# Triangulated triangular prism (EntityTopic, 13)

### From Hi.gher. Space

The **triangulated triangular prism** is one of the non-CRF facets of CRF duals currently being studied by Keiji.

Here is a projection based off its appearance in a projection of the trixylodiminished hydrochoron:

It has chiral biaxial symmetry C_{2}, as can be envisioned by imagining rotating the figure around a line between the midpoints of the leftmost and rightmost edge in the above projection.

When constructed using three edge lengths, *a*, *b* and *c* from shortest to longest, it has two kites *aabb*, two isosceles triangles *abb* and two isosceles triangles *bbc*. If *a* = *b* (turning the kites into squares) then the two *bbc* triangles become coplanar and form a square; if the edge between them is removed a non-uniform triangular prism results.

## Incidence matrix

Dual: *Self-dual*

# | TXID | Va | Vb | Vc | Ea | Eb | Ec | Ed | Ee | Ef | 3a | 3b | 4a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | Va | = point | ; | ||||||||||||

1 | Vb | = point | ; | ||||||||||||

2 | Vc | = point | ; | ||||||||||||

3 | Ea | 2 | 0 | 0 | = digon | ; | |||||||||

4 | Eb | 1 | 0 | 1 | = digon | ; | |||||||||

5 | Ec | 0 | 1 | 1 | = digon | ; | |||||||||

6 | Ed | 1 | 0 | 1 | = digon | ; | |||||||||

7 | Ee | 1 | 1 | 0 | = digon | ; | |||||||||

8 | Ef | 0 | 2 | 0 | = digon | ; | |||||||||

9 | 3a | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | = triangle | ; | |||

10 | 3b | 2 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | = triangle | ; | |||

11 | 4a | 1 | 2 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | = square | ; | |||

12 | C1a | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | = triangulated triangular prism |
; |

## Usage as facets

- 72× 1-facets of a trixylodiminished hydrochoron
- 16× 1-facets of a (dual of 4D analog of J37)
- 32× 1-facets of a (dual of 4D analog of J37)
- 12× 1-facets of a (dual of triangular hebesphenorotundaeic rhombochoron)