View source for Rectangular trapezoprism

{{Infobox polytope
|img = auto
|rank = 3
|obsa = {{BSAhelp|Rect|rectangular|a|antipodium}}
|type = [[Isogonal]]
|coxeter = {{CDD|node_h|2|node_h|4|node_1}}
|symmetry = [[Digonal antiprismatic symmetry|(B<sub>2</sub>×A<sub>1</sub>)/2]], order 8
|orbits = 6
|army = '''Rectra'''
|reg = '''Rectra'''
|faces = 4 [[isosceles trapezoid]]s, 2 [[rectangle]]s
|edges = 4+4+4
|vertices = 8
|flags = 48
|verf = [[Scalene triangle]]
|els = {{mvar|a}}, {{mvar|b}} (base), {{mvar|c}} (lacing)
|circum = <math>\sqrt{\frac{c^2}{2}+\frac{(a+b)^2}{8}}</math>
|height = <math>\sqrt{c^2-\frac{(b-a)^2}{2}}</math>
|dual = [[Digonal scalenohedron]]
|conjugate = '''Rectangular trapezoprism'''
|conv = Yes
|orient = Yes
|nat = Tame
}}
The '''rectangular trapezoprism''' is a variant of the [[cube]] with digonal antiprism symmetry. It is isogonal, with 2 orthogonal [[rectangle]]s as bases connected by 4 [[isosceles trapezoid]]s. 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 <math>1+\sqrt2</math> and lacing edges of length <math>\sqrt2</math> 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]].

==Vertex coordinates==
{{Missing coords|date=April 2024}}

==In vertex figures==

A rectangular trapezoprism with base edges of lengths 1 and <math>\sqrt2</math> and lacing edges of length <math>\sqrt{2-\sqrt2}</math> occurs as the [[vertex figure]] of the [[antifrustary distetracontoctachoron]].

==External links==

* {{Incmats|rectangular%20trapezoprism|rectangular trapezoprism}}

[[Category:3D trapezoprisms]]
[[Category:Recta army]]
[[Category:(B2×A1)/2 symmetry]]
[[Category:Polyhedra with 6 faces]]