Bicupolic ring (EntityClass, 16)
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|<[#img [hash PGJPJECSKG22E2EEJEHJ4GBTZA] [height 50]]><br/>[[Pentagonal magnabicupolic ring|K4.165]] | |<[#img [hash PGJPJECSKG22E2EEJEHJ4GBTZA] [height 50]]><br/>[[Pentagonal magnabicupolic ring|K4.165]] | ||
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| + | ==Structure== | ||
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| + | Each of these bicupolic rings consists of two n-gonal cupolae, a linking element, an opposite element corresponding with a Stott-expanded n-gon, and a ring of lateral cells that fill up the gaps in between. | ||
| + | * For the orthobicupolic rings, the linking element is an n-gonal prism, and the opposite element is a 2n-gon. The lateral cells consist of alternating tetrahedra and triangular prisms. | ||
| + | * For the gyrobicupolic rings, the linking element is an n-gonal antiprism, and the opposite element is a 2n-gon. The lateral cells consist of a ring of square pyramids in alternating orientations. | ||
| + | * For the magnabicupolic rings, the linking element is just an n-gon, and the opposite element is a 2n-gonal prism. The lateral cells consist of an alternating ring of triangular prisms and square pyramids. | ||
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| + | In the digonal bicupolic rings, the digonal prism is simply the square, the digonal antiprism is the tetrahedron, and the 2n-gon is also the square (tetragon). Hence, the digonal cupola is just the triangular prism (the digon and the tetragon in parallel planes joined by a ring of alternating squares and triangles). | ||
Revision as of 08:05, 10 February 2014
There are twelve bicupolic rings in Klitzing's list of segmentochora, two of which turn out to be prisms.
| Digonal | Trigonal | Square | Pentagonal | |
|---|---|---|---|---|
| ortho- | ExPar: [#img] is obsolete, use [#embed] instead K4.9 | ExPar: [#img] is obsolete, use [#embed] instead K4.25 | ExPar: [#img] is obsolete, use [#embed] instead K4.73 | ExPar: [#img] is obsolete, use [#embed] instead K4.154 |
| gyro- | ExPar: [#img] is obsolete, use [#embed] instead K4.8 | ExPar: [#img] is obsolete, use [#embed] instead K4.27 | ExPar: [#img] is obsolete, use [#embed] instead K4.64 | ExPar: [#img] is obsolete, use [#embed] instead K4.133 |
| magna- | ExPar: [#img] is obsolete, use [#embed] instead K4.12 | ExPar: [#img] is obsolete, use [#embed] instead K4.51 | ExPar: [#img] is obsolete, use [#embed] instead K4.105 | ExPar: [#img] is obsolete, use [#embed] instead K4.165 |
Structure
Each of these bicupolic rings consists of two n-gonal cupolae, a linking element, an opposite element corresponding with a Stott-expanded n-gon, and a ring of lateral cells that fill up the gaps in between.
- For the orthobicupolic rings, the linking element is an n-gonal prism, and the opposite element is a 2n-gon. The lateral cells consist of alternating tetrahedra and triangular prisms.
- For the gyrobicupolic rings, the linking element is an n-gonal antiprism, and the opposite element is a 2n-gon. The lateral cells consist of a ring of square pyramids in alternating orientations.
- For the magnabicupolic rings, the linking element is just an n-gon, and the opposite element is a 2n-gonal prism. The lateral cells consist of an alternating ring of triangular prisms and square pyramids.
In the digonal bicupolic rings, the digonal prism is simply the square, the digonal antiprism is the tetrahedron, and the 2n-gon is also the square (tetragon). Hence, the digonal cupola is just the triangular prism (the digon and the tetragon in parallel planes joined by a ring of alternating squares and triangles).
