pentachoron

{{Infobox polychoron | Name=5-cell(4-simplex) | Image_File=5-cell.gif | Image_Caption=A 3D orthogonal projection of a 5-cell performing a simple rotation | Type=Convex regular 4-polytope | Family=Simplex | Last= | Index=1 | Next=2 | Schläfli={3,3,3} | CD= | Cell_List=5 {3,3} 20px | Face_List= 10 {3} 20px | Edge_Count= 10 | Vertex_Count= 5 | Petrie_Polygon=pentagon | Coxeter_Group= A4, [3,3,3] | Vertex_Figure=80px|class=skin-invert(tetrahedron) | Dual=Self-dual | Property_List=convex, isogonal, isotoxal, isohedral, projectively unique }}

In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, hypertetrahedron, pentachoron, pentatope, pentahedroid, tetrahedral pyramid, or 4-simplex (Coxeter's \alpha_4 polytope), the simplest possible convex 4-polytope, and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions. The 5-cell is a 4-dimensional pyramid with a tetrahedral base and four tetrahedral sides.