Trixylodiminished hydrochoron (EntityTopic, 10)
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| elements=72, 216, 192, 48 | | elements=72, 216, 192, 48 | ||
| extra={{STS Polytope | | extra={{STS Polytope | ||
| + | | dual=[[Bixylodiminished hydrochoron]] | ||
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The '''trixylodiminished hydrochoron''', abbreviated '''TrXD''', is a polychoron obtained by removing the vertices of three of the five inscribed [[xylochora]] from a [[hydrochoron]]. Removing the vertices of only one yields the [[snub demitesseract]], and removing the vertices of two yields the [[bixylodiminished hydrochoron]] (BXD), a [[CRF]] polychoron. Surprisingly, it is precisely the dual of the BXD, and is the only known case where removing a fraction of the vertices of a polytope forms its dual. Being the dual of the BXD, it exists in two chiral forms, and is both cell- and vertex-transitive; its 72 cells are [[triangulated triangular prism]]s. | The '''trixylodiminished hydrochoron''', abbreviated '''TrXD''', is a polychoron obtained by removing the vertices of three of the five inscribed [[xylochora]] from a [[hydrochoron]]. Removing the vertices of only one yields the [[snub demitesseract]], and removing the vertices of two yields the [[bixylodiminished hydrochoron]] (BXD), a [[CRF]] polychoron. Surprisingly, it is precisely the dual of the BXD, and is the only known case where removing a fraction of the vertices of a polytope forms its dual. Being the dual of the BXD, it exists in two chiral forms, and is both cell- and vertex-transitive; its 72 cells are [[triangulated triangular prism]]s. | ||
Latest revision as of 15:04, 12 March 2016
The trixylodiminished hydrochoron, abbreviated TrXD, is a polychoron obtained by removing the vertices of three of the five inscribed xylochora from a hydrochoron. Removing the vertices of only one yields the snub demitesseract, and removing the vertices of two yields the bixylodiminished hydrochoron (BXD), a CRF polychoron. Surprisingly, it is precisely the dual of the BXD, and is the only known case where removing a fraction of the vertices of a polytope forms its dual. Being the dual of the BXD, it exists in two chiral forms, and is both cell- and vertex-transitive; its 72 cells are triangulated triangular prisms.
Projections
One cell highlighted:
Two cells highlighted, sharing a single vertex:
Incidence matrix
Dual: bixylodiminished hydrochoron
| # | TXID | Va | Ea | Eb | Ec | 4a | 3a | C1a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||||
| 1 | Ea | 2 | = digon | ; | ||||||
| 2 | Eb | 2 | = digon | ; | ||||||
| 3 | Ec | 2 | = digon | ; | ||||||
| 4 | 4a | 4 | 3 | 1 | 0 | = square | ; | |||
| 5 | 3a | 3 | 1 | 1 | 1 | = triangle | ; | |||
| 6 | C1a | 6 | 5 | 3 | 2 | 2 | 4 | = triangulated triangular prism | ; | |
| 7 | H4.1a | 48 | 72 | 72 | 48 | 72 | 144 | 72 | = trixylodiminished hydrochoron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
