Tetrahedron (EntityTopic, 18)
From Hi.gher. Space
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*The [[planar]] [[cross-section]]s (''n'') of a tetrahedron are: | *The [[planar]] [[cross-section]]s (''n'') of a tetrahedron are: | ||
<blockquote>''Unknown''</blockquote> | <blockquote>''Unknown''</blockquote> | ||
- | + | ||
+ | == Use == | ||
+ | Tetrahedral cells are found in these tetrashapes on FGwiki: | ||
+ | *[[Hexacosichoron]] (600×, 100%) | ||
+ | *[[Hexadecachoron]] (8×, 100%) | ||
+ | *[[Pentachoron]] (5×, 100%) | ||
+ | *[[Square dipyramid]] (4×, 67%) | ||
+ | |||
{{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 11:30, 22 September 2007
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%)
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 |