Dodecagonal-dodecagrammic duoprism

Dodecagonal-dodecagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Coxeter diagram	x12o x12/5o ()
Elements
Cells	12 dodecagonal prisms, 12 dodecagrammic prisms
Faces	144 squares, 12 dodecagons, 12 dodecagrams
Edges	144+144
Vertices	144
Vertex figure	Digonal disphenoid, edge lengths (√6+√2)/2 (base 1), (√6–√2)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	2
Hypervolume	9
Dichoral angles	Stwip–12/5–stwip: 150°
	Twip–4–stwip: 90°
	Twip–12–twip: 30°
Central density	5
Number of external pieces	36
Level of complexity	12
Related polytopes
Army	Semi-uniform twaddip
Dual	Dodecagonal-dodecagrammic duotegum
Conjugate	Dodecagonal-dodecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12)×I2(12), order 576
Convex	No
Nature	Tame

The dodecagonal-dodecagrammic duoprism, also known as the 12/5-12 duoprism, is a uniform duoprism that consists of 12 dodecagonal prisms and 12 dodecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of an dodecagonal-dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:

$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),$
$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),$
$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{2-\sqrt3}{2},\,±\frac12\right),$
$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),$
$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),$
$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{2-\sqrt3}{2},\,±\frac12\right),$
$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),$
$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),$
$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2-\sqrt3}{2},\,±\frac12\right).$