Table 2.
Typical Welsh tetrahedra
| Points | Welsh high: 24 symmetries |
Welsh medial: 6 symmetries |
Welsh low: 4 symmetries |
|||
|---|---|---|---|---|---|---|
| Coordinates | Type | Coordinates | Type | Coordinates | Type | |
| Vertices | (3/4, 3/4, 3/4) | 23 | (0, 0, 0) | 0 | (0, 0, 0) | 0 |
| (3/4, 1/4, 1/4) | 23 | (3/4, 1/4, 1/4) | 23 | (−1/2, 1/2, 1/2) | 1 | |
| (1/4, 3/4, 1/4) | 23 | (1/4, 3/4, 1/4) | 23 | (1/4, 3/4, 1/4) | 23 | |
| (1/4, 1/4, 3/4) | 23 | (1/4, 1/4, 3/4) | 23 | (1/4, 1/4, 3/4) | 23 | |
| Node | (1/2, 1/2, 1/2) | 3 | (11/40, 11/40, 11/40) | 03 | (−2/48, 17/48, 17/48) | 130 |
Dodecahedral vocells have nuclei 23 and volume 14267/46080. Dodecatetrahedral ones have nuclei 0 or 1 and volume 8773/23040. Here 03 = (11/20)·0 + (9/20)·3 and 130 = (19/48)·1 + (15/48)·3 + (14/48)·0. Nodes are all points 2, 3, 02, 03, 12, 13, 021, 031, 120, or 130 with the above proportions.