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

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<[#ontology [kind topic] [cats Essays]]>
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 solid]]s. This page lists them in order of discovery.
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 solid]]s. This page lists them in order of discovery.
;[[Triangulated triangular prism]]
;[[Triangulated triangular prism]]
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: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.
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:First discovered in the dual of the [[BXD]] and appeared again shortly after in the dual of the [[(4D analog of J37)]]. It also appears in the dual of the [[J92 rhombochoron]] and so far it is the most commonly appearing polytope in this list. Self-dual and chiral.
:<[#embed [hash KANNJNWXZK01GRRZNPD5M6VHMQ]]>
:<[#embed [hash KANNJNWXZK01GRRZNPD5M6VHMQ]]>
;[[Hexagonal cupolawedge]]
;[[Hexagonal cupolawedge]]
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: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.
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:First discovered in the dual of the [[bilunabirotunda pseudopyramid]] and appeared later in the [[tetraaugmented J92 rhombochoron]]. Dual is the [[hexagonal pyrawedge]] which has not yet been seen in any other polytopes. Not chiral.
:<[#embed [hash MDQEEHDGNAYMWKAPQHDQJMG555]]> <[#embed [hash X0WFTDFDXVZDGTFY8K7JMGSJZ9]]>
:<[#embed [hash MDQEEHDGNAYMWKAPQHDQJMG555]]> <[#embed [hash X0WFTDFDXVZDGTFY8K7JMGSJZ9]]>
;[[Square cupolawedge]]
;[[Square cupolawedge]]
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: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.
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:First discovered in the dual of the [[triangular hebesphenorotunda pseudopyramid]] and appeared later at the same position in the [[tetraaugmented J92 rhombochoron]]. Dual is the [[pentagonal cupolawedge]] which has not yet been seen in any other polytopes. Not chiral.
:<[#embed [hash NMPDRSK10VNMEVGNSFETT6QJQ4]]> <[#embed [hash F753M7PD4FTV2H4ZXG88EW229H]]>
:<[#embed [hash NMPDRSK10VNMEVGNSFETT6QJQ4]]> <[#embed [hash F753M7PD4FTV2H4ZXG88EW229H]]>
;[[Rhombocupolawedge]]
;[[Rhombocupolawedge]]
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:First discovered in the dual of the [[CJ4.7]]. Dual is the [[rhombopyrawedge]] which has not yet been seen in any other polytopes. Not chiral.
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: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.
:<[#embed [hash DSZETFT3TKTBG6HXKZQGAPEY3M]]> <[#embed [hash MVPMW7ASJP59RS9N114AMZ80QX]]>
:<[#embed [hash DSZETFT3TKTBG6HXKZQGAPEY3M]]> <[#embed [hash MVPMW7ASJP59RS9N114AMZ80QX]]>
;[[Metabigyrotriangulated cube]]
;[[Metabigyrotriangulated cube]]
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:First discovered in the dual of the [[CJ4.7]]. Self-dual and chiral.
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:First discovered in the dual of the [[D4.7]]. Self-dual and chiral.
:<[#embed [hash NE7GGHKG7YKNYN5GE1CKW92GMM]]>
:<[#embed [hash NE7GGHKG7YKNYN5GE1CKW92GMM]]>
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;[[Parabiorthotriangulated cube]]
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: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.
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:<[#embed [hash QCDARJ11XZ5NRFPB75CKTYEP6D]]>
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;[[Triangulated pinched triangular cupola]]
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: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.)
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:<[#embed [hash YKN1Y2N0W2J0JKRQ4GDYPCKRTD]]> <[#embed [hash QKGRPCQJBNHJPMXD2RENEX2E2G]]>
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;[[Biunpinched cube]]
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:First discovered in the dual of the [[J92 rhombochoron]] and appeared shortly after at the same position in the [[tetraaugmented 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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:<[#embed [hash 5Y4BMY6S841DRWE5DGVCRAQ1VM]]> <[#embed [hash B90HPT0FCA90TAMXM89QM8JM54]]>
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;[[Digon-unpinched pentagonal prism]]
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:First discovered in the dual of the [[tetraaugmented J92 rhombochoron]]. Dual is the [[snub disphenoid]], which makes it the first discovered non-CRF to be both the dual of a CRF, and the cell of a dual of a CRF, at the same time.
 +
:<[#embed [hash MA7NMH1QYSQFPPGBA3K9MGGA6X]]> <[#embed [hash A267YZ2WP5WSTZ5CB56YGYETSJ]]>
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;[[Square transcupolawedge]]
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:First discovered in the dual of the [[tetraaugmented J92 rhombochoron]]. Dual is the [[pentagonal transcupolawedge]] which has not yet been seen in any other polytopes. This pair is very similar to the square cupolawedge and pentagonal cupolawedge described above, with the only difference that a pair of edges is swapped.
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:<[#embed [hash SZ9JG9RNYS5CGS3JNJ584PYQWG]]> <[#embed [hash 672GWGHN051H61FH2YRCWQW8DG]]>
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;[[Transposed diminished cube]]
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:First discovered in the dual of the [[D4.16]]. Dual is the [[digon-unpinched square pyramid]] which has not yet been seen in any other polytopes.
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:<[#embed [hash HF0Q2WHG19WTTHZBWT5Z4SDCH9]]> <[#embed [hash TAEHA64N5E8JR4Y8X3S5E65NNX]]>

Latest revision as of 01:34, 15 March 2016

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). It also appears in the dual of the J92 rhombochoron and so far it is the most commonly appearing polytope in this list. Self-dual and chiral.
(image)
Hexagonal cupolawedge
First discovered in the dual of the bilunabirotunda pseudopyramid and appeared later in the tetraaugmented J92 rhombochoron. Dual is the hexagonal pyrawedge which has not yet been seen in any other polytopes. Not chiral.
(image) (image)
Square cupolawedge
First discovered in the dual of the triangular hebesphenorotunda pseudopyramid and appeared later at the same position in the tetraaugmented J92 rhombochoron. Dual is the pentagonal cupolawedge which has not yet been seen in any other polytopes. Not chiral.
(image) (image)
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.
(image) (image)
Metabigyrotriangulated cube
First discovered in the dual of the D4.7. Self-dual and chiral.
(image)
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.
(image)
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.)
(image) (image)
Biunpinched cube
First discovered in the dual of the J92 rhombochoron and appeared shortly after at the same position in the tetraaugmented J92 rhombochoron. Dual is the parabiorthotriangulated orthopinched triangular cupola which has not yet been seen in any other polytopes. Not chiral.
(image) (image)
Digon-unpinched pentagonal prism
First discovered in the dual of the tetraaugmented J92 rhombochoron. Dual is the snub disphenoid, which makes it the first discovered non-CRF to be both the dual of a CRF, and the cell of a dual of a CRF, at the same time.
(image) (image)
Square transcupolawedge
First discovered in the dual of the tetraaugmented J92 rhombochoron. Dual is the pentagonal transcupolawedge which has not yet been seen in any other polytopes. This pair is very similar to the square cupolawedge and pentagonal cupolawedge described above, with the only difference that a pair of edges is swapped.
(image) (image)
Transposed diminished cube
First discovered in the dual of the D4.16. Dual is the digon-unpinched square pyramid which has not yet been seen in any other polytopes.
(image) (image)

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