Bicupolic ring (EntityClass, 16)

From Hi.gher. Space

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|ortho-
|ortho-
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|style='vertical-align: bottom;'|<[#img [hash 2Y6EC6FJBFXCPWWPHGZ9G626QE] [height 50]]><br/>[[Tetrahedral prism|K4.9]]
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|style='vertical-align: bottom;'|<[#embed [hash 2Y6EC6FJBFXCPWWPHGZ9G626QE] [height 50]]><br/>[[Tetrahedral prism|K4.9]]
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|<[#img [hash G1H1TK4VFZV38VZG5K66EQ0A4P] [height 50]]><br/>[[Trigonal orthobicupolic ring|K4.25]]
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|<[#embed [hash G1H1TK4VFZV38VZG5K66EQ0A4P] [height 50]]><br/>[[Trigonal orthobicupolic ring|K4.25]]
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|<[#img [hash RR35Y43QTQ6BY8FHP7E8M8PPEQ] [height 50]]><br/>[[Square orthobicupolic ring|K4.73]]
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|<[#embed [hash RR35Y43QTQ6BY8FHP7E8M8PPEQ] [height 50]]><br/>[[Square orthobicupolic ring|K4.73]]
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|<[#img [hash ANKWCX42212YR7P9SGS7MPQEG2] [height 50]]><br/>[[Pentagonal orthobicupolic ring|K4.154]]
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|<[#embed [hash ANKWCX42212YR7P9SGS7MPQEG2] [height 50]]><br/>[[Pentagonal orthobicupolic ring|K4.154]]
|-
|-
|gyro-
|gyro-
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|<[#img [hash 2TCT0MYSHNJBPK594VWD8RYRSG] [height 50]]><br/>[[Digonal gyrobicupolic ring|K4.8]]
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|<[#embed [hash 2TCT0MYSHNJBPK594VWD8RYRSG] [height 50]]><br/>[[Digonal gyrobicupolic ring|K4.8]]
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|<[#img [hash N2BYGAZRMM4R665BCK6WTK7XT0] [height 50]]><br/>[[Trigonal gyrobicupolic ring|K4.27]]
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|<[#embed [hash N2BYGAZRMM4R665BCK6WTK7XT0] [height 50]]><br/>[[Trigonal gyrobicupolic ring|K4.27]]
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|<[#img [hash 84ZQE0313240PWV0MBZWTCYHRV] [height 50]]><br/>[[Square gyrobicupolic ring|K4.64]]
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|<[#embed [hash 84ZQE0313240PWV0MBZWTCYHRV] [height 50]]><br/>[[Square gyrobicupolic ring|K4.64]]
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|<[#img [hash EFF0R80EYX6GWM0ZN10BPD1FFW] [height 50]]><br/>[[Pentagonal gyrobicupolic ring|K4.133]]
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|<[#embed [hash EFF0R80EYX6GWM0ZN10BPD1FFW] [height 50]]><br/>[[Pentagonal gyrobicupolic ring|K4.133]]
|-
|-
|magna-
|magna-
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|style='vertical-align: bottom;'|<[#img [hash 3NWJRDYM6HJXT8XWXVHRTK4HH2] [height 50]]><br/>[[Square pyramid prism|K4.12]]
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|style='vertical-align: bottom;'|<[#embed [hash 3NWJRDYM6HJXT8XWXVHRTK4HH2] [height 50]]><br/>[[Square pyramid prism|K4.12]]
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|<[#img [hash PV974PFM6RMXYH518NV9TT7YG6] [height 50]]><br/>[[Trigonal magnabicupolic ring|K4.51]]
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|<[#embed [hash PV974PFM6RMXYH518NV9TT7YG6] [height 50]]><br/>[[Trigonal magnabicupolic ring|K4.51]]
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|<[#img [hash WYC8PWYW55BDYQA32GE1AJYVH6] [height 50]]><br/>[[Square magnabicupolic ring|K4.105]]
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|<[#embed [hash WYC8PWYW55BDYQA32GE1AJYVH6] [height 50]]><br/>[[Square magnabicupolic ring|K4.105]]
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|<[#img [hash PGJPJECSKG22E2EEJEHJ4GBTZA] [height 50]]><br/>[[Pentagonal magnabicupolic ring|K4.165]]
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|<[#embed [hash PGJPJECSKG22E2EEJEHJ4GBTZA] [height 50]]><br/>[[Pentagonal magnabicupolic ring|K4.165]]
|}
|}

Revision as of 20:51, 11 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- (image)
K4.9
(image)
K4.25
(image)
K4.73
(image)
K4.154
gyro- (image)
K4.8
(image)
K4.27
(image)
K4.64
(image)
K4.133
magna- (image)
K4.12
(image)
K4.51
(image)
K4.105
(image)
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).

Pages in this category (12)