Compound of three cubes (prismatic symmetry)

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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
Volume3
Dihedral angle90°
Height1
Central density3
Number of external pieces26
Level of complexity6
Related polytopes
ArmySemi-uniform Twip, edge lengths (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[edit | edit source]

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