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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 , 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

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
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