Tetrahedron (EntityTopic, 18)
From Hi.gher. Space
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| - | {{Shape|Tetrahedron|http://img123.imageshack.us/img123/704/tetrahedron5jf.png|3|4, 6, 4|0|{[[Triangle|3,]]3} or sr{2,2}|<nowiki>3 | 2 3 or | 2 2 2</nowiki>|[[Line (object)|E]][[Triangle|T]]T|N/A|Equilateral [[triangle]], edge 1|Tet|''Self-dual''|9|N/A|N/A|pure}} | + | {{Shape|Tetrahedron|http://img123.imageshack.us/img123/704/tetrahedron5jf.png|3|4, 6, 4|0|{[[Triangle|3,]]3} or sr{2,2}|<nowiki>3 | 2 3 or | 2 2 2</nowiki>|[[Line (object)|E]][[Triangle|T]]T|N/A|Equilateral [[triangle]], edge 1|Tet|''Self-dual''|9|N/A|N/A|pure|~0.1225|⅓}} |
== Geometry == | == Geometry == | ||
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 14:44, 16 September 2007
Geometry
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
| 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 |
