Compound of four triangular prisms (prismatic symmetry)

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Compound of four triangular prisms (prismatic symmetry)
Rank3
TypeUniform
Elements
Components4 triangular prisms
Faces12 squares, 8 triangles as 2 tetratriangles
Edges12+24
Vertices24
Vertex figureIsosceles triangle, edge lengths 1, 2, 2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles4–3: 90°
 4–4: 60°
Height1
Central density4
Number of external pieces26
Level of complexity6
Related polytopes
ArmySemi-uniform Twip, edge lengths (base), 1 (sides)
Regiment*
DualCompound of four triangular tegums
ConjugateCompound of four triangular prisms
Abstract & topological properties
Flag count144
OrientableYes
Properties
SymmetryI2(12)×A1, order 48
ConvexNo
NatureTame

The tetratriangular prism or compound of four triangular prisms with prismatic symmetry is a prismatic uniform polyhedron compound. It consists of 2 tetratriangles and 12 squares. Each vertex joins one tetratriangle and two squares. As the name suggests, it is a prism based on a tetratriangle.

Its quotient prismatic equivalent is the triangular tetrahedroorthowedge prism, which is six-dimensional.

Vertex coordinates[edit | edit source]

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

Variations[edit | edit source]

This compound has variants where the bases are non-regular compounds of four triangles (seen as two-hexagram compounds). In these cases the compound has only hexagonal prismatic symmetry and the convex hull is a dihexagonal prism.