Editing Trapezohedron (section)

==Forms==
An '''{{mvar|n}}-trapezohedron''' is defined by a [[Regular skew polygon|regular zig-zag skew]] {{math|'''2'''''n''}}-gon base, two symmetric [[Apex (geometry)|apices]] with no [[Degrees of freedom|degree of freedom]] right above and right below the base, and [[quadrilateral]] faces connecting each pair of [[Adjacent side (polygon)|adjacent]] basal edges to one apex.

An {{mvar|n}}-trapezohedron has two apical vertices on its polar axis, and {{math|2''n''}} basal vertices in two regular {{mvar|n}}-gonal rings. It has {{math|'''2'''''n''}} [[Congruence (geometry)|congruent]] [[Kite (geometry)|kite]] faces, and it is [[Isohedral figure|isohedral]].

{{Trapezohedra}}

=== Special cases ===
* {{math|1=''n'' = 2}}. A degenerate form of trapezohedron: a geometric figure with 6 vertices, 8 edges, and 4 degenerate [[Kite (geometry)|kite]] faces that are visually identical to triangles. As such, the trapezohedron itself is visually identical to the regular [[tetrahedron]]. Its dual is a degenerate form of [[antiprism]] that also resembles the regular tetrahedron.

* {{math|1=''n'' = 3}}. The dual of a ''triangular antiprism'': the kites are rhombi (or squares); hence these trapezohedra are also [[zonohedra]]. They are called '''[[rhombohedra]]'''. They are [[cube]]s scaled in the direction of a body diagonal. They are also the [[parallelepiped]]s with congruent rhombic faces.[[File:Gyroelongated triangular bipyramid.png|thumb|A {{math|60°}} rhombohedron, [[Dissection (geometry)|dissected]] into a central regular octahedron and two regular tetrahedra]]
** A special case of a rhombohedron is one in which the rhombi forming the faces have angles of {{math|60°}} and {{math|120°}}. It can be decomposed into two equal regular tetrahedra and a regular [[octahedron]]. Since parallelepipeds can [[Tessellation|fill space]], so can a [[Tetrahedral-octahedral honeycomb|combination of regular tetrahedra and regular octahedra]].

* {{math|1=''n'' = 5}}. The [[pentagonal trapezohedron]] is the only polyhedron other than the [[Platonic solid]]s commonly used as a [[Dice|die]] in [[roleplaying games]] such as ''[[Dungeons & Dragons]]''. Being [[Convex set|convex]] and [[Isohedral figure|face-transitive]], it makes [[fair dice]]. Having 10 sides, it can be used in repetition to generate any decimal-based [[Uniform distribution (discrete)|uniform probability]] desired. Typically, two dice of different colors are used for the two [[Numerical digit|digits]] to represent numbers from {{math|00}} to {{math|99}}.