In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells. It is also known as the pentachoron, pentatope, or hyperpyramid. It is a 4-simplex, the simplest possible convex regular 4-polytope (four-dimensional analogue of a polyhedron), and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions.
The regular 5-cell is bounded by regular tetrahedra, and is one of the six regular convex polych...
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In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells. It is also known as the pentachoron, pentatope, or hyperpyramid. It is a 4-simplex, the simplest possible convex regular 4-polytope (four-dimensional analogue of a polyhedron), and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions.
The regular 5-cell is bounded by regular tetrahedra, and is one of the six regular convex polychora, represented by Schläfli symbol {3,3,3}.
The 5-cell is self-dual, and its vertex figure is a tetrahedron. Its maximal intersection with 3-dimensional space is the triangular prism. Its dihedral angle is cos(1/4), or approximately 75.52°.
The 5-cell can be constructed from a tetrahedron by adding a 5th vertex such that it is equidistant from all the other vertices of the tetrahedron. (The 5-cell is essentially a 4-dimensional pyramid with a tetrahedral base.)
The Cartesian coordinates of the vertices of an origin-centered regular 5-cell...
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