5-cell

A Pentachoron (also 5 - Zeller, Pentatop or hyper- pyramid called ) is a 4 - simplex, the simplest Polychoron ( a four-dimensional figure). It consists of five tetrahedral cells and is the analog to the triangle (2- simplex) and the tetrahedron (3- simplex).

The regular Pentachoron is one of the six regular convex Polychora and is represented by the Schläfli symbol { 3,3,3 }. The Pentachoron is one of six Platonic solids in four -dimensional space.

Geometry

A Pentachoron consists of five cells, all of which are tetrahedral in shape. His Eckfigur is a tetrahedron. Its maximum intersection with the three-dimensional space is the triangular prism.

Pictures

Construction

A Pentachoron can be constructed by a fifth area is added to a tetrahedron, the same distance of the other corners, like the other corners to each other. ( Essentially a Pentachoron is a four-dimensional pyramid with a tetrahedron shaped base. )

Projections

A possible projection of Pentachorons is a pentagram within a pentagon.

Both the first corner and the cell - to-parallel projection of the first Pentachorons in three dimensions to have a tetrahedron- shaped envelope. The next and the most distant cell is projected onto the tetrahedron itself, while the other four cells are mapped to the four tetrahedral compressed regions surrounding the center.

The edge -first and face -first projection of the Pentachorons in three dimensions have a double triangular pyramid-shaped shell. Two of the cells are projected on the upper and lower halves of the double- pyramid while the remaining three three non- regular tetrahedron -shaped body about the central axis of the double pyramid with angles of 120 ° to each other.