## FANDOM

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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 $\{4,3\}$, 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=Edit

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 Edit

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