# Triangular-great rhombicuboctahedral duoprism

Triangular-great rhombicuboctahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymTragirco
Coxeter diagramx3o x4x3x ()
Elements
Tera12 triangular-square duoprisms, 8 triangular-hexagonal duoprisms, 6 triangular-octagonal duoprisms, 3 great rhombicuboctahedral prisms
Cells24+24+24 triangular prisms, 36 cubes, 24 hexagonal prisms, 18 octagonal prisms
Faces48 triangles, 36+72+72+72 squares, 24 hexagons, 18 octagons
Edges72+72+72+144
Vertices144
Vertex figureMirror-symmetric pentachoron, edge lengths 2, 3, 2+2 (base triangle), 1 (top edge), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {43+18{\sqrt {2}}}{12}}}\approx 2.38844}$
Hypervolume${\displaystyle {\frac {11{\sqrt {3}}+7{\sqrt {6}}}{2}}\approx 18.09949}$
Diteral anglesTisdip–trip–thiddip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
Tisdip–trip–todip: 135°
Thiddip–trip–todip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Tisdip–cube–gircope: 90°
Thiddip–hip–gircope: 90°
Todip–op–gircope: 90°
Gircope–girco–gircope: 60°
Height${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Central density1
Number of external pieces29
Level of complexity60
Related polytopes
ArmyTragirco
RegimentTragirco
DualTriangular-disdyakis dodecahedral duotegum
ConjugateTriangular-quasitruncated cuboctahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×A2, order 288
ConvexYes
NatureTame

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:

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