Trigonal gyrobicupolic ring (EntityTopic, 17)
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The '''triangular gyrobicupolic ring''' is a [[CRF polychoron]] discovered by [[Keiji]]. It is a member of the family of [[bicupolic ring]]s, which contains eight other similar polychora. It is formed by attaching two [[triangular cupola]]e by their [[hexagon]]al faces, folding them into the fourth dimension with their [[triangular]] ends connected by an [[octahedron]], and then filling in the gaps with 6 [[square pyramid]]s. | The '''triangular gyrobicupolic ring''' is a [[CRF polychoron]] discovered by [[Keiji]]. It is a member of the family of [[bicupolic ring]]s, which contains eight other similar polychora. It is formed by attaching two [[triangular cupola]]e by their [[hexagon]]al faces, folding them into the fourth dimension with their [[triangular]] ends connected by an [[octahedron]], and then filling in the gaps with 6 [[square pyramid]]s. | ||
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| + | == Cartesian coordinates == | ||
| + | |||
| + | Hexagon: | ||
| + | (±sqrt(3), ±1, 0, 0) | ||
| + | (0, ±2, 0, 0) | ||
| + | Triangle 1: | ||
| + | (-1/sqrt(3), ±1, sqrt(2/3), sqrt(2)) | ||
| + | (2/sqrt(3), 0, sqrt(2/3), sqrt(2)) | ||
| + | Triangle 2: | ||
| + | (1/sqrt(3), ±1, -sqrt(2/3), sqrt(2)) | ||
| + | (-2/sqrt(3), 0, -sqrt(2/3), sqrt(2)) | ||
Revision as of 23:39, 27 August 2012
The triangular gyrobicupolic ring is a CRF polychoron discovered by Keiji. It is a member of the family of bicupolic rings, which contains eight other similar polychora. It is formed by attaching two triangular cupolae by their hexagonal faces, folding them into the fourth dimension with their triangular ends connected by an octahedron, and then filling in the gaps with 6 square pyramids.
Cartesian coordinates
Hexagon:
(±sqrt(3), ±1, 0, 0) (0, ±2, 0, 0)
Triangle 1:
(-1/sqrt(3), ±1, sqrt(2/3), sqrt(2)) (2/sqrt(3), 0, sqrt(2/3), sqrt(2))
Triangle 2:
(1/sqrt(3), ±1, -sqrt(2/3), sqrt(2)) (-2/sqrt(3), 0, -sqrt(2/3), sqrt(2))
