In geometry, the pentachoron is a four-dimensional object bounded by 5 tetrahedral cells. It is also known as the 5-cell, 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 pentachoron is bounded by regular tetrahedra, and is one of the six regular convex polychora, represented by Schläfli symbol {3,3,3}.
The pentachoron is self-dual, and its vertex figure is a tetrahedron. Its maximal intersection with 3-dimensional space is the triangular prism.
The regular pentachoron is bounded by regular tetrahedra, and is one of the six regular convex polychora, represented by Schläfli symbol {3,3,3}.
The pentachoron is self-dual, and its vertex figure is a tetrahedron. Its maximal intersection with 3-dimensional space is the triangular prism.
A 3D projection of a 5-cell performing a double rotation about two orthogonal planes
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