Tetrahedron (EntityTopic, 18)
From Hi.gher. Space
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| notation=1<sup>2</sup> x<sup>yz</sup> | | notation=1<sup>2</sup> x<sup>yz</sup> | ||
| index=9 | | index=9 | ||
| + | }}{{STS Polytope | ||
| + | | flayout={{FLD|a3|end|e3}} | ||
| + | | petrie=4,1 | ||
| + | | dual=''Self-dual'' | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>3 | 2 3 or | 2 2 2</nowiki> | | wythoff=<nowiki>3 | 2 3 or | 2 2 2</nowiki> | ||
| schlaefli={[[Triangle|3,]]3} or sr{2,2} | | schlaefli={[[Triangle|3,]]3} or sr{2,2} | ||
| conway=Y3 | | conway=Y3 | ||
| - | |||
| vfigure=Equilateral [[triangle]], edge 1 | | vfigure=Equilateral [[triangle]], edge 1 | ||
| bowers=Tet | | bowers=Tet | ||
| kana=ﾃ | | kana=ﾃ | ||
| - | |||
}}}} | }}}} | ||
Revision as of 10:53, 1 November 2009
A tetrahedron is a special case of a pyramid where the base is a triangle.
Equations
- Variables:
l ⇒ length of edges of tetrahedron
- All points (x, y, z) that lie on the surface of a tetrahedron will satisfy the following equations:
Unknown
- All points (x, y, z) that lie on the edges of a tetrahedron will satisfy the following equations:
Unknown
- The hypervolumes of a tetrahedron are given by:
total edge length = 6l
surface area = sqrt(3)l2
volume = 12-1sqrt(2)l3
- The perpendicular height h of a tetrahedron is given by:
h = 3-1sqrt(6)l
- The planar cross-sections (n) of a tetrahedron are:
Unknown
Use
Tetrahedral cells are found in these tetrashapes on FGwiki:
- Hexacosichoron (600×, 100%)
- Hexadecachoron (8×, 100%)
- Pentachoron (5×, 100%)
- Square dipyramid (4×, 67%)
- Pentachoric hemicate (5×, 50%)
| 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 |
