Dodecagonal-small rhombicuboctahedral duoprism

Dodecagonal-small rhombicuboctahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Twasirco
Coxeter diagram	x12o x4o3x ()
Elements
Tera	8 triangular-dodecagonal duoprisms, 6+12 square-dodecagonal duoprisms, 12 small rhombicuboctahedral prisms
Cells	96 triangular prisms, 72+144 cubes, 24+24 dodecagonal prisms, 12 small rhombicuboctahedra
Faces	96 triangles, 72+144+288+288 squares, 24 dodecagons
Edges	288+288+288
Vertices	288
Vertex figure	Isosceles-trapezoidal scalene, edge lengths 1, √2, √2, √2 (base trapezoid), √2+√3 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {13+2{\sqrt {2}}+4{\sqrt {3}}}}{2}}\approx 2.38520$
Hypervolume	$2(12+10{\sqrt {2}}+6{\sqrt {3}}+5{\sqrt {6}})\approx 97.56378$
Diteral angles	Sircope–sirco–sircope: 150°
	Titwadip–twip–sitwadip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Sitwadip–twip–sitwadip: 135°
	Titwadip–trip–sircope: 90°
	Sitwadip–cube–sircope: 90°
Central density	1
Number of external pieces	38
Level of complexity	40
Related polytopes
Army	Twasirco
Regiment	Twasirco
Dual	Dodecagonal-deltoidal icositetrahedral duotegum
Conjugates	Dodecagrammic-small rhombicuboctahedral duoprism, Dodecagonal-quasirhombicuboctahedral duoprism, Dodecagrammic-quasirhombicuboctahedral duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3×I2(12), order 1152
Convex	Yes
Nature	Tame

The dodecagonal-small rhombicuboctahedral duoprism or twasirco is a convex uniform duoprism that consists of 12 small rhombicuboctahedral prisms, 18 square-dodecagonal duoprisms of two kinds, and 8 triangular-dodecagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular-dodecagonal duoprism, and 3 square-dodecagonal duoprisms.

This polyteron can be tetrahedrally alternated into a hexagonal-truncated tetrahedral duoalterprism, although it cannot be made scaliform. It can also be tetrahedrally edge-snubbed to create a truncated tetrahedral-hexagonal prismalterprismoid, which is also not scaliform.

Vertex coordinates

The vertices of a dodecagonal-small rhombicuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

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

Representations

A dodecagonal-small rhombicuboctahedral duoprism has the following Coxeter diagrams:

• x12o x4o3x () (full symmetry)
• x6x x4o3x () (dodecagons as dihexagons)