Segmentotope (EntityClass, 11)

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Below are some useful properties of selected segmentochora. Measurements are given in terms of E, the edge length.
Below are some useful properties of selected segmentochora. Measurements are given in terms of E, the edge length.
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===Triangular cupola||triangular cupola===
===Triangular cupola||triangular cupola===

Revision as of 18:31, 9 January 2012

A segmentochoron is a polychoron whose vertices lie on two parallel hyperplanes. The set of all convex segmentochora having regular polygon ridges has been enumerated by Dr. Richard Klitzing. There are 177 of them, some of which includes polychora from other categories (such as cube||cube, which is the same as the tesseract).

Nomenclature

A segmentochoron is denoted by the notation A||B, where A and B are lower-dimensional polytopes. A and B are usually polyhedra, although one of them can be lower-dimensional, as is the case with the wedges and pyramids.

Some segmentochora may have multiple designations, for example, triangular_prism||hexagonal_prism is the same as triangular_cupola||triangular_cupola. Where multiple names are possible, the name listed by Klitzing takes precedence.


Properties

Below are some useful properties of selected segmentochora. Measurements are given in terms of E, the edge length.

Triangular cupola||triangular cupola

Other names: triangular prism||hexagonal prism

Distance between hexagonal prism and antipodal triangular prism: E*sqrt(2/3). (Same as the height of a triangular cupola.)

Square cupola||square cupola

Other names: cube||octagonal prism

Distance between octagonal prism and antipodal cube: E*sqrt(2)/2. (Same as height of square cupola.)

Pentagonal cupola||pentagonal cupola

Other names: pentagonal prism||decagonal prism

Distance between pentagonal prism and decagonal prism: E*(sqrt(2*sqrt(2*(3*sqrt(5)+7)) - (12*sqrt(5)+20)/5)/2). (Same as height of pentagonal cupola.)

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