_check(); checking for repeat row identifiers."
ECHO: "[ INFO ] table_check(); table size: 164 rows by 9 columns."
ECHO: "[ INFO ] table_check(); end table check"
ECHO: 
ECHO: "confirming calculations stored in table:"
ECHO: "  (1) spherical with converted cartesian coordinates:"
ECHO: "  (2) edge list from faces definition:"
ECHO: "[ INFO ] root(); edge-list not sorted: id=anti_prisms_triangular_antiprism"
ECHO: "[ INFO ] root(); edge-list not sorted: id=archimedean_duals_rhombic_dodecahedron"
ECHO: "[ INFO ] root(); edge-list not sorted: id=archimedean_cuboctahedron"
ECHO: "[ INFO ] root(); edge-list not sorted: id=cupolas_triangular_gyrobicupola"
ECHO: "[ INFO ] root(); edge-list not sorted: id=platonic_octahedron"
ECHO: 
ECHO: "164 polyhedra checked."

Anti Prisms

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/anti_prisms.scad>;

Examples
(1)	(2)	(3)	(4)
decagonal antiprism	hexagonal antiprism	octagonal antiprism	pentagonal antiprism
(5)	(6)
square antiprism	triangular antiprism

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	decagonal_antiprism	-	20	22	40	3^x²⁰, 10^x²	20.8^x⁴⁰, 35.8^x⁴⁰, 84.8^x⁴⁰, 95.2^x⁴⁰	0.597^x⁴⁰	36^x²⁰, 120^x⁶⁰
2	hexagonal_antiprism	-	12	14	24	3^x¹², 6^x²	34.8^x²⁴, 59.2^x²⁴, 81.1^x²⁴, 98.9^x²⁴	0.919^x²⁴	60^x¹², 120^x³⁶
3	octagonal_antiprism	-	16	18	32	3^x¹⁶, 8^x²	26^x³², 44.7^x³², 83.4^x³², 96.6^x³²	0.727^x³²	45^x¹⁶, 120^x⁴⁸
4	pentagonal_antiprism	-	10	12	20	3^x¹⁰, 5^x²	41.8^x²⁰, 70.5^x²⁰, 79.2^x²⁰, 100.8^x²⁰	1.05^x²⁰	72^x¹⁰, 120^x³⁰
5	square_antiprism	-	8	10	16	3^x⁸, 4^x²	52.4^x¹⁶, 76.2^x¹⁶, 86.7^x¹⁶, 103.8^x¹⁶	1.22^x¹⁶	90^x⁸, 120^x²⁴
6	triangular_antiprism	Octahedron	6	8	12	3^x⁸	70.5^x²⁴, 109.5^x²⁴	1.41^x¹²	120^x²⁴

Archimedean Duals

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/archimedean_duals.scad>;

Examples
(1)	(2)	(3)	(4)
disdyakis dodecahedron	disdyakis triacontahedron	kite hexecontahedron	kite icositetrahedron
(5)	(6)	(7)	(8)
pentagonal hexecontahedron	pentagonal icositetrahedron	pentakis dodecahedron	rhombic dodecahedron
(9)	(10)	(11)	(12)
rhombic triacontahedron	tetrakis hexahedron	triakis icosahedron	triakis octahedron
(13)
triakis tetrahedron

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	disdyakis_dodecahedron	Hexakis-Octahedron	26	48	72	3^x⁴⁸	6.9^x⁴⁸, 32.7^x⁴⁸, 38.2^x⁹⁶, 43.1^x⁹⁶, 47.3^x⁹⁶, 50.6^x⁴⁸, 54.6^x⁴⁸, 55.1^x⁹⁶	0.606^x²⁴, 0.765^x²⁴, 0.919^x²⁴	96.7^x⁴⁸, 124.2^x⁴⁸, 139.1^x⁴⁸
2	disdyakis_triacontahedron	Hexakis-Icosahedron	62	120	180	3^x¹²⁰	15.1^x³⁶⁰, 21.4^x¹²⁰, 26.3^x²⁴⁰, 29^x²⁴⁰, 30.5^x¹²⁰, 40.3^x²⁴⁰, 47.7^x²⁴⁰, 50.4^x¹²⁰	0.37^x⁶⁰, 0.581^x⁶⁰, 0.683^x⁶⁰	91^x¹²⁰, 121.8^x¹²⁰, 147.2^x¹²⁰
3	kite_hexecontahedron	-	62	60	120	4^x⁶⁰	25.9^x²⁴⁰, 36.9^x¹²⁰, 42.5^x¹²⁰	0.37^x⁶⁰, 0.569^x⁶⁰	61.7^x⁶⁰, 93^x¹²⁰, 112.2^x⁶⁰
4	kite_icositetrahedron	-	26	24	48	4^x²⁴	41.9^x⁹⁶, 60.7^x⁷²	0.592^x²⁴, 0.765^x²⁴	64.7^x²⁴, 98.4^x⁷²
5	pentagonal_hexecontahedron	-	92	60	150	5^x⁶⁰	26.8^x³⁰⁰, 44.1^x¹²⁰	0.278^x⁹⁰, 0.486^x⁶⁰	61.9^x²⁴⁰, 112.5^x⁶⁰
6	pentagonal_icositetrahedron	-	38	24	60	5^x²⁴	43.7^x¹²⁰, 63.5^x²⁴	0.436^x³⁶, 0.619^x²⁴	65.2^x⁹⁶, 99.2^x²⁴
7	pentakis_dodecahedron	-	32	60	90	3^x⁶⁰	23.3^x¹⁸⁰, 38.1^x¹²⁰, 40.9^x²⁴⁰, 47.6^x¹²⁰	0.678^x⁶⁰, 0.764^x³⁰	111.4^x⁶⁰, 124.3^x¹²⁰
8	rhombic_dodecahedron	-	14	12	24	4^x¹²	60^x⁴⁸, 90^x²⁴	0.866^x²⁴	70.5^x²⁴, 109.5^x²⁴
9	rhombic_triacontahedron	-	32	30	60	4^x³⁰	36^x¹²⁰, 60^x¹²⁰	0.691^x⁶⁰	63.4^x⁶⁰, 116.6^x⁶⁰
10	tetrakis_hexahedron	-	14	24	36	3^x²⁴	36.9^x⁷², 53.1^x²⁴, 66.4^x⁹⁶, 78.5^x⁴⁸	1.06^x²⁴, 1.41^x¹²	96.4^x²⁴, 131.8^x⁴⁸
11	triakis_icosahedron	-	32	60	90	3^x⁶⁰	19.4^x¹⁸⁰, 37.4^x²⁴⁰, 52.3^x²⁴⁰, 62.4^x²⁴⁰, 66^x¹²⁰	0.717^x⁶⁰, 1.24^x³⁰	61^x⁶⁰, 149.5^x¹²⁰
12	triakis_octahedron	-	14	24	36	3^x²⁴	32.6^x⁷², 62.6^x⁹⁶, 85.5^x⁹⁶, 94.5^x⁴⁸	1.17^x²⁴, 2^x¹²	62.8^x²⁴, 148.6^x⁴⁸
13	triakis_tetrahedron	-	8	12	18	3^x¹²	50.5^x³⁶, 95.2^x⁴⁸, 117^x²⁴	1.7^x¹², 2.83^x⁶	67.1^x¹², 146.4^x²⁴

Archimedean

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/archimedean.scad>;

Examples
(1)	(2)	(3)	(4)
cuboctahedron	icosidodecahedron	rhombicosidodecahedron	rhombicuboctahedron
(5)	(6)	(7)	(8)
snub cuboctahedron	snub icosidodecahedron	truncated cube	truncated cuboctahedron
(9)	(10)	(11)	(12)
truncated dodecahedron	truncated icosahedron	truncated icosidodecahedron	truncated octahedron
(13)
truncated tetrahedron

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	cuboctahedron	-	12	14	24	3^x⁸, 4^x⁶	54.7^x⁴⁸, 70.5^x²⁴, 90^x²⁴	1.41^x²⁴	90^x²⁴, 120^x²⁴
2	icosidodecahedron	-	30	32	60	3^x²⁰, 5^x¹²	37.4^x¹²⁰, 41.8^x⁶⁰, 63.4^x⁶⁰	0.65^x⁶⁰	72^x⁶⁰, 120^x⁶⁰
3	rhombicosidodecahedron	-	60	62	120	3^x²⁰, 4^x³⁰, 5^x¹²	20.9^x¹²⁰, 31.7^x¹²⁰, 36^x¹²⁰, 37.4^x¹²⁰	0.46^x¹²⁰	72^x⁶⁰, 90^x¹²⁰, 120^x⁶⁰
4	rhombicuboctahedron	-	24	26	48	3^x⁸, 4^x¹⁸	35.3^x⁴⁸, 45^x⁴⁸, 54.7^x⁴⁸, 60^x⁴⁸	0.765^x⁴⁸	90^x⁷², 120^x²⁴
5	snub_cuboctahedron	-	24	38	60	3^x³², 4^x⁶	26.8^x⁷², 37^x⁴⁸, 45.9^x⁹⁶, 50.4^x⁴⁸, 54.7^x⁹⁶	0.802^x⁶⁰	90^x²⁴, 120^x⁹⁶
6	snub_icosidodecahedron	Snub Dodecahedron	60	92	150	3^x⁸⁰, 5^x¹²	15.8^x¹⁸⁰, 27.1^x¹²⁰, 27.3^x²⁴⁰, 31^x¹²⁰, 37.4^x²⁴⁰	0.477^x¹⁵⁰	72^x⁶⁰, 120^x²⁴⁰
7	truncated_cube	-	24	14	36	3^x⁸, 8^x⁶	54.7^x⁴⁸, 90^x²⁴	0.586^x³⁶	45^x⁴⁸, 120^x²⁴
8	truncated_cuboctahedron	Great Rhombicuboctahedron	48	26	72	4^x¹², 6^x⁸, 8^x⁶	35.3^x⁴⁸, 45^x⁴⁸, 54.7^x⁴⁸	0.442^x⁷²	45^x⁴⁸, 60^x⁴⁸, 90^x⁴⁸
9	truncated_dodecahedron	-	60	32	90	3^x²⁰, 10^x¹²	37.4^x¹²⁰, 63.4^x⁶⁰	0.342^x⁹⁰	36^x¹²⁰, 120^x⁶⁰
10	truncated_icosahedron	Soccer Ball	60	32	90	5^x¹², 6^x²⁰	37.4^x¹²⁰, 41.8^x⁶⁰	0.412^x⁹⁰	60^x¹²⁰, 72^x⁶⁰
11	truncated_icosidodecahedron	Great Rhombicosidodecahedron	120	62	180	4^x³⁰, 6^x²⁰, 10^x¹²	20.9^x¹²⁰, 31.7^x¹²⁰, 37.4^x¹²⁰	0.265^x¹⁸⁰	36^x¹²⁰, 60^x¹²⁰, 90^x¹²⁰
12	truncated_octahedron	-	24	14	36	4^x⁶, 6^x⁸	54.7^x⁴⁸, 70.5^x²⁴	1.41^x³⁶	60^x⁴⁸, 90^x²⁴
13	truncated_tetrahedron	-	12	8	18	3^x⁴, 6^x⁴	70.5^x²⁴, 109.5^x¹²	2.83^x¹⁸	60^x²⁴, 120^x¹²

Cupolas

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/cupolas.scad>;

Examples
(1)	(2)	(3)	(4)
pentagonal cupola	pentagonal gyrobicupola	pentagonal orthobicupola	square cupola
(5)	(6)	(7)	(8)
square gyrobicupola	square orthobicupola	triangular cupola	triangular gyrobicupola
(9)
triangular orthobicupola

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	pentagonal_cupola	J5	15	12	25	3^x⁵, 4^x⁵, 5^x¹, 10^x¹	20.9^x²⁰, 31.7^x¹⁰, 36^x¹⁰, 37.4^x¹⁰, 142.6^x¹⁰, 148.3^x¹⁰	0.614^x²⁵	36^x¹⁰, 72^x⁵, 90^x²⁰, 120^x¹⁵
2	pentagonal_gyrobicupola	J31	20	22	40	3^x¹⁰, 4^x¹⁰, 5^x²	20.9^x⁴⁰, 31.7^x²⁰, 36^x²⁰, 37.4^x²⁰, 109.5^x²⁰, 110.9^x²⁰, 120^x²⁰	0.618^x⁴⁰	72^x¹⁰, 90^x⁴⁰, 120^x³⁰
3	pentagonal_orthobicupola	J30	20	22	40	3^x¹⁰, 4^x¹⁰, 5^x²	20.9^x⁴⁰, 31.7^x²⁰, 36^x²⁰, 37.4^x²⁰, 105.2^x¹⁰, 114.7^x⁴⁰, 116.6^x¹⁰	0.618^x⁴⁰	72^x¹⁰, 90^x⁴⁰, 120^x³⁰
4	square_cupola	J4	12	10	20	3^x⁴, 4^x⁵, 8^x¹	35.3^x¹⁶, 45^x⁸, 54.7^x⁸, 60^x⁸, 125.3^x⁸, 135^x⁸	0.753^x²⁰	45^x⁸, 90^x²⁰, 120^x¹²
5	square_gyrobicupola	J29	16	18	32	3^x⁸, 4^x¹⁰	35.3^x³², 45^x¹⁶, 54.7^x¹⁶, 60^x¹⁶, 80.3^x¹⁶, 82.1^x¹⁶, 98.4^x¹⁶	0.765^x³²	90^x⁴⁰, 120^x²⁴
6	square_orthobicupola	J28	16	18	32	3^x⁸, 4^x¹⁰	35.3^x³², 45^x¹⁶, 54.7^x¹⁶, 60^x¹⁶, 70.5^x⁸, 90^x⁴⁰	0.765^x³²	90^x⁴⁰, 120^x²⁴
7	triangular_cupola	J3	9	8	15	3^x⁴, 4^x³, 6^x¹	54.7^x¹⁸, 70.5^x⁶, 90^x⁶, 109.5^x⁶, 125.3^x⁶	0.965^x¹⁵	60^x⁶, 90^x¹², 120^x¹²
8	triangular_gyrobicupola	Cuboctahedron	12	14	24	3^x⁸, 4^x⁶	54.7^x⁴⁸, 70.5^x²⁴, 90^x²⁴	1^x²⁴	90^x²⁴, 120^x²⁴
9	triangular_orthobicupola	J27	12	14	24	3^x⁸, 4^x⁶	38.9^x⁶, 54.7^x³⁶, 70.5^x¹⁸, 78.9^x²⁴, 90^x¹²	1^x²⁴	90^x²⁴, 120^x²⁴

Dipyramids

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/dipyramids.scad>;

Examples
(1)	(2)	(3)	(4)
decagonal bi pyramid	hexagonal bi pyramid	octagonal di pyramid	pentagonal di pyramid
(5)	(6)
square di pyramid	triangular di pyramid

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	decagonal_bi_pyramid	-	12	20	30	3^x²⁰	34.3^x⁶⁰, 49.4^x⁴⁰, 68.3^x⁴⁰, 101.2^x⁴⁰, 130.6^x⁴⁰, 145.7^x²⁰	0.201^x¹⁰, 1.05^x²⁰	95.5^x⁴⁰, 169^x²⁰
2	hexagonal_bi_pyramid	-	8	12	18	3^x¹²	53.1^x³⁶, 78.5^x²⁴, 101.5^x²⁴, 126.9^x¹²	0.577^x⁶, 1.15^x¹²	104.5^x²⁴, 151^x¹²
3	octagonal_di_pyramid	-	10	16	24	3^x¹⁶	41.9^x⁴⁸, 60.7^x³², 82.7^x³², 119.3^x³², 138.1^x¹⁶	0.317^x⁸, 1.08^x¹⁶	98.4^x³², 163.2^x¹⁶
4	pentagonal_di_pyramid	-	7	10	15	3^x¹⁰	60.9^x³⁰, 91.6^x²⁰, 110.2^x²⁰	0.854^x⁵, 1.24^x¹⁰	110.2^x²⁰, 139.6^x¹⁰
5	square_di_pyramid	Octahedron	6	8	12	3^x⁸	70.5^x²⁴, 109.5^x²⁴	1.41^x¹²	120^x²⁴
6	triangular_di_pyramid	-	5	6	9	3^x⁶	81.8^x¹⁸, 135.6^x¹²	1.15^x⁶, 1.73^x³	82.8^x⁶, 138.6^x¹²

Johnson

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/johnson.scad>;

Examples
(1)	(2)	(3)	(4)
augmented dodecahedron	augmented hexagonal prism	augmented pentagonal prism	augmented sphenocorona
(5)	(6)	(7)	(8)
augmented triangular prism	augmented tridiminished icosahedron	augmented truncated cube	augmented truncated dodecahedron
(9)	(10)	(11)	(12)
augmented truncated tetrahedron	biaugmented pentagonal prism	biaugmented triangular prism	biaugmented truncated cube
(13)	(14)	(15)	(16)
bigyrate diminished rhombicosidodecahedron	bilunabirotunda	diminished rhombicosidodecahedron	disphenocingulum
(17)	(18)	(19)	(20)
elongated pentagonal cupola	elongated pentagonal dipyramid	elongated pentagonal gyrobicupola	elongated pentagonal gyrobirotunda
(21)	(22)	(23)	(24)
elongated pentagonal gyrocupolarotunda	elongated pentagonal orthobicupola	elongated pentagonal orthobirotunda	elongated pentagonal orthocupolarotunda
(25)	(26)	(27)	(28)
elongated pentagonal pyramid	elongated pentagonal rotunds	elongated square cupola	elongated square dipyramid
(29)	(30)	(31)	(32)
elongated square gyrobicupola	elongated square pyramid	elongated triangular cupola	elongated triangular dipyramid
(33)	(34)	(35)	(36)
elongated triangular gyrobicupola	elongated triangular orthobicupola	elongated triangular pyramid	gyrate bidiminished rhombicosidodecahedron
(37)	(38)	(39)	(40)
gyrate rhombicosidodecahedron	gyrobifastigium	gyroelongated pentagonal bicupola	gyroelongated pentagonal birotunda
(41)	(42)	(43)	(44)
gyroelongated pentagonal cupola	gyroelongated pentagonal cupolarotunda	gyroelongated pentagonal pyramid	gyroelongated pentagonal rotunda
(45)	(46)	(47)	(48)
gyroelongated square bicupola	gyroelongated square cupola	gyroelongated square dipyramid	gyroelongated square pyramid
(49)	(50)	(51)	(52)
gyroelongated triangular bicupola	gyroelongated triangular cupola	hebesphenomegacorona	metabiaugmented dodecahedron
(53)	(54)	(55)	(56)
metabiaugmented hexagonal prism	metabiaugmented truncated dodecahedron	metabidiminished icosahedron	metabidiminished rhombicosidodecahedron
(57)	(58)	(59)	(60)
metabigyrate rhombicosidodecahedron	metagyrate diminished rhombicosidodecahedron	parabiaugmented dodecahedron	parabiaugmented hexagonal prism
(61)	(62)	(63)	(64)
parabiaugmented truncated dodecahedron	parabidiminished rhombicosidodecahedron	parabigyrate rhombicosidodecahedron	paragyrate diminished rhombicosidodecahedron
(65)	(66)	(67)	(68)
pentagonal cupola	pentagonal dipyramid	pentagonal gyrobicupola	pentagonal gyrocupolarotunda
(69)	(70)	(71)	(72)
pentagonal orthobicupola	pentagonal orthobirotunda	pentagonal orthocupolarontunda	pentagonal pyramid
(73)	(74)	(75)	(76)
pentagonal rotunda	snub disphenoid	snub square antiprism	sphenocorona
(77)	(78)	(79)	(80)
sphenomegacorona	square cupola	square gyrobicupola	square orthobicupola
(81)	(82)	(83)	(84)
square pyramid	triangular cupola	triangular dipyramid	triangular hebesphenorotunda
(85)	(86)	(87)	(88)
triangular orthobicupola	triaugmented dodecahedron	triaugmented hexagonal prism	triaugmented triangular prism
(89)	(90)	(91)	(92)
triaugmented truncated dodecahedron	tridiminished icosahedron	tridiminished rhombicosidodecahedron	trigyrate rhombicosidodecahedron

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	augmented_dodecahedron	J58	21	16	35	3^x⁵, 5^x¹¹	26.1^x¹⁰, 41.8^x¹⁰, 58.5^x²⁰, 63.4^x⁵⁰, 70.5^x¹⁰	0.641^x³⁵	72^x⁵⁵, 120^x¹⁵
2	augmented_hexagonal_prism	J54	13	11	22	3^x⁴, 4^x⁵, 6^x²	5.3^x⁴, 35.3^x⁴, 60^x⁸, 70.5^x⁸, 73.2^x⁸, 90^x²⁸, 109.5^x⁴	0.689^x²²	60^x¹², 90^x²⁰, 120^x¹²
3	augmented_pentagonal_prism	J52	11	10	19	3^x⁴, 4^x⁴, 5^x²	17.3^x⁴, 35.3^x⁴, 70.5^x⁸, 72^x⁶, 79.7^x⁸, 90^x²⁴, 109.5^x⁴	0.788^x¹⁹	72^x¹⁰, 90^x¹⁶, 120^x¹²
4	augmented_sphenocorona	J87	11	17	26	3^x¹⁶, 4^x¹	8.2^x², 15.7^x⁴, 20.1^x⁴, 27.8^x², 31^x⁴, 36.5^x⁸, 44^x⁸, 48.6^x², 61.1^x⁸, 61.7^x⁴, 62^x⁴, 68.2^x⁸, 69.7^x⁴, 70.5^x¹², 70.7^x⁴, 72^x⁸, 72.3^x⁸, 74^x⁴, 74.8^x⁴, 78.9^x⁸, 81.3^x⁴, 82.5^x², 82.7^x⁸, 85.7^x⁴, 87.5^x⁸, 104.5^x⁴, 109.5^x⁴	0.858^x²⁶	90^x⁴, 120^x⁴⁸
5	augmented_triangular_prism	J49	7	8	13	3^x⁶, 4^x²	35.3^x⁴, 65.3^x⁴, 70.5^x⁸, 90^x¹⁶, 106.8^x⁸, 109.5^x⁴, 120^x²	1.14^x¹³	90^x⁸, 120^x¹⁸
6	augmented_tridiminished_icosahedron	J64	10	10	18	3^x⁷, 5^x³	8.7^x⁶, 41.8^x⁶, 70.5^x⁶, 79.2^x¹², 100.8^x⁶, 109.5^x⁶, 113.6^x¹², 116.6^x⁶	0.976^x¹⁸	72^x¹⁵, 120^x²¹
7	augmented_truncated_cube	J66	28	22	48	3^x¹², 4^x⁵, 8^x⁵	9.7^x⁸, 35.3^x²⁴, 36.4^x¹⁶, 45^x⁸, 54.7^x⁴⁸, 60^x²⁴, 90^x¹⁶	0.506^x⁴⁸	45^x⁴⁰, 90^x²⁰, 120^x³⁶
8	augmented_truncated_dodecahedron	J68	65	42	105	3^x²⁵, 4^x⁵, 5^x¹, 10^x¹¹	5.7^x¹⁰, 20.9^x²⁰, 21.6^x²⁰, 26.1^x¹⁰, 31.7^x¹⁰, 36^x¹⁰, 37.4^x¹²⁰, 40.5^x²⁰, 63.4^x⁵⁰	0.316^x¹⁰⁵	36^x¹¹⁰, 72^x⁵, 90^x²⁰, 120^x⁷⁵
9	augmented_truncated_tetrahedron	J65	15	14	27	3^x⁸, 4^x³, 6^x³	15.8^x⁶, 38.9^x⁶, 54.7^x¹⁸, 56.3^x¹², 70.5^x²⁴, 78.9^x¹², 90^x⁶, 109.5^x⁶	0.7^x²⁷	60^x¹⁸, 90^x¹², 120^x²⁴
10	biaugmented_pentagonal_prism	J53	12	13	23	3^x⁸, 4^x³, 5^x²	17.3^x⁸, 35.3^x⁸, 70.5^x¹⁶, 72^x², 79.7^x¹⁶, 90^x²⁸, 109.5^x⁸	0.727^x²³	72^x¹⁰, 90^x¹², 120^x²⁴
11	biaugmented_triangular_prism	J50	8	11	17	3^x¹⁰, 4^x¹	10.5^x², 35.3^x⁸, 60^x⁴, 65.3^x⁴, 70.5^x¹⁶, 76^x⁸, 90^x²⁰, 106.8^x⁸, 109.5^x⁸	1.06^x¹⁷	90^x⁴, 120^x³⁰
12	biaugmented_truncated_cube	J67	32	30	60	3^x¹⁶, 4^x¹⁰, 8^x⁴	9.7^x¹⁶, 35.3^x⁴⁸, 36.4^x³², 45^x¹⁶, 54.7^x⁴⁸, 60^x⁴⁸, 90^x⁸	0.49^x⁶⁰	45^x³², 90^x⁴⁰, 120^x⁴⁸
13	bigyrate_diminished_rhombicosidodecahedron	J79	55	52	105	3^x¹⁵, 4^x²⁵, 5^x¹¹, 10^x¹	20.9^x⁷⁰, 26.1^x²⁰, 26.6^x²⁰, 31.7^x⁸⁰, 33.3^x⁴⁰, 36^x⁵⁰, 37.4^x⁵⁰, 40.5^x⁴⁰, 58.3^x¹⁰, 63.4^x¹⁰	0.423^x¹⁰⁵	36^x¹⁰, 72^x⁵⁵, 90^x¹⁰⁰, 120^x⁴⁵
14	bilunabirotunda	J91	14	14	26	3^x⁸, 4^x², 5^x⁴	20.9^x⁸, 37.4^x¹⁶, 41.8^x⁴, 63.4^x⁴, 69.1^x⁸, 70.5^x¹⁶, 79.2^x¹⁶, 90^x¹⁶, 116.6^x⁴	0.714^x²⁶	72^x²⁰, 90^x⁸, 120^x²⁴
15	diminished_rhombicosidodecahedron	J76	55	52	105	3^x¹⁵, 4^x²⁵, 5^x¹¹, 10^x¹	20.9^x⁹⁰, 31.7^x¹⁰⁰, 36^x⁹⁰, 37.4^x⁹⁰, 58.3^x¹⁰, 63.4^x¹⁰	0.423^x¹⁰⁵	36^x¹⁰, 72^x⁵⁵, 90^x¹⁰⁰, 120^x⁴⁵
16	disphenocingulum	J90	16	24	38	3^x²⁰, 4^x⁴	13.2^x⁸, 25.6^x⁸, 31.6^x¹⁶, 39.7^x¹⁶, 43.7^x¹⁶, 46.4^x¹⁶, 49.3^x¹⁶, 53.9^x¹⁶, 55.3^x⁸, 62.3^x¹⁶, 64.2^x¹⁶, 66.6^x¹⁶, 74.3^x¹⁶, 77.7^x⁸, 79.8^x⁴, 82.6^x¹⁶	0.825^x³⁸	90^x¹⁶, 120^x⁶⁰
17	elongated_pentagonal_cupola	J20	25	22	45	3^x⁵, 4^x¹⁵, 5^x¹, 10^x¹	20.9^x²⁰, 31.7^x¹⁰, 36^x³⁰, 37.4^x¹⁰, 52.6^x¹⁰, 58.3^x¹⁰, 60.6^x²⁰, 64.8^x²⁰, 90^x²⁰	0.567^x⁴⁵	36^x¹⁰, 72^x⁵, 90^x⁶⁰, 120^x¹⁵
18	elongated_pentagonal_dipyramid	J16	12	15	25	3^x¹⁰, 4^x⁵	41.8^x²⁰, 52.6^x²⁰, 70.5^x²⁰, 72^x¹⁰, 79.2^x⁴⁰	0.975^x²⁵	90^x²⁰, 120^x³⁰
19	elongated_pentagonal_gyrobicupola	J39	30	32	60	3^x¹⁰, 4^x²⁰, 5^x²	20.9^x⁴⁰, 31.7^x²⁰, 36^x⁴⁰, 37.4^x²⁰, 52.6^x²⁰, 58.3^x²⁰, 60.6^x⁴⁰, 64.8^x⁴⁰	0.59^x⁶⁰	72^x¹⁰, 90^x⁸⁰, 120^x³⁰
20	elongated_pentagonal_gyrobirotunda	J43	40	42	80	3^x²⁰, 4^x¹⁰, 5^x¹²	10.8^x²⁰, 26.6^x²⁰, 36^x²⁰, 37.4^x¹⁴⁰, 41.8^x⁴⁰, 43.6^x⁴⁰, 63.4^x⁴⁰	0.485^x⁸⁰	72^x⁶⁰, 90^x⁴⁰, 120^x⁶⁰
21	elongated_pentagonal_gyrocupolarotunda	J41	35	37	70	3^x¹⁵, 4^x¹⁵, 5^x⁷	10.8^x¹⁰, 20.9^x²⁰, 26.6^x¹⁰, 31.7^x¹⁰, 36^x³⁰, 37.4^x⁸⁰, 41.8^x²⁰, 43.6^x²⁰, 52.6^x¹⁰, 58.3^x¹⁰, 60.6^x²⁰, 63.4^x²⁰, 64.8^x²⁰	0.552^x⁷⁰	72^x³⁵, 90^x⁶⁰, 120^x⁴⁵
22	elongated_pentagonal_orthobicupola	J38	30	32	60	3^x¹⁰, 4^x²⁰, 5^x²	20.9^x⁴⁰, 31.7^x²⁰, 36^x⁴⁰, 37.4^x²⁰, 52.6^x²⁰, 58.3^x²⁰, 60.6^x⁴⁰, 64.8^x⁴⁰	0.59^x⁶⁰	72^x¹⁰, 90^x⁸⁰, 120^x³⁰
23	elongated_pentagonal_orthobirotunda	J42	40	42	80	3^x²⁰, 4^x¹⁰, 5^x¹²	10.8^x²⁰, 26.6^x²⁰, 36^x²⁰, 37.4^x¹⁴⁰, 41.8^x⁴⁰, 43.6^x⁴⁰, 63.4^x⁴⁰	0.485^x⁸⁰	72^x⁶⁰, 90^x⁴⁰, 120^x⁶⁰
24	elongated_pentagonal_orthocupolarotunda	J40	35	37	70	3^x¹⁵, 4^x¹⁵, 5^x⁷	10.8^x¹⁰, 20.9^x²⁰, 26.6^x¹⁰, 31.7^x¹⁰, 36^x³⁰, 37.4^x⁸⁰, 41.8^x²⁰, 43.6^x²⁰, 52.6^x¹⁰, 58.3^x¹⁰, 60.6^x²⁰, 63.4^x²⁰, 64.8^x²⁰	0.552^x⁷⁰	72^x³⁵, 90^x⁶⁰, 120^x⁴⁵
25	elongated_pentagonal_pyramid	J9	11	11	20	3^x⁵, 4^x⁵, 5^x¹	41.8^x¹⁰, 52.6^x¹⁰, 70.5^x¹⁰, 72^x¹⁰, 79.2^x²⁰, 90^x¹⁰	0.964^x²⁰	72^x⁵, 90^x²⁰, 120^x¹⁵
26	elongated_pentagonal_rotunds	J21	30	27	55	3^x¹⁰, 4^x¹⁰, 5^x⁶, 10^x¹	10.8^x¹⁰, 26.6^x¹⁰, 36^x²⁰, 37.4^x⁷⁰, 41.8^x²⁰, 43.6^x²⁰, 63.4^x²⁰, 90^x²⁰	0.52^x⁵⁵	36^x¹⁰, 72^x³⁰, 90^x⁴⁰, 120^x³⁰
27	elongated_square_cupola	J19	20	18	36	3^x⁴, 4^x¹³, 8^x¹	35.3^x²⁴, 45^x³², 54.7^x²⁴, 60^x²⁴, 90^x¹⁶	0.666^x³⁶	45^x⁸, 90^x⁵², 120^x¹²
28	elongated_square_dipyramid	J15	10	12	20	3^x⁸, 4^x⁴	35.3^x¹⁶, 70.5^x¹⁶, 90^x⁴⁰, 109.5^x⁸	0.828^x²⁰	90^x¹⁶, 120^x²⁴
29	elongated_square_gyrobicupola	J37	24	26	48	3^x⁸, 4^x¹⁸	35.3^x⁴⁸, 45^x⁴⁸, 54.7^x⁴⁸, 60^x⁴⁸	0.715^x⁴⁸	90^x⁷², 120^x²⁴
30	elongated_square_pyramid	J8	9	9	16	3^x⁴, 4^x⁵	35.3^x⁸, 70.5^x⁸, 90^x³², 109.5^x⁴	0.932^x¹⁶	90^x²⁰, 120^x¹²
31	elongated_triangular_cupola	J18	15	14	27	3^x⁴, 4^x⁹, 6^x¹	19.5^x⁶, 35.3^x⁶, 54.7^x¹⁸, 60^x¹², 61.9^x¹², 65.9^x¹², 70.5^x⁶, 90^x¹⁸	0.795^x²⁷	60^x⁶, 90^x³⁶, 120^x¹²
32	elongated_triangular_dipyramid	J14	8	9	15	3^x⁶, 4^x³	19.5^x¹², 109.5^x¹², 118.1^x²⁴, 120^x⁶	0.76^x¹⁵	90^x¹², 120^x¹⁸
33	elongated_triangular_gyrobicupola	J36	18	20	36	3^x⁸, 4^x¹²	19.5^x¹², 35.3^x¹², 54.7^x³⁶, 60^x¹², 61.9^x²⁴, 65.9^x²⁴, 70.5^x¹², 90^x¹²	0.696^x³⁶	90^x⁴⁸, 120^x²⁴
34	elongated_triangular_orthobicupola	J35	18	20	36	3^x⁸, 4^x¹²	19.5^x¹², 35.3^x¹², 54.7^x³⁶, 60^x¹², 61.9^x²⁴, 65.9^x²⁴, 70.5^x¹², 90^x¹²	0.696^x³⁶	90^x⁴⁸, 120^x²⁴
35	elongated_triangular_pyramid	J7	7	7	12	3^x⁴, 4^x³	19.5^x⁶, 90^x⁶, 109.5^x⁶, 118.1^x¹², 120^x⁶	0.886^x¹²	90^x¹², 120^x¹²
36	gyrate_bidiminished_rhombicosidodecahedron	J82	50	42	90	3^x¹⁰, 4^x²⁰, 5^x¹⁰, 10^x²	20.9^x⁵⁰, 26.1^x¹⁰, 26.6^x¹⁰, 31.7^x⁷⁰, 33.3^x²⁰, 36^x⁴⁰, 37.4^x⁴⁰, 40.5^x²⁰, 58.3^x²⁰, 63.4^x²⁰	0.41^x⁹⁰	36^x²⁰, 72^x⁵⁰, 90^x⁸⁰, 120^x³⁰
37	gyrate_rhombicosidodecahedron	J72	60	62	120	3^x²⁰, 4^x³⁰, 5^x¹²	20.9^x¹¹⁰, 26.1^x¹⁰, 26.6^x¹⁰, 31.7^x¹¹⁰, 33.3^x²⁰, 36^x¹⁰⁰, 37.4^x¹⁰⁰, 40.5^x²⁰	0.448^x¹²⁰	72^x⁶⁰, 90^x¹²⁰, 120^x⁶⁰
38	gyrobifastigium	J26	8	8	14	3^x⁴, 4^x⁴	30^x⁸, 90^x²⁴, 104.5^x⁸, 120^x⁴	1^x¹⁴	90^x¹⁶, 120^x¹²
39	gyroelongated_pentagonal_bicupola	J46	30	42	70	3^x³⁰, 4^x¹⁰, 5^x²	20.8^x⁴⁰, 20.9^x⁴⁰, 31.7^x²⁰, 35.8^x⁴⁰, 36^x²⁰, 37.4^x²⁰, 47.4^x²⁰, 53^x²⁰, 55.8^x⁴⁰, 59.9^x⁸⁰, 65.2^x⁴⁰	0.597^x⁷⁰	72^x¹⁰, 90^x⁴⁰, 120^x⁹⁰
40	gyroelongated_pentagonal_birotunda	J48	40	52	90	3^x⁴⁰, 5^x¹²	5.6^x²⁰, 20.8^x⁴⁰, 21.3^x²⁰, 24.1^x⁴⁰, 35.8^x⁴⁰, 36.1^x⁴⁰, 36.3^x⁴⁰, 37.4^x¹⁰⁰, 40.4^x⁴⁰, 41.8^x⁴⁰, 63.4^x⁴⁰	0.501^x⁹⁰	72^x⁶⁰, 120^x¹²⁰
41	gyroelongated_pentagonal_cupola	J24	25	32	55	3^x²⁵, 4^x⁵, 5^x¹, 10^x¹	20.8^x⁴⁰, 20.9^x²⁰, 31.7^x¹⁰, 35.8^x⁴⁰, 36^x¹⁰, 37.4^x¹⁰, 47.4^x¹⁰, 53^x¹⁰, 55.8^x²⁰, 59.8^x¹², 59.9^x²⁸, 65.2^x²⁰, 84.8^x²⁰, 95.2^x²⁰	0.577^x⁵⁵	36^x¹⁰, 72^x⁵, 90^x²⁰, 120^x⁷⁵
42	gyroelongated_pentagonal_cupolarotunda	J47	35	47	80	3^x³⁵, 4^x⁵, 5^x⁷	5.6^x¹⁰, 20.8^x⁴⁰, 20.9^x²⁰, 21.3^x¹⁰, 24.1^x²⁰, 31.7^x¹⁰, 35.8^x⁴⁰, 36^x¹⁰, 36.1^x²⁰, 36.3^x²⁰, 37.4^x⁶⁰, 40.4^x²⁰, 41.8^x²⁰, 47.4^x¹⁰, 53^x¹⁰, 55.8^x²⁰, 59.9^x⁴⁰, 63.4^x²⁰, 65.2^x²⁰	0.563^x⁸⁰	72^x³⁵, 90^x²⁰, 120^x¹⁰⁵
43	gyroelongated_pentagonal_pyramid	J11	11	16	25	3^x¹⁵, 5^x¹	41.8^x⁴⁰, 70.5^x⁷⁰, 79.2^x¹⁰, 100.8^x¹⁰	1.01^x²⁵	72^x⁵, 120^x⁴⁵
44	gyroelongated_pentagonal_rotunda	J25	30	37	65	3^x³⁰, 5^x⁶, 10^x¹	5.6^x¹⁰, 20.8^x⁴⁰, 21.3^x¹⁰, 24.1^x²⁰, 35.8^x⁴⁰, 36.1^x²⁰, 36.3^x²⁰, 37.4^x⁵⁰, 40.4^x²⁰, 41.8^x²⁰, 63.4^x²⁰, 84.8^x²⁰, 95.2^x²⁰	0.591^x⁶⁵	36^x¹⁰, 72^x³⁰, 120^x⁹⁰
45	gyroelongated_square_bicupola	J45	24	34	56	3^x²⁴, 4^x¹⁰	26^x³², 28.7^x¹⁶, 35.3^x³², 38.4^x¹⁶, 44.7^x³², 45^x¹⁶, 46.9^x³², 50.2^x³², 54.7^x⁴⁸, 55.4^x³², 60^x¹⁶	0.727^x⁵⁶	90^x⁴⁰, 120^x⁷²
46	gyroelongated_square_cupola	J23	20	26	44	3^x²⁰, 4^x⁵, 8^x¹	26^x³², 28.7^x⁸, 35.3^x¹⁶, 38.4^x⁸, 44.7^x³², 45^x⁸, 46.9^x¹⁶, 50.2^x¹⁶, 54.7^x²⁴, 55.4^x¹⁶, 60^x⁸, 83.4^x¹⁶, 96.6^x¹⁶	0.741^x⁴⁴	45^x⁸, 90^x²⁰, 120^x⁶⁰
47	gyroelongated_square_dipyramid	J17	10	16	24	3^x¹⁶	21.4^x¹⁶, 52.4^x¹⁶, 65^x³², 70.5^x¹⁶, 82.1^x³², 86.7^x¹⁶, 109.5^x⁸	0.887^x²⁴	120^x⁴⁸
48	gyroelongated_square_pyramid	J10	9	13	20	3^x¹², 4^x¹	21.4^x⁸, 52.4^x¹⁶, 65^x¹⁶, 70.5^x⁸, 76.2^x⁸, 82.1^x¹⁶, 86.7^x¹⁶, 103.8^x⁸, 109.5^x⁴	0.998^x²⁰	90^x⁴, 120^x³⁶
49	gyroelongated_triangular_bicupola	J44	18	26	42	3^x²⁰, 4^x⁶	10.6^x¹², 26.4^x¹², 34.8^x²⁴, 41^x²⁴, 52.5^x²⁴, 54.7^x³⁶, 58.8^x²⁴, 59.2^x²⁴, 60.5^x²⁴, 70.5^x¹², 90^x¹²	0.729^x⁴²	90^x²⁴, 120^x⁶⁰
50	gyroelongated_triangular_cupola	J22	15	20	33	3^x¹⁶, 4^x³, 6^x¹	10.6^x⁶, 26.4^x⁶, 34.8^x²⁴, 41^x¹², 52.5^x¹², 54.7^x¹⁸, 58.8^x¹², 59.2^x²⁴, 60.5^x¹², 70.5^x⁶, 81.1^x¹², 90^x⁶, 98.9^x¹²	0.891^x³³	60^x⁶, 90^x¹², 120^x⁴⁸
51	hebesphenomegacorona	J89	14	21	33	3^x¹⁸, 4^x³	22.9^x¹⁶, 27^x⁴, 30.4^x², 38.7^x⁸, 39.3^x⁸, 46^x¹², 51.5^x¹⁶, 51.8^x⁸, 53.3^x⁸, 56.4^x⁸, 60^x⁸, 65.1^x¹⁶, 65.5^x⁴, 68.3^x⁴, 70.2^x⁸, 76^x⁸, 77.5^x⁴, 80.7^x¹⁶, 81.3^x¹⁶, 85.3^x⁸	0.889^x³³	90^x¹², 120^x⁵⁴
52	metabiaugmented_dodecahedron	J60	22	20	40	3^x¹⁰, 5^x¹⁰	26.1^x²⁰, 41.8^x²⁰, 58.5^x⁴⁰, 63.4^x⁴⁰, 70.5^x²⁰	0.625^x⁴⁰	72^x⁵⁰, 120^x³⁰
53	metabiaugmented_hexagonal_prism	J56	14	14	26	3^x⁸, 4^x⁴, 6^x²	5.3^x⁸, 35.3^x⁸, 60^x⁴, 70.5^x¹⁶, 73.2^x¹⁶, 90^x³², 109.5^x⁸	0.658^x²⁶	60^x¹², 90^x¹⁶, 120^x²⁴
54	metabiaugmented_truncated_dodecahedron	J70	70	52	120	3^x³⁰, 4^x¹⁰, 5^x², 10^x¹⁰	5.7^x²⁰, 20.9^x⁴⁰, 21.6^x⁴⁰, 26.1^x²⁰, 31.7^x²⁰, 36^x²⁰, 37.4^x¹²⁰, 40.5^x⁴⁰, 63.4^x⁴⁰	0.313^x¹²⁰	36^x¹⁰⁰, 72^x¹⁰, 90^x⁴⁰, 120^x⁹⁰
55	metabidiminished_icosahedron	J62	10	12	20	3^x¹⁰, 5^x²	41.8^x²², 70.5^x³², 79.2^x¹⁶, 100.8^x¹², 116.6^x²	0.964^x²⁰	72^x¹⁰, 120^x³⁰
56	metabidiminished_rhombicosidodecahedron	J81	50	42	90	3^x¹⁰, 4^x²⁰, 5^x¹⁰, 10^x²	20.9^x⁶⁰, 31.7^x⁸⁰, 36^x⁶⁰, 37.4^x⁶⁰, 58.3^x²⁰, 63.4^x²⁰	0.41^x⁹⁰	36^x²⁰, 72^x⁵⁰, 90^x⁸⁰, 120^x³⁰
57	metabigyrate_rhombicosidodecahedron	J74	60	62	120	3^x²⁰, 4^x³⁰, 5^x¹²	20.9^x¹⁰⁰, 26.1^x²⁰, 26.6^x²⁰, 31.7^x¹⁰⁰, 33.3^x⁴⁰, 36^x⁸⁰, 37.4^x⁸⁰, 40.5^x⁴⁰	0.448^x¹²⁰	72^x⁶⁰, 90^x¹²⁰, 120^x⁶⁰
58	metagyrate_diminished_rhombicosidodecahedron	J78	55	52	105	3^x¹⁵, 4^x²⁵, 5^x¹¹, 10^x¹	20.9^x⁸⁰, 26.1^x¹⁰, 26.6^x¹⁰, 31.7^x⁹⁰, 33.3^x²⁰, 36^x⁷⁰, 37.4^x⁷⁰, 40.5^x²⁰, 58.3^x¹⁰, 63.4^x¹⁰	0.423^x¹⁰⁵	36^x¹⁰, 72^x⁵⁵, 90^x¹⁰⁰, 120^x⁴⁵
59	parabiaugmented_dodecahedron	J59	22	20	40	3^x¹⁰, 5^x¹⁰	26.1^x²⁰, 41.8^x²⁰, 58.5^x⁴⁰, 63.4^x⁴⁰, 70.5^x²⁰	0.61^x⁴⁰	72^x⁵⁰, 120^x³⁰
60	parabiaugmented_hexagonal_prism	J55	14	14	26	3^x⁸, 4^x⁴, 6^x²	5.3^x⁸, 35.3^x⁸, 60^x⁴, 70.5^x¹⁶, 73.2^x¹⁶, 90^x³², 109.5^x⁸	0.636^x²⁶	60^x¹², 90^x¹⁶, 120^x²⁴
61	parabiaugmented_truncated_dodecahedron	J69	70	52	120	3^x³⁰, 4^x¹⁰, 5^x², 10^x¹⁰	5.7^x²⁰, 20.9^x⁴⁰, 21.6^x⁴⁰, 26.1^x²⁰, 31.7^x²⁰, 36^x²⁰, 37.4^x¹²⁰, 40.5^x⁴⁰, 63.4^x⁴⁰	0.319^x¹²⁰	36^x¹⁰⁰, 72^x¹⁰, 90^x⁴⁰, 120^x⁹⁰
62	parabidiminished_rhombicosidodecahedron	J80	50	42	90	3^x¹⁰, 4^x²⁰, 5^x¹⁰, 10^x²	20.9^x⁶⁰, 31.7^x⁸⁰, 36^x⁶⁰, 37.4^x⁶⁰, 58.3^x²⁰, 63.4^x²⁰	0.448^x⁹⁰	36^x²⁰, 72^x⁵⁰, 90^x⁸⁰, 120^x³⁰
63	parabigyrate_rhombicosidodecahedron	J73	60	62	120	3^x²⁰, 4^x³⁰, 5^x¹²	20.9^x¹⁰⁰, 26.1^x²⁰, 26.6^x²⁰, 31.7^x¹⁰⁰, 33.3^x⁴⁰, 36^x⁸⁰, 37.4^x⁸⁰, 40.5^x⁴⁰	0.448^x¹²⁰	72^x⁶⁰, 90^x¹²⁰, 120^x⁶⁰
64	paragyrate_diminished_rhombicosidodecahedron	J77	55	52	105	3^x¹⁵, 4^x²⁵, 5^x¹¹, 10^x¹	20.9^x⁸⁰, 26.1^x¹⁰, 26.6^x¹⁰, 31.7^x⁹⁰, 33.3^x²⁰, 36^x⁷⁰, 37.4^x⁷⁰, 40.5^x²⁰, 58.3^x¹⁰, 63.4^x¹⁰	0.423^x¹⁰⁵	36^x¹⁰, 72^x⁵⁵, 90^x¹⁰⁰, 120^x⁴⁵
65	pentagonal_cupola	J5	15	12	25	3^x⁵, 4^x⁵, 5^x¹, 10^x¹	20.9^x²⁰, 31.7^x¹⁰, 36^x¹⁰, 37.4^x¹⁰, 142.6^x¹⁰, 148.3^x¹⁰	0.614^x²⁵	36^x¹⁰, 72^x⁵, 90^x²⁰, 120^x¹⁵
66	pentagonal_dipyramid	J13	7	10	15	3^x¹⁰	41.8^x²⁰, 70.5^x²⁰, 105.2^x¹⁰, 121.2^x²⁰	1.18^x¹⁵	120^x³⁰
67	pentagonal_gyrobicupola	J31	20	22	40	3^x¹⁰, 4^x¹⁰, 5^x²	20.9^x⁴⁰, 31.7^x²⁰, 36^x²⁰, 37.4^x²⁰, 109.5^x²⁰, 110.9^x²⁰, 120^x²⁰	0.618^x⁴⁰	72^x¹⁰, 90^x⁴⁰, 120^x³⁰
68	pentagonal_gyrocupolarotunda	J33	25	27	50	3^x¹⁵, 4^x⁵, 5^x⁷	20.9^x²⁰, 31.7^x¹⁰, 36^x¹⁰, 37.4^x⁶⁰, 41.8^x²⁰, 63.4^x³⁰, 75^x²⁰, 84.8^x¹⁰, 85.2^x²⁰	0.605^x⁵⁰	72^x³⁵, 90^x²⁰, 120^x⁴⁵
69	pentagonal_orthobicupola	J30	20	22	40	3^x¹⁰, 4^x¹⁰, 5^x²	20.9^x⁴⁰, 31.7^x²⁰, 36^x²⁰, 37.4^x²⁰, 105.2^x¹⁰, 114.7^x⁴⁰, 116.6^x¹⁰	0.618^x⁴⁰	72^x¹⁰, 90^x⁴⁰, 120^x³⁰
70	pentagonal_orthobirotunda	J34	30	32	60	3^x²⁰, 5^x¹²	21.6^x¹⁰, 37.4^x¹⁰⁰, 41.8^x⁴⁰, 51.2^x⁴⁰, 53.1^x¹⁰, 63.4^x⁴⁰	0.618^x⁶⁰	72^x⁶⁰, 120^x⁶⁰
71	pentagonal_orthocupolarontunda	J32	25	27	50	3^x¹⁵, 4^x⁵, 5^x⁷	20.9^x²⁰, 31.7^x¹⁰, 36^x¹⁰, 37.4^x⁶⁰, 41.8^x²⁰, 63.4^x²⁰, 69.1^x¹⁰, 70.5^x²⁰, 79.2^x¹⁰, 90^x²⁰	0.605^x⁵⁰	72^x³⁵, 90^x²⁰, 120^x⁴⁵
72	pentagonal_pyramid	J2	6	6	10	3^x⁵, 5^x¹	41.8^x¹⁰, 70.5^x¹⁰, 142.6^x¹⁰	1.17^x¹⁰	72^x⁵, 120^x¹⁵
73	pentagonal_rotunda	J6	20	17	35	3^x¹⁰, 5^x⁶, 10^x¹	37.4^x⁵⁰, 41.8^x²⁰, 63.4^x²⁰, 100.8^x¹⁰, 116.6^x¹⁰	0.584^x³⁵	36^x¹⁰, 72^x³⁰, 120^x³⁰
74	snub_disphenoid	J84	8	12	18	3^x¹²	13.5^x², 13.6^x⁶, 58.2^x⁴, 58.3^x¹², 65.7^x¹⁶, 83.8^x¹², 90.6^x⁴, 90.7^x¹², 94.9^x⁸, 111.5^x¹⁶	1.08^x¹⁸	120^x³⁶
75	snub_square_antiprism	J85	16	26	40	3^x²⁴, 4^x²	15.7^x¹⁶, 34.6^x¹⁶, 35.9^x³², 45.5^x³², 47.3^x¹⁶, 59.9^x³², 61^x¹⁶, 65.4^x¹⁶, 73.9^x³², 85.9^x³²	0.815^x⁴⁰	90^x⁸, 120^x⁷²
76	sphenocorona	J86	10	14	22	3^x¹², 4^x²	20.1^x⁴, 36.5^x⁸, 44^x⁸, 48.6^x², 61.1^x⁸, 62^x⁴, 63^x², 68.2^x⁸, 70.5^x⁸, 72^x⁸, 72.3^x⁸, 74^x⁴, 81.3^x⁸, 82.5^x⁴, 82.7^x⁸, 87.5^x⁸, 104.5^x⁸	1^x²²	90^x⁸, 120^x³⁶
77	sphenomegacorona	J88	12	18	28	3^x¹⁶, 4^x²	8.3^x⁴, 8.4^x⁴, 18.6^x², 25.3^x⁸, 36.3^x⁸, 41^x⁸, 42.8^x⁴, 48.4^x⁸, 50.6^x⁸, 55.1^x⁸, 61.6^x⁴, 62.6^x⁴, 62.7^x⁴, 65.8^x⁸, 67^x¹², 67.1^x⁴, 72.8^x⁴, 72.9^x⁴, 83.8^x⁸, 93.3^x⁸, 97.4^x⁸, 100.6^x⁴, 105.4^x⁸, 107^x², 114.9^x⁸	0.761^x²⁶, 0.762^x²	90^x⁸, 120^x⁴⁸
78	square_cupola	J4	12	10	20	3^x⁴, 4^x⁵, 8^x¹	35.3^x¹⁶, 45^x⁸, 54.7^x⁸, 60^x⁸, 125.3^x⁸, 135^x⁸	0.753^x²⁰	45^x⁸, 90^x²⁰, 120^x¹²
79	square_gyrobicupola	J29	16	18	32	3^x⁸, 4^x¹⁰	35.3^x³², 45^x¹⁶, 54.7^x¹⁶, 60^x¹⁶, 80.3^x¹⁶, 82.1^x¹⁶, 98.4^x¹⁶	0.765^x³²	90^x⁴⁰, 120^x²⁴
80	square_orthobicupola	J28	16	18	32	3^x⁸, 4^x¹⁰	35.3^x³², 45^x¹⁶, 54.7^x¹⁶, 60^x¹⁶, 70.5^x⁸, 90^x⁴⁰	0.765^x³²	90^x⁴⁰, 120^x²⁴
81	square_pyramid	J1	5	5	8	3^x⁴, 4^x¹	70.5^x⁸, 109.5^x⁴, 125.3^x⁸	1.41^x⁸	90^x⁴, 120^x¹²
82	triangular_cupola	J3	9	8	15	3^x⁴, 4^x³, 6^x¹	54.7^x¹⁸, 70.5^x⁶, 90^x⁶, 109.5^x⁶, 125.3^x⁶	0.965^x¹⁵	60^x⁶, 90^x¹², 120^x¹²
83	triangular_dipyramid	J12	5	6	9	3^x⁶	38.9^x⁶, 109.5^x¹², 123.7^x¹²	1.22^x⁹	120^x¹⁸
84	triangular_hebesphenorotunda	J92	18	20	36	3^x¹³, 4^x³, 5^x³, 6^x¹	20.9^x¹², 37.4^x¹⁸, 41.8^x²⁴, 54.7^x¹², 63.4^x⁶, 69.1^x¹², 70.5^x³⁰, 79.2^x¹², 90^x¹², 100.8^x⁶	0.661^x³⁶	60^x⁶, 72^x¹⁵, 90^x¹², 120^x³⁹
85	triangular_orthobicupola	J27	12	14	24	3^x⁸, 4^x⁶	38.9^x⁶, 54.7^x³⁶, 70.5^x¹⁸, 78.9^x²⁴, 90^x¹²	1^x²⁴	90^x²⁴, 120^x²⁴
86	triaugmented_dodecahedron	J61	23	24	45	3^x¹⁵, 5^x⁹	26.1^x³⁰, 41.8^x³⁰, 58.5^x⁶⁰, 63.4^x³⁰, 70.5^x³⁰	0.613^x⁴⁵	72^x⁴⁵, 120^x⁴⁵
87	triaugmented_hexagonal_prism	J57	15	17	30	3^x¹², 4^x³, 6^x²	5.3^x¹², 35.3^x¹², 70.5^x²⁴, 73.2^x²⁴, 90^x³⁶, 109.5^x¹²	0.636^x³⁰	60^x¹², 90^x¹², 120^x³⁶
88	triaugmented_triangular_prism	J51	9	14	21	3^x¹⁴	10.5^x⁶, 35.3^x¹², 60^x¹², 70.5^x²⁴, 76^x²⁴, 90^x²⁴, 109.5^x¹²	1^x²¹	120^x⁴²
89	triaugmented_truncated_dodecahedron	J71	75	62	135	3^x³⁵, 4^x¹⁵, 5^x³, 10^x⁹	5.7^x³⁰, 9.8^x⁴, 11.3^x², 18^x⁸, 20.9^x⁶⁰, 21.6^x⁶⁰, 26.1^x²⁶, 31.7^x³⁰, 36^x³⁰, 37.4^x¹²⁰, 40.5^x⁵², 63.4^x³²	0.307^x¹³⁵	36^x⁹⁰, 72^x¹⁵, 90^x⁶⁰, 120^x¹⁰⁵
90	tridiminished_icosahedron	J63	9	8	15	3^x⁵, 5^x³	41.8^x⁶, 70.5^x⁶, 79.2^x¹⁸, 100.8^x⁶, 116.6^x⁶	1^x¹⁵	72^x¹⁵, 120^x¹⁵
91	tridiminished_rhombicosidodecahedron	J83	45	32	75	3^x⁵, 4^x¹⁵, 5^x⁹, 10^x³	20.9^x³⁰, 31.7^x⁶⁰, 36^x³⁰, 37.4^x³⁰, 58.3^x³⁰, 63.4^x³⁰	0.424^x⁷⁵	36^x³⁰, 72^x⁴⁵, 90^x⁶⁰, 120^x¹⁵
92	trigyrate_rhombicosidodecahedron	J75	60	62	120	3^x²⁰, 4^x³⁰, 5^x¹²	20.9^x⁹⁰, 26.1^x³⁰, 26.6^x³⁰, 31.7^x⁹⁰, 33.3^x⁶⁰, 36^x⁶⁰, 37.4^x⁶⁰, 40.5^x⁶⁰	0.448^x¹²⁰	72^x⁶⁰, 90^x¹²⁰, 120^x⁶⁰

Platonic

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/platonic.scad>;

Examples
(1)	(2)	(3)	(4)
cube	dodecahedron	icosahedron	octahedron
(5)
tetrahedron

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	cube	Hexahedron	8	6	12	4^x⁶	90^x²⁴	2^x¹²	90^x²⁴
2	dodecahedron	-	20	12	30	5^x¹²	63.4^x⁶⁰	0.714^x³⁰	72^x⁶⁰
3	icosahedron	-	12	20	30	3^x²⁰	41.8^x⁶⁰, 70.5^x¹²⁰	1.24^x³⁰	120^x⁶⁰
4	octahedron	-	6	8	12	3^x⁸	70.5^x²⁴, 109.5^x²⁴	1.41^x¹²	120^x²⁴
5	tetrahedron	-	4	4	6	3^x⁴	109.5^x¹²	2.83^x⁶	120^x¹²

Prisms

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/prisms.scad>;

Examples
(1)	(2)	(3)	(4)
decagonal prism	hexagonal prism	octagonal prism	pentagonal prism
(5)	(6)
square prism	triangular prism

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	decagonal_prism	-	20	12	30	4^x¹⁰, 10^x²	36^x²⁰, 90^x⁴⁰	0.59^x³⁰	36^x²⁰, 90^x⁴⁰
2	hexagonal_prism	-	12	8	18	4^x⁶, 6^x²	60^x¹², 90^x²⁴	0.894^x¹⁸	60^x¹², 90^x²⁴
3	octagonal_prism	-	16	10	24	4^x⁸, 8^x²	45^x¹⁶, 90^x³²	0.715^x²⁴	45^x¹⁶, 90^x³²
4	pentagonal_prism	-	10	7	15	4^x⁵, 5^x²	72^x¹⁰, 90^x²⁰	1.01^x¹⁵	72^x¹⁰, 90^x²⁰
5	square_prism	Cube	8	6	12	4^x⁶	90^x²⁴	1.15^x¹²	90^x²⁴
6	triangular_prism	-	6	5	9	3^x², 4^x³	90^x¹², 120^x⁶	1.31^x⁹	90^x¹², 120^x⁶

Pyramids

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/pyramids.scad>;

Examples
(1)	(2)	(3)	(4)
pentagonal dipyramid	pentagonal pyramid	square dipryamid	square pyramid
(5)	(6)
triangular dipyramid	triangular pyramid

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	pentagonal_dipyramid	J13	7	10	15	3^x¹⁰	41.8^x²⁰, 70.5^x²⁰, 105.2^x¹⁰, 121.2^x²⁰	1.18^x¹⁵	120^x³⁰
2	pentagonal_pyramid	J2	6	6	10	3^x⁵, 5^x¹	41.8^x¹⁰, 70.5^x¹⁰, 142.6^x¹⁰	1.17^x¹⁰	72^x⁵, 120^x¹⁵
3	square_dipryamid	Octahedron	6	8	12	3^x⁸	70.5^x²⁴, 109.5^x²⁴	1.41^x¹²	120^x²⁴
4	square_pyramid	J1	5	5	8	3^x⁴, 4^x¹	70.5^x⁸, 109.5^x⁴, 125.3^x⁸	1.41^x⁸	90^x⁴, 120^x¹²
5	triangular_dipyramid	J12	5	6	9	3^x⁶	38.9^x⁶, 109.5^x¹², 123.7^x¹²	1.22^x⁹	120^x¹⁸
6	triangular_pyramid	Tetrahedron	4	4	6	3^x⁴	109.5^x¹²	1.63^x⁶	120^x¹²

Trapezohedron

Requires:
include <omdl-base.scad>;
include <database/geometry/polyhedra/trapezohedron.scad>;

Examples
(1)	(2)	(3)	(4)
decagonal trapezohedron	enneagonal trapezohedron	heptagonal trapezohedron	hexagonal trapezohedron
(5)	(6)	(7)	(8)
octagonal trapezohedron	pentagonal trapezohedron	square trapezohedron	triangular trapezohedron

Autostats

no.	id	other name	vertices	faces	edges	face-verticies	face-angles	edge-lengths	edge-angles
1	decagonal_trapezohedron	-	22	20	40	4^x²⁰	34.7^x⁸⁰, 69.2^x⁴⁰, 102.8^x⁴⁰, 133.6^x⁴⁰, 150.2^x²⁰	0.0991^x²⁰, 1.01^x²⁰	63.2^x⁶⁰, 170.4^x²⁰
2	enneagonal_trapezohedron	-	20	18	36	4^x¹⁸	38.3^x⁷², 76.1^x³⁶, 112.3^x³⁶, 141.7^x³⁶	0.122^x¹⁸, 1.02^x¹⁸	63.9^x⁵⁴, 168.3^x¹⁸
3	heptagonal_trapezohedron	-	16	14	28	4^x¹⁴	48^x⁵⁶, 94.2^x²⁸, 132^x²⁸	0.203^x¹⁴, 1.03^x¹⁴	66.4^x⁴², 160.9^x¹⁴
4	hexagonal_trapezohedron	-	14	12	24	4^x¹²	54.7^x⁴⁸, 105.5^x²⁴, 133.7^x¹²	0.277^x¹², 1.04^x¹²	68.5^x³⁶, 154.4^x¹²
5	octagonal_trapezohedron	-	18	16	32	4^x¹⁶	42.6^x⁶⁴, 84.4^x³², 122.7^x³², 143.6^x¹⁶	0.155^x¹⁶, 1.02^x¹⁶	64.9^x⁴⁸, 165.2^x¹⁶
6	pentagonal_trapezohedron	-	12	10	20	4^x¹⁰	63.4^x⁴⁰, 116.6^x²⁰	0.402^x¹⁰, 1.05^x¹⁰	72^x³⁰, 144^x¹⁰
7	square_trapezohedron	-	10	8	16	4^x⁸	74.9^x³², 118.5^x⁸	0.634^x⁸, 1.08^x⁸	78^x²⁴, 125.9^x⁸
8	triangular_trapezohedron	Cube	8	6	12	4^x⁶	90^x²⁴	1.15^x¹²	90^x²⁴

Variable Documentation

◆ dtc_polyhedra_anti_prisms

dtc_polyhedra_anti_prisms

<map> anti_prisms polyhedra data table columns definition.

Definition at line 197 of file anti_prisms.scad.

◆ dtc_polyhedra_archimedean

dtc_polyhedra_archimedean

<map> archimedean polyhedra data table columns definition.

Definition at line 197 of file archimedean.scad.

◆ dtc_polyhedra_archimedean_duals

dtc_polyhedra_archimedean_duals

<map> archimedean_duals polyhedra data table columns definition.

Definition at line 197 of file archimedean_duals.scad.

◆ dtc_polyhedra_cupolas

dtc_polyhedra_cupolas

<map> cupolas polyhedra data table columns definition.

Definition at line 197 of file cupolas.scad.

◆ dtc_polyhedra_dipyramids

dtc_polyhedra_dipyramids

<map> dipyramids polyhedra data table columns definition.

Definition at line 197 of file dipyramids.scad.

◆ dtc_polyhedra_johnson

dtc_polyhedra_johnson

<map> johnson polyhedra data table columns definition.

Definition at line 197 of file johnson.scad.

◆ dtc_polyhedra_platonic

dtc_polyhedra_platonic

<map> platonic polyhedra data table columns definition.

Definition at line 197 of file platonic.scad.

◆ dtc_polyhedra_polyhedra_all

dtc_polyhedra_polyhedra_all

<map> polyhedra_all polyhedra data table columns definition.

Definition at line 134 of file polyhedra_all.scad.

◆ dtc_polyhedra_prisms

dtc_polyhedra_prisms

<map> prisms polyhedra data table columns definition.

Definition at line 197 of file prisms.scad.

◆ dtc_polyhedra_pyramids

dtc_polyhedra_pyramids

<map> pyramids polyhedra data table columns definition.

Definition at line 197 of file pyramids.scad.

◆ dtc_polyhedra_trapezohedron

dtc_polyhedra_trapezohedron

<map> trapezohedron polyhedra data table columns definition.

Definition at line 197 of file trapezohedron.scad.

◆ dtr_polyhedra_anti_prisms

dtr_polyhedra_anti_prisms

<table> anti_prisms polyhedra data table rows.

Definition at line 212 of file anti_prisms.scad.

◆ dtr_polyhedra_archimedean

dtr_polyhedra_archimedean

<table> archimedean polyhedra data table rows.

Definition at line 212 of file archimedean.scad.

◆ dtr_polyhedra_archimedean_duals

dtr_polyhedra_archimedean_duals

<table> archimedean_duals polyhedra data table rows.

Definition at line 212 of file archimedean_duals.scad.

◆ dtr_polyhedra_cupolas

dtr_polyhedra_cupolas

<table> cupolas polyhedra data table rows.

Definition at line 212 of file cupolas.scad.

◆ dtr_polyhedra_dipyramids

dtr_polyhedra_dipyramids

<table> dipyramids polyhedra data table rows.

Definition at line 212 of file dipyramids.scad.

◆ dtr_polyhedra_johnson

dtr_polyhedra_johnson

<table> johnson polyhedra data table rows.

Definition at line 212 of file johnson.scad.

◆ dtr_polyhedra_platonic

dtr_polyhedra_platonic

<table> platonic polyhedra data table rows.

Definition at line 212 of file platonic.scad.

◆ dtr_polyhedra_polyhedra_all

dtr_polyhedra_polyhedra_all

<table> polyhedra_all polyhedra data table rows.

Definition at line 149 of file polyhedra_all.scad.

◆ dtr_polyhedra_prisms

dtr_polyhedra_prisms

<table> prisms polyhedra data table rows.

Definition at line 212 of file prisms.scad.

◆ dtr_polyhedra_pyramids

dtr_polyhedra_pyramids

<table> pyramids polyhedra data table rows.

Definition at line 212 of file pyramids.scad.

◆ dtr_polyhedra_trapezohedron

dtr_polyhedra_trapezohedron

<table> trapezohedron polyhedra data table rows.

Definition at line 212 of file trapezohedron.scad.

Variables
	dtc_polyhedra_polyhedra_all

	dtr_polyhedra_polyhedra_all

	dtc_polyhedra_anti_prisms

	dtr_polyhedra_anti_prisms

	dtc_polyhedra_archimedean_duals

	dtr_polyhedra_archimedean_duals

	dtc_polyhedra_archimedean

	dtr_polyhedra_archimedean

	dtc_polyhedra_cupolas

	dtr_polyhedra_cupolas

	dtc_polyhedra_dipyramids

	dtr_polyhedra_dipyramids

	dtc_polyhedra_johnson

	dtr_polyhedra_johnson

	dtc_polyhedra_platonic

	dtr_polyhedra_platonic

	dtc_polyhedra_prisms

	dtr_polyhedra_prisms

	dtc_polyhedra_pyramids

	dtr_polyhedra_pyramids

	dtc_polyhedra_trapezohedron

	dtr_polyhedra_trapezohedron

Files

Variables

Detailed Description

Anti Prisms

Archimedean Duals

Archimedean

Cupolas

Dipyramids

Johnson

Platonic

Prisms

Pyramids

Trapezohedron

Variable Documentation

◆ dtc_polyhedra_anti_prisms

◆ dtc_polyhedra_archimedean

◆ dtc_polyhedra_archimedean_duals

◆ dtc_polyhedra_cupolas

◆ dtc_polyhedra_dipyramids

◆ dtc_polyhedra_johnson

◆ dtc_polyhedra_platonic

◆ dtc_polyhedra_polyhedra_all

◆ dtc_polyhedra_prisms

◆ dtc_polyhedra_pyramids

◆ dtc_polyhedra_trapezohedron

◆ dtr_polyhedra_anti_prisms

◆ dtr_polyhedra_archimedean

◆ dtr_polyhedra_archimedean_duals

◆ dtr_polyhedra_cupolas

◆ dtr_polyhedra_dipyramids

◆ dtr_polyhedra_johnson

◆ dtr_polyhedra_platonic

◆ dtr_polyhedra_polyhedra_all

◆ dtr_polyhedra_prisms

◆ dtr_polyhedra_pyramids

◆ dtr_polyhedra_trapezohedron