Cube (EntityTopic, 20)
From Hi.gher. Space
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| image=http://img112.imageshack.us/img112/7352/cube7ty.png | | image=http://img112.imageshack.us/img112/7352/cube7ty.png | ||
| dim=3 | | dim=3 | ||
| elements=6, 12, 18 | | elements=6, 12, 18 | ||
| genus=0 | | genus=0 | ||
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| ssc=[xyz], [x<sup>3</sup>] or {G4<sup>3</sup>} | | ssc=[xyz], [x<sup>3</sup>] or {G4<sup>3</sup>} | ||
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| pv_circle=≈0.3676 | | pv_circle=≈0.3676 | ||
| pv_square=1 | | pv_square=1 | ||
| + | | extra={{STS Rotope | ||
| + | | attrib=pure | ||
| + | | notation=111 xyz | ||
| + | | index=5 | ||
| + | }}{{STS Bracketope | ||
| + | | index=5 | ||
| + | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>3 | 2 4, 2 4 | 2, or 2 2 2 |</nowiki> | | wythoff=<nowiki>3 | 2 4, 2 4 | 2, or 2 2 2 |</nowiki> | ||
| schlaefli={[[Square|4,]]3}, t{2,4} or tr{2,2} | | schlaefli={[[Square|4,]]3}, t{2,4} or tr{2,2} | ||
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| kana=ｷｭ | | kana=ｷｭ | ||
| dual=[[Octahedron]] | | dual=[[Octahedron]] | ||
| - | }} | + | }}}} |
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 08:14, 14 March 2008
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
Use
Cubic cells are found in these tetrashapes on FGwiki:
- Tesseract (8×, 100%)
- Cubinder (1×, 20%)
- Cubic pyramid (1×, 14%)
| 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 | ||
