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The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron.
It is also called the 5-cell, since it consists of five vertices, or pentachoron.
The pentatope is the four-dimensional simplex, and can
be viewed as a regular tetrahedron 
in which a point 
along the fourth dimension through the center of 
is chosen so that 
. The pentatope has Schläfli
symbol 
.
It is one of the six regular polychora.
The skeleton of the pentatope is isomorphic to the complete graph 
,
known as the pentatope graph.
The pentatope is self-dual, has five three-dimensional facets (each the shape of a tetrahedron), 10 ridges (faces), 10 edges, and five vertices. In the above figure, the pentatope is shown projected onto one of the four mutually perpendicular three-spaces within the four-space obtained by dropping one of the four vertex components (R. Towle).
." Disc. Math. 186, 69-94, 1998.Cvetković,
D. M.; Doob, M.; and Sachs, H.