Cube (EntityTopic, 20)
From Hi.gher. Space
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| - | {{Shape|Cube|http://img112.imageshack.us/img112/7352/cube7ty.png|3|6, 12, 8|0|{[[Square|4,]]3}, t{2,4}, or tr{2,2}|<nowiki>3 | 2 4, 2 4 | 2, or 2 2 2 |</nowiki>|[[Line (object)|E]][[Square|E]]E|111 x,y,z|Equilateral [[triangle]], edge sqrt(2)|Cube|[[Octahedron]]}} | + | {{Shape|Cube|http://img112.imageshack.us/img112/7352/cube7ty.png|3|6, 12, 8|0|{[[Square|4,]]3}, t{2,4}, or tr{2,2}|<nowiki>3 | 2 4, 2 4 | 2, or 2 2 2 |</nowiki>|[[Line (object)|E]][[Square|E]]E|111 x,y,z|Equilateral [[triangle]], edge sqrt(2)|Cube|[[Octahedron]]|5}} |
== Geometry == | == Geometry == | ||
A '''cube''' is a special case of a [[prism]] where the base is a [[square]]. | A '''cube''' is a special case of a [[prism]] where the base is a [[square]]. | ||
Revision as of 12:02, 17 June 2007
Geometry
A cube is a special case of a prism where the base is a square.
Equations
- Assumption: Cube is centered at the origin.
- Variables:
l ⇒ length of edges of the cube
- The hypervolumes of a cube are given by:
total edge length = 12l
surface area = 6l2
volume = l3
- The planar cross-sections (n) of a cube are:
[!x,!y,!z] ⇒ square with side length l
| 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 |
