Tetrahedron (EntityTopic, 18)
From Hi.gher. Space
(Difference between revisions)
m |
m |
||
| Line 61: | Line 61: | ||
*[[Pentachoric hemicate]] (5×, 50%) | *[[Pentachoric hemicate]] (5×, 50%) | ||
| + | {{Simplices}} | ||
{{Trishapes}} | {{Trishapes}} | ||
{{Rotope Nav|8|9|10|I'I<br>Triangular prism|<nowiki>I''</nowiki><br>Tetrahedron|(I'I)<br>Triangular torus|hedra}} | {{Rotope Nav|8|9|10|I'I<br>Triangular prism|<nowiki>I''</nowiki><br>Tetrahedron|(I'I)<br>Triangular torus|hedra}} | ||
[[Category:Regular polyhedra]] | [[Category:Regular polyhedra]] | ||
Revision as of 16:22, 21 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%)
| Simplices |
| triangle • tetrahedron • pyrochoron • pyroteron • pyropeton |
| 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 |
