Triangular prism (EntityTopic, 20)
From Hi.gher. Space
The triangular prism is the prism whose base is a triangle. If the sides are squares, it is a uniform polyhedron.
Coordinates
The coordinates of a triangular prism of side 2 are:
(±1, -√3/3, ±1)
(0, 2√3/3, ±1)
Equations
- Variables:
l ⇒ length of edges of triangular prism
- The hypervolumes of a triangular prism are given by:
total edge length = 9l
surface area = (3 + √3∕2) · l2
volume = √3∕4 · l3
- The planar cross-sections (n) of a triangular prism are:
[!x,!y] ⇒ square [!z] ⇒ triangle
Incidence matrix
Dual: triangular bipyramid
# | TXID | Va | Ea | Eb | 4a | 3a | Type | Name |
---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | |||||
1 | Ea | 2 | = digon | ; | ||||
2 | Eb | 2 | = digon | ; | ||||
3 | 4a | 4 | 2 | 2 | = square | ; | ||
4 | 3a | 3 | 0 | 3 | = base of prism: triangle | ; | ||
5 | C1a | 6 | 3 | 6 | 3 | 2 | = triangular prism | ; |
Usage as facets
- 6× 1-facets of a duotrianglinder
- 8× 1-facets of a octahedral prism
- 4× 1-facets of a tetrahedral prism
- prism: 4× 1-facets of a triangular diprism
- 18× 1-facets of a (dual of triangular octagoltriate) (named squashed prisms)
- 6× 1-facets of a triangular octagoltriate (named prisms)
- 4× 1-facets of a square pyramid prism
- 4× 1-facets of a gyrated octahedral prism (named in-out)
- 4× 1-facets of a gyrated octahedral prism (named walls)
- 8× 1-facets of a K4.13 dual
- 2× 1-facets of a K4.8
- 2× 1-facets of a bilunabirotunda pseudopyramid
- 1× 1-facets of a D4.16
- 4× 1-facets of a bitrigonal diminished pyrocantichoron
- 16× 1-facets of a (4D analog of J37)
- 8× 1-facets of a (4D analog of J37)
- 8× 1-facets of a (4D analog of J37)
- 3× 1-facets of a triangular hebesphenorotunda pseudopyramid (named square to roof)
- 6× 1-facets of a triangular hebesphenorotundaeic rhombochoron
- 6× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named oooogg)
- 12× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named square to roof)
- 6× 1-facets of a D4.7
- 12× 2-facets of a triangular triprism
Notable Trishapes | |
Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
Snubs: | snub staurohedron • snub rhodohedron |
Curved: | sphere • torus • cylinder • cone • frustum • crind |
9. [11]1 Square pyramid | 10. 111 Triangular prism | 11. 12 Tetrahedron |
List of tapertopes |