Segmentotope (EntityClass, 11)
From Hi.gher. Space
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</td><td> | </td><td> | ||
*2 [[tetrahedra]] | *2 [[tetrahedra]] | ||
- | *3 square | + | *3 [[square pyramid]]s |
- | *1 trigonal prism | + | *1 [[trigonal prism]] |
</td><td> | </td><td> | ||
*Height of triangular prism pyramid: E*sqrt(5/12) | *Height of triangular prism pyramid: E*sqrt(5/12) | ||
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K 4.26 | K 4.26 | ||
</td><td> | </td><td> | ||
- | '''[[square]] || square_pyramid''' | + | '''[[square]] || [[square_pyramid]]''' |
*[[cubical pyramid]] | *[[cubical pyramid]] | ||
- | *point || [[cube]] | + | *[[point]] || [[cube]] |
*square prism pyramid | *square prism pyramid | ||
</td><td> | </td><td> | ||
- | *6 square | + | *6 [[square pyramid]]s |
- | *1 cube | + | *1 [[cube]] |
</td><td> | </td><td> | ||
*Dichoral angle between square pyramid and cube: 45° (exact) | *Dichoral angle between square pyramid and cube: 45° (exact) | ||
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</td><td> | </td><td> | ||
'''[[hexagon]] || [[trigonal_cupola]]''' | '''[[hexagon]] || [[trigonal_cupola]]''' | ||
- | *[[triangle]] || | + | *[[triangle]] || [[hexagonal_prism]] |
*[[trigonal orthobicupolic ring]] | *[[trigonal orthobicupolic ring]] | ||
</td><td> | </td><td> | ||
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</td><td> | </td><td> | ||
'''[[square_cupola]] || square_cupola''' | '''[[square_cupola]] || square_cupola''' | ||
- | *'''cube || [[octagonal_prism]]''' | + | *'''[[cube]] || [[octagonal_prism]]''' |
</td><td> | </td><td> | ||
</td><td> | </td><td> | ||
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K 4.105 | K 4.105 | ||
</td><td> | </td><td> | ||
- | '''[[octagon]] || square_cupola''' | + | '''[[octagon]] || [[square_cupola]]''' |
- | *[[square]] || octagonal_prism | + | *[[square]] || [[octagonal_prism]] |
*[[square orthobicupolic ring]] | *[[square orthobicupolic ring]] | ||
</td><td> | </td><td> | ||
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</td><td> | </td><td> | ||
'''[[pentagon]] || [[pentagonal_pyramid]]''' | '''[[pentagon]] || [[pentagonal_pyramid]]''' | ||
- | *[[point]] || pentagonal_prism | + | *[[point]] || [[pentagonal_prism]] |
</td><td> | </td><td> | ||
</td><td> | </td><td> | ||
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</td><td> | </td><td> | ||
'''[[decagon]] || [[pentagonal_cupola]]''' | '''[[decagon]] || [[pentagonal_cupola]]''' | ||
- | *pentagon || [[decagonal_prism]] | + | *[[pentagon]] || [[decagonal_prism]] |
*[[pentagonal orthobicupolic ring]] | *[[pentagonal orthobicupolic ring]] | ||
</td><td> | </td><td> |
Revision as of 20:03, 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, including some polychora from other categories (such as cube || cube, which is the same as the tesseract). The full list can be obtained from Klitzing's paper (PDF format).
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. Klitzing's numbering is written as "K 4.n", as given in his PhD dissertation. Measurements are given in terms of E, the edge length.
# | Name(s) | Cells | Values |
---|---|---|---|
K 4.7 |
|
| |
K 4.26 |
|
|
|
K 4.45 |
triangular_cupola || triangular_cupola |
| |
K 4.51 |
| ||
K 4.69 |
square_cupola || square_cupola |
| |
K 4.105 |
| ||
K 4.117 |
pentagonal_cupola || pentagonal_cupola |
| |
K 4.141 |
| ||
K 4.165 |
|