# Rectangular trapezoprism

Rectangular trapezoprism
Rank3
TypeIsogonal
Notation
Bowers style acronymRecta
Coxeter diagram
Elements
Faces4 isosceles trapezoids, 2 rectangles
Edges4+4+4
Vertices8
Vertex figureScalene triangle
Measures (edge lengths a , b  (base), c  (lacing))
Circumradius${\displaystyle {\sqrt {{\frac {c^{2}}{2}}+{\frac {(a+b)^{2}}{8}}}}}$
Height${\displaystyle {\sqrt {c^{2}-{\frac {(b-a)^{2}}{2}}}}}$
Central density1
Related polytopes
ArmyRectra
RegimentRectra
DualDigonal scalenohedron
ConjugateRectangular trapezoprism
Abstract & topological properties
Flag count48
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(B2×A1)/2, order 8
Flag orbits6
ConvexYes
NatureTame

The rectangular trapezoprism is a variant of the cube with digonal antiprism symmetry. It is isogonal, with 2 orthogonal rectangles as bases connected by 4 isosceles trapezoids. It can be obtained by bevelling two opposite edges of a tetrahedron.

If the edges of the rectangles are equal, the result is a square prism.

A version with rectangles of side lengths 1 and ${\displaystyle 1+{\sqrt {2}}}$ and lacing edges of length ${\displaystyle {\sqrt {2}}}$ occurs as an edge-alternation of the uniform octagonal prism.

Specific variants of the rectangular trapezoprism can be holo-alternated to form the altered stella octangula.

## In vertex figures

A rectangular trapezoprism with base edges of lengths 1 and ${\displaystyle {\sqrt {2}}}$ and lacing edges of length ${\displaystyle {\sqrt {2-{\sqrt {2}}}}}$ occurs as the vertex figure of the antifrustary distetracontoctachoron.