Tridecahedron

A tridecahedron is a polyhedron with thirteen faces. There are numerous topologically distinct forms of a tridecahedron, for example the dodecagonal pyramid and hendecagonal prism. However, a tridecahedron cannot be a regular polyhedron, because there is no regular polygon that can form a regular tridecahedron, and there are only five known regular polyhedra.[notes 1][1]

Convex

There are 96,262,938 topologically distinct convex tridecahedra, excluding mirror images, having at least 9 vertices.[2] (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.) There is a pseudo-space-filling tridecahedron that can fill all of 3-space together with its mirror-image.[3]

Examples

The following list gives examples of tridecahedra.

Notes
  1. Even if there were 13 faces that were all congruent, it would still not be considered a regular polyhedra. In addition to being congruent on each face of a regular polyhedron, the angles and sides on each face must be equal in size. Only regular polygons meet this condition, but the faces of a thirteen-sided shape do not, so there cannot be a regular tridecahedron.

References
  1. proof of platonic solids Archived 2015-11-21 at the Wayback Machine mathsisfun.com [2016-1-10]
  2. Counting polyhedra
  3. Ludacer, Randy. "Honeycombs and Structural Package Design: More Ways of Taking Up Space". Beach Branding & Packaging Design. Archived from the original on 2016-03-07.


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