# Decagonal-cubic duoprism

Decagonal-cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymDacube
Coxeter diagramx10o x4o3o ()
Elements
Tera10 tesseracts, 6 square-decagonal duoprisms
Cells10+60 cubes, 12 decagonal prisms
Faces60+120 squares, 8 decagons
Edges80+120
Vertices80
Vertex figureTriangular scalene, edge lengths (5+5)/2 (top), 2 (base triangle and sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {9+2{\sqrt {5}}}}{2}}\approx 1.83522}$
Hypervolume${\displaystyle 5{\frac {\sqrt {5+2{\sqrt {5}}}}{2}}\approx 7.69421}$
Diteral anglesTes–cube–tes: 144°
Height1
Central density1
Number of external pieces16
Level of complexity10
Related polytopes
ArmyDacube
RegimentDacube
DualDecagonal-octahedral duotegum
ConjugateDecagrammic-cubic duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(10), order 960
ConvexYes
NatureTame

The decagonal-cubic duoprism or dacube, also known as the square-decagonal duoprismatic prism, is a convex uniform duoprism that consists of 10 tesseracts and 6 square-decagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-decagonal duoprisms. It is a duoprism based on a square and a decagonal prism, which makes it a convex segmentoteron.

This polyteron can be alternated into a pentagonal-tetrahedral duoantiprism, although it cannot be made uniform.

## Vertex coordinates

The vertices of a decagonal-cubic duoprism of edge length 1 are given by:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{2}},\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).}$

## Representations

A decagonal-cubic duoprism has the following Coxeter diagrams:

• x10o x4o3o () (full symmetry)
• x x4o x10o () (square-decagonal duoprismatic prism)
• x x x x10o () (decagonal prismatic prismatic prism)