Pentachoron
In geometry a Pentachoron is an object in four-dimensional (4D) space. It is a regular polytope and a 4-simplex. It is also called hyperpyramid, 5-cell or pentatope. It has 5 points, 10 edges, 10 faces, and 5 cells. Cells are the four dimensional equivalent of faces. Just like how a face is a 2d shape on a 3d shape, a cell is a 3d shape on a 4d one.
Each cell in the pentachoron is a tetrahedron.
Each of the pentachoron's points are connected to every other point in it.
The Dual polytope of the pentachoron is itself.
The biggest 3d view of the pentachoron is a triangular prism.
Pentachoron Media
5-cell vertex figure.
Grünbaum's rotationally symmetrical 5-set Venn diagram, 1975
A 3D projection of a 5-cell performing a double rotation.
Vertex-first perspective projection of the pentachoron into 3D. The nearest vertex to the 4D viewpoint is shown, projecting to the center of the image.
Edge-first projection of the pentachoron (5-cell) into 3D, with nearest edge shown.
Face-first projection of the 5-cell into 3D, with nearest face highlighted.
Cell-first projection of the 5-cell into 3D, hidden cells culled.
A 3-cube dissected into six 3-orthoschemes. Three are left-handed and three are right handed. A left and a right meet at each square face.
5-simplex vertex figure
Simply rotating in X-Y plane
Simply rotating in Z-W plane
Double rotating in X-Y and Z-W planes with angular velocities in a 4:3 ratio
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