Changes: Cube

Revision as of 15:30, 7 August 2018

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 ${ \{ \} }^{ 3 }$ as it is the product of three line segments, $\{ 4\} \times \{ \}$ as it is the product of a square and a line segment (in other words, a square-based prism) and $t\{ 2,4\}$ 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

vertex count = $8$
edge length = $12 l$
surface area = $6l^2$
volume = $l^3$

Subfacets

8 points (0D)
12 line segments (1D)
6 squares (2D)


	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

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-'''[[File:Куб.jpeg|thumb]]'''A '''Сube''' is the [[space|3-dimensional]] [[hypercube]]. It is also the only [[platonic solid]] that can perfectly tessellate [[space]] by itself in a [[honeycomb]].
+A '''cube''' is the [[space|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 [[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 [[truncation|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 [[square|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 [[hexagon|hexagons]], then goes back to a triangle (oriented the other way) which then shrinks.
 === Hypervolumes ===
-* vertex count = <math>8</math>
+* [[vertex count]] = <math>8</math>
-* edge length = <math>12l</math>
+* [[edge length]] = <math>12l</math>
-* surface area = <math>6{ l }^{ 2 }</math>
+* [[surface area]] = <math>6l^2</math>
-* volume = <math>{ l }^{ 3 }</math>
+* [[volume]] = <math>l^3</math>
-=== Hidden figures ===
+=== Subfacets ===
-*6 [[square]]s
+*8 [[Point|points]] (0D)
-*12 [[line]]s
+*12 [[Line Segment|line segments]] (1D)
-*8 [[point]]s
+*6 [[Square|squares]] (2D)
 === See Also ===
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 [[Category:List of 3rd dimension]]
 [[Category:Hypercube]]
-[[Category:Pages with broken file links]]
+[[Category:Rotatopes]]
+[[Category:Polyhedra]]
+[[Category:Regular polyhedra]]