Tetrahedron (EntityTopic, 18)
From Hi.gher. Space
(Difference between revisions)
m (→Use) |
m |
||
| Line 1: | Line 1: | ||
| - | {{Shape | + | {{STS Shape |
| - | + | ||
| name=Tetrahedron | | name=Tetrahedron | ||
| image=http://img123.imageshack.us/img123/704/tetrahedron5jf.png | | image=http://img123.imageshack.us/img123/704/tetrahedron5jf.png | ||
| Line 6: | Line 5: | ||
| elements=4, 6, 4 | | elements=4, 6, 4 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc=xPP or {G3<sup>3</sup>} | | ssc=xPP or {G3<sup>3</sup>} | ||
| - | |||
| pv_circle=~0.1225 | | pv_circle=~0.1225 | ||
| pv_square=⅓ | | pv_square=⅓ | ||
| + | | extra={{STS Rotope | ||
| + | | attrib=pure | ||
| + | | index=9 | ||
| + | }}{{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} | ||
| Line 18: | Line 19: | ||
| kana=ﾃ | | kana=ﾃ | ||
| dual=''Self-dual'' | | dual=''Self-dual'' | ||
| - | }} | + | }}}} |
| + | |||
A '''tetrahedron''' is a special case of a [[pyramid]] where the base is a [[triangle]]. | A '''tetrahedron''' is a special case of a [[pyramid]] where the base is a [[triangle]]. | ||
Revision as of 09:08, 14 March 2008
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 |
