Triangular-great rhombicuboctahedral duoprism

Triangular-great rhombicuboctahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Tragirco
Coxeter diagram	x3o x4x3x ()
Elements
Tera	12 triangular-square duoprisms, 8 triangular-hexagonal duoprisms, 6 triangular-octagonal duoprisms, 3 great rhombicuboctahedral prisms
Cells	24+24+24 triangular prisms, 36 cubes, 24 hexagonal prisms, 18 octagonal prisms
Faces	48 triangles, 36+72+72+72 squares, 24 hexagons, 18 octagons
Edges	72+72+72+144
Vertices	144
Vertex figure	Mirror-symmetric pentachoron, edge lengths √2, √3, √2+√2 (base triangle), 1 (top edge), √2 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {43+18{\sqrt {2}}}{12}}}\approx 2.38844$
Hypervolume	${\frac {11{\sqrt {3}}+7{\sqrt {6}}}{2}}\approx 18.09949$
Diteral angles	Tisdip–trip–thiddip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Tisdip–trip–todip: 135°
	Thiddip–trip–todip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Tisdip–cube–gircope: 90°
	Thiddip–hip–gircope: 90°
	Todip–op–gircope: 90°
	Gircope–girco–gircope: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	29
Level of complexity	60
Related polytopes
Army	Tragirco
Regiment	Tragirco
Dual	Triangular-disdyakis dodecahedral duotegum
Conjugate	Triangular-quasitruncated cuboctahedral duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3×A2, order 288
Convex	Yes
Nature	Tame

The triangular-great rhombicuboctahedral duoprism or tragirco is a convex uniform duoprism that consists of 3 great rhombicuboctahedral prisms, 6 triangular-octagonal duoprisms, 8 triangular-hexagonal duoprisms, and 12 triangular-square duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 triangular-square duoprism, 1 triangular-hexagonal duoprism, and 1 triangular-octagonal duoprism. It is a duoprism based on a triangle and a great rhombicuboctahedron, which makes it a convex segmentoteron.

Vertex coordinates

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

• $\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1+2{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1+2{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right).$

External links

• Klitzing, Richard. "tragirco".