# 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.

## 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 |
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## Usage as facets

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