# Cuboid

Cuboid
Rank3
TypeSemi-uniform
Notation
Bowers style acronymCuboid
Coxeter diagramx y z
Elements
Faces2+2+2 rectangles
Edges4+4+4
Vertices8
Vertex figureScalene triangle
Measures (edge lengths a , b , c )
Circumradius${\displaystyle {\frac {\sqrt {a^{2}+b^{2}+c^{2}}}{2}}}$
Volume${\displaystyle abc}$
Dihedral angle90°
Central density1
Related polytopes
ArmyCuboid
RegimentCuboid
DualRhombic tegum
ConjugateCuboid
Abstract & topological properties
Flag count48
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK3, order 8
Flag orbits6
ConvexYes
NatureTame

The cuboid or rectangular prism is a variant of the cube with 3 pairs of identical parallel rectangles as faces. All of its dihedral angles measure 90° and all cuboids are isogonal.

A cuboid with edges of length a, b, and c can be alternated into a rhombic disphenoid with edges of length ${\displaystyle {\sqrt {a^{2}+b^{2}}}}$, ${\displaystyle {\sqrt {a^{2}+c^{2}}}}$, and ${\displaystyle {\sqrt {b^{2}+c^{2}}}}$.

## Vertex coordinates

A cuboid with edges of length a, b, and c has coordinates given by:

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