Square prism

Square prism
Rank3
TypeSemi-uniform
Notation
Bowers style acronymSquip
Coxeter diagramx y4o
Elements
Faces4 rectangles, 2 squares
Edges4+8
Vertices8
Vertex figureIsosceles triangle
Measures (edge lengths a (base), b (lacing))
Circumradius${\displaystyle {\sqrt {{\frac {a^{2}}{2}}+{\frac {b^{2}}{4}}}}}$
Volume${\displaystyle a^{2}b}$
Dihedral angle90°
Height${\displaystyle b}$
Central density1
Related polytopes
ArmySquip
RegimentSquip
DualSquare tegum
ConjugateSquare prism
Abstract & topological properties
Flag count48
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryB2×A1, order 16
Flag orbits3
ConvexYes
NatureTame

The square prism, or squip, is a prism with a square base. The uniform square prism is simply the regular cube. If the edges of the base square and the side edges of the prism are different, the result is a semi-uniform polyhedron with 2 squares and 4 rectangles as faces.

A square prism with base edges of length a and side edges of length b can be alternated into a tetragonal disphenoid with base edges of length ${\displaystyle a{\sqrt {2}}}$ and side edges of length ${\displaystyle {\sqrt {a^{2}+b^{2}}}}$.

Vertex coordinates

A square prism with base edges of length a and side edges of length b has coordinates given by:

• ${\displaystyle \left(\pm {\frac {a}{2}},\,\pm {\frac {a}{2}},\,\pm {\frac {b}{2}}\right)}$.

In vertex figures

A square prism with base edges of length 1 and side edges of length ${\displaystyle {\sqrt {2}}}$ occurs as the vertex figure of the Euclidean rectified cubic honeycomb.