Rectangular trapezoprism

Rectangular trapezoprism
Rank	3
Type	Isogonal
Notation
Bowers style acronym	Recta
Coxeter diagram
Elements
Faces	4 isosceles trapezoids, 2 rectangles
Edges	4+4+4
Vertices	8
Vertex figure	Scalene triangle
Measures (edge lengths a , b  (base), c  (lacing))
Circumradius	${\sqrt {{\frac {c^{2}}{2}}+{\frac {(a+b)^{2}}{8}}}}$
Height	${\sqrt {c^{2}-{\frac {(b-a)^{2}}{2}}}}$
Central density	1
Related polytopes
Army	Rectra
Regiment	Rectra
Dual	Digonal scalenohedron
Conjugate	Rectangular trapezoprism
Abstract & topological properties
Flag count	48
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	(B2×A1)/2, order 8
Flag orbits	6
Convex	Yes
Nature	Tame

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 $1+{\sqrt {2}}$ and lacing edges of length ${\sqrt {2}}$ 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 ${\sqrt {2}}$ and lacing edges of length ${\sqrt {2-{\sqrt {2}}}}$ occurs as the vertex figure of the antifrustary distetracontoctachoron.

External links

• Klitzing, Richard. "rectangular trapezoprism".