Non-CRF facets of CRF duals (ConceptTopic, 3)

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Revision as of 11:32, 29 March 2014

The set of non-CRF facets of CRF duals is currently being studied by Keiji. A proper name for the set has not yet been thought up. They are reminiscent of the Catalan solids. This page lists them in order of discovery.

Triangulated triangular prism

First discovered in the dual of the BXD and appeared again shortly after in the dual of the (4D analog of J37). Self-dual and chiral.

Hexagonal cupolawedge

First discovered in the dual of the bilunabirotunda pseudopyramid. Dual is the hexagonal pyrawedge which has not yet been seen in any other polytopes. Not chiral.

Square cupolawedge

First discovered in the dual of the triangular hebesphenorotunda pseudopyramid. Dual is the pentagonal cupolawedge which has not yet been seen in any other polytopes. Not chiral.

Rhombocupolawedge

First discovered in the dual of the D4.7 and appeared again in the dual of the D4.11. Dual is the rhombopyrawedge which has not yet been seen in any other polytopes. Not chiral.

Metabigyrotriangulated cube

First discovered in the dual of the D4.7. Self-dual and chiral.

Parabiorthotriangulated cube

First discovered in the dual of the J92 rhombochoron. Self-dual, but not chiral. It is the first such known polytope (in this list, anyway) and is also the first to break an incorrect assumption made by the current version of the polytope explorer, which will thus not accept the polytope as legitimately self-dual.

Triangulated pinched triangular cupola

First discovered in the dual of the J92 rhombochoron. Self-dual. Has no symmetry at all, and is therefore chiral. (The parabiorthotriangulated metapinched triangular cupola displayed to the right was previously thought to be the dual by mistake.)

Biunpinched cube

First discovered in the dual of the J92 rhombochoron. Dual is the parabiorthotriangulated orthopinched triangular cupola which has not yet been seen in any other polytopes. Not chiral.

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