Triangular diprism (EntityTopic, 16)
From Hi.gher. Space
A triangular diprism is a special case of the prism where the base is a triangular prism. It is also a duoprism with parameters of 3 and 4.
Equations
- Variables:
l ⇒ length of each line in the triangular diprism
- The hypervolumes of a triangular diprism are given by:
total edge length = 24l
total surface area = (15 + 2√3) · l2
surcell volume = (3 + 2√3) · l3
bulk = √3∕2 · l4
- The realmic cross-sections (n) of a triangular diprism are:
[!x,!y] ⇒ cuboid with a various size
[!z,!w] ⇒ triangular prism
Net
The net of a triangular diprism is three cubes with four triangular prisms attached to the middle cube:
No image
Projection
The parallel projection of a triangular diprism is the following:
Incidence matrix
Dual: (dual of triangular diprism)
# | TXID | Va | Ea | Eb | 3a | 4a | 4b | C1a | C2a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | ||||||||
1 | Ea | 2 | = digon | ; blue | |||||||
2 | Eb | 2 | = digon | ; black | |||||||
3 | 3a | 3 | 3 | 0 | = triangle | ; joins 2 triangular prisms | |||||
4 | 4a | 4 | 0 | 4 | = square | ; joins 2 cubes | |||||
5 | 4b | 4 | 2 | 2 | = square | ; joins triangular prism to cube | |||||
6 | C1a | 6 | 6 | 3 | 2 | 0 | 3 | = base of prism: triangular prism | ; | ||
7 | C2a | 8 | 4 | 8 | 0 | 2 | 4 | = cube | ; | ||
8 | H4.1a | 12 | 12 | 12 | 4 | 3 | 12 | 4 | 3 | = triangular diprism | ; |
Usage as facets
- prism: 6× 1-facets of a triangular triprism
Notable Tetrashapes | |
Regular: | pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |
Powertopes: | triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |
Circular: | glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder |
Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
20. 211 Cyltrianglinder | 21. 1111 Triangular diprism | 22. 22 Dicone |
List of tapertopes |