5-simplex

5-simplex
Hexateron (hix)
Type uniform 5-polytope
Schläfli symbol {34}
Coxeter diagram
4-faces 6 6 {3,3,3}
Cells 15 15 {3,3}
Faces 20 20 {3}
Edges 15
Vertices 6
Vertex figure
5-cell
Coxeter group A5, [34], order 720
Dual self-dual
Base point (0,0,0,0,0,1)
Circumradius 0.645497
Properties convex, isogonal regular, self-dual

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets. It has a dihedral angle of cos−1(1/5), or approximately 78.46°.

The 5-simplex is a solution to the problem: Make 20 equilateral triangles using 15 matchsticks, where each side of every triangle is exactly one matchstick.