Dodecagonal duoprismatic prism

Dodecagonal duoprismatic prism
	(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Twatwip
Coxeter diagram	x x12o x12o ()
Elements
Tera	24 square-dodecagonal duoprisms, 2 dodecagonal duoprisms
Cells	144 cubes, 24+48 dodecagonal prisms
Faces	288+288 squares, 48 dodecagons
Edges	144+576
Vertices	288
Vertex figure	Tetragonal disphenoidal pyramid, edge lengths √2+√3 (disphenoid bases) and √2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral angles	Sitwadip–twip–sitwadip: 150°
	Sitwadip–cube–sitwadip: 90°
	Twaddip–twip–sitwadip: 90°
Height	1
Central density	1
Number of external pieces	26
Level of complexity	15
Related polytopes
Army	Twatwip
Regiment	Twatwip
Dual	Dodecagonal duotegmatic tegum
Conjugate	Dodecagrammic duoprismatic prism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	I2(12)≀S2×A1, order 2304
Convex	Yes
Nature	Tame

The dodecagonal duoprismatic prism or twatwip, also known as the dodecagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 dodecagonal duoprisms and 24 square-dodecagonal duoprisms. Each vertex joins 4 square-dodecagonal duoprisms and 1 dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a hexagonal duoantiprismatic antiprism, although it cannot be made uniform. Half of the dodecagons can also be alternated into long ditrigons to create a hexagonal-hexagonal prismatic prismantiprismoid, which is also nonuniform.

Vertex coordinates[edit | edit source]

The vertices of an dodecagonal duoprismatic prism of edge length 1 are given by:

$\left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)$ ,
$\left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)$ ,
$\left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)$ ,
$\left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)$ ,
$\left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)$ ,
$\left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)$ ,
$\left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)$ ,
$\left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)$ ,
$\left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)$ .