# Octagonal-great rhombicuboctahedral duoprism

Octagonal-great rhombicuboctahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymOgirco
Coxeter diagramx8o x4x3x ()
Elements
Tera12 square-octagonal duoprisms, 8 hexagonal-octagonal duoprisms, 6 octagonal duoprisms, 8 great rhombicuboctahedral prisms
Cells96 cubes, 64 hexagonal prisms, 24+24+24+48 octagonal prisms, 8 great rhombicuboctahedra
Faces96+192+192+192 squares, 64 hexagons, 48+48 octagons
Edges192+192+192+384
Vertices384
Vertex figureMirror-symmetric pentachoron, edge lengths 2, 3, 2+2 (base triangle), 2+2 (top edge), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {17+8{\sqrt {2}}}}{2}}\approx 2.66053}$
Hypervolume${\displaystyle 4(25+18{\sqrt {2}})\approx 201.82338}$
Diteral anglesSodip–op–hodip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
Sodip–op–odip: 135°
Gircope–girco–gircope: 135°
Hodip–op–odip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Sodip–cube–gircope: 90°
Hodip–hip–gircope: 90°
Odip–op–gircope: 90°
Central density1
Number of external pieces34
Level of complexity60
Related polytopes
ArmyOgirco
RegimentOgirco
DualOctagonal-disdyakis dodecahedral duotegum
ConjugateOctagrammic-quasitruncated cuboctahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(8), order 768
ConvexYes
NatureTame

The octagonal-great rhombicuboctahedral duoprism or ogirco is a convex uniform duoprism that consists of 8 great rhombicuboctahedral prisms, 6 octagonal duoprisms, 8 hexagonal-octagonal duoprisms, and 12 square-octagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-octagonal duoprism, 1 hexagonal-octagonal duoprism, and 1 octagonal duoprism.

The octagonal-great rhombicuboctahedral duoprism can be vertex-inscribed into the cellirhombated penteractitriacontaditeron.

This polyteron can be alternated into a square-snub cubic duoantiprism, although it cannot be made uniform. The octagons can also be edge-snubbed to create a snub cubic-square prismantiprismoid or the great rhombicuboctahedra to create a square-pyritohedral prismantiprismoid, which are also both nonuniform.

## Vertex coordinates

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

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

## Representations

An octagonal-great rhombicuboctahedral duoprism has the following Coxeter diagrams:

• x8o x4x3x (full symmetry)
• x4x x4x3x () (BC3×BC2 symmetry, octagons as ditetragons)