# Compound of three cubes (prismatic symmetry)

Compound of three cubes (prismatic symmetry)
Rank3
TypeUniform
Elements
Components3 cubes
Faces12 squares, 6 squares as 2 trisquares
Edges12+24
Vertices24
Vertex figureEquilateral triangle, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Volume3
Dihedral angle90°
Height1
Central density3
Number of external pieces26
Level of complexity6
Related polytopes
ArmySemi-uniform Twip, edge lengths ${\displaystyle {\frac {{\sqrt {3}}-1}{2}}}$ (base), 1 (sides)
Regiment*
DualCompound of three octahedra
ConjugateCompound of three cubes
Abstract & topological properties
Flag count144
OrientableYes
Properties
SymmetryI2(12)×A1, order 48
ConvexNo
NatureTame

The trisquare prism or compound of three cubes with prismatic symmetry is a prismatic uniform polyhedron compound. It consists of 2 trisquares and 12 squares. Each vertex joins one trisquare and two squares. As the name suggests, it is a prism based on a trisquare.

Its quotient prismatic equivalent is the 12-4 step prismatic prism, which is five-dimensional.

## Vertex coordinates

Coordinates for the vertices of a trisquare prism of edge length 1 centered at the origin are given by:

• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,0,\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(0,\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {\sqrt {6}}{4}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {6}}{4}},\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {1}{2}}\right).}$