Trixylodiminished hydrochoron (EntityTopic, 10)

From Hi.gher. Space

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.


One cell highlighted:


Two cells highlighted, sharing a single vertex:


Incidence matrix

Dual: bixylodiminished hydrochoron

0 Va = point ;
1 Ea 2 = digon ;
2 Eb 2 = digon ;
3 Ec 2 = digon ;
4 4a 4310 = square ;
5 3a 3111 = triangle ;
6 C1a 653224 = triangulated triangular prism ;
7 H4.1a 487272487214472 = trixylodiminished hydrochoron ;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.

Software models