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| − | {{Shape |
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| − | |image = Куб.jpeg |
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| − | |schlafli symbol = <math>\{4,3\}</math> |
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| − | |dimensionality = 3 |
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| − | |0d hypervolume = <math>8</math> |
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| − | |1d hypervolume = <math>12l</math> |
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| − | |2d hypervolume = <math>6l^2</math> |
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| − | |3d hypervolume = <math>l^3</math> |
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| − | |0d subfacets = 8 [[Point|points]] |
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| − | |1d subfacets = 12 [[Line Segment|line segments]] |
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| − | |2d subfacets = 6 [[Square|squares]] |
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| − | |3d subfacets = 1 cube |
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| − | }} |
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| − | [[File:Куб.jpeg|thumb|right]] |
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| − | It has the [[Schläfli symbol]] |
+ | It has the [[Schläfli symbol]] , meaning that it is made of [[Square|squares]], three of which meet at each [[vertex]]. It can also be represented by the [[Schläfli symbol|Schläfli symbols]] <math>{ \{ \} }^{ 3 }</math> as it is the product of three [[Ditelon|line segments]], <math>\{ 4\} \times \{ \} </math> as it is the product of a [[square]] and a [[Ditelon|line segment]] (in other words, a [[square]]-based [[List of Prism Polyhedra|prism]]) and <math>t\{ 2,4\}</math> as it is a truncated Square Hosohedron. |
==Structure and sections=== |
==Structure and sections=== |
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* [[edge length]] = <math>12l</math> |
* [[edge length]] = <math>12l</math> |
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* [[surface area]] = <math>6l^2</math> |
* [[surface area]] = <math>6l^2</math> |
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| − | * |
+ | *[[surcell volume]] = <math>l^3</math> |
=== Subfacets === |
=== Subfacets === |
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[[Category:Polyhedra]] |
[[Category:Polyhedra]] |
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[[Category:Regular polyhedra]] |
[[Category:Regular polyhedra]] |
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| + | [[Category:What the wiki once used to be]] |
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Latest revision as of 10:51, 8 February 2021
A cube is the 3-dimensional hypercube. It is also the only platonic solid that can perfectly tessellate space by itself in a honeycomb.
It has the Schläfli symbol , meaning that it is made of squares, three of which meet at each vertex. It can also be represented by the Schläfli symbols as it is the product of three line segments, as it is the product of a square and a line segment (in other words, a square-based prism) and as it is a truncated Square Hosohedron.
Structure and sections=
The cube is composed of many squares stack on each other. It is composed of two parallel squares linked by a ring of four squares. Three squares join at each corner.
When viewed from a square face, it appears as a constant sized square. When viewed from an edge, it looks like a line expanding to a rectangle and back. Finally, when viewed from a corner, it is a point that expands into an equilateral triangle, then truncates to various hexagons, then goes back to a triangle (oriented the other way) which then shrinks.
Hypervolumes
Subfacets
- 8 points (0D)
- 12 line segments (1D)
- 6 squares (2D)
See Also
| Zeroth | First | Second | Third | Fourth | Fifth | Sixth | Seventh | Eighth | Ninth | Tenth | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Simplex | Point | Line | Triangle | Tetrahedron | Pentachoron | Hexateron | Heptapeton | Octaexon | Enneazetton | Decayotton | Hendecaxennon |
| Hypercube | Point | Line | Square | Cube | Tesseract | Penteract | Hexeract | Hepteract | Octeract | Enneract | Dekeract |
| Cross | Point | Line | Square | Octahedron | Hexadecachoron | Pentarss | Hexarss | Heptarss | Octarss | Ennearss | Decarss |
| Hypersphere | Point | Line | Circle | Sphere | Glome | Hyperglome | Hexaphere | Heptaphere | Octaphere | Enneaphere | Decaphere |