Cube (EntityTopic, 20)
From Hi.gher. Space
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Revision as of 09:57, 22 September 2007
Geometry
A cube is a special case of a prism where the base is a square.
Equations
- 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
Segmentation
The cube of side 2 may be segmented into:
- 6× square pyramid with base side 2 and height 1
- 12× irregular tetrahedron with sides 3×32-1, 2×2, 22-1
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 |
4. (xy) Circle | 5. [xyz] Cube | 6. [ Cuboid |
List of bracketopes |