Tetrahedron, Puzzle, Triangular Pyramid, Dissection, Four Pentahedra

cults3d

Dissecting a Regular Tetrahedron into Four Congruent Pentahedra The regular tetrahedron (a Platonic solid) can be dissected in multiple ways for a puzzle. In this project, a tetrahedron is sliced into four congruent pieces using two planes containing the midpoints of three edges (see figure below). Each piece is a pentahedron with two equilateral triangles, two right triangles, and a rhombus. You would need 4 copies for a tetrahedral puzzle. This can be used as a entry project to learn about 3D sketching, extruding at a taper angle, etc. The Dihedral angle of a regular tetrahedron is arccos (1/3). Of course, we can also make a tetrahedron by slicing a cube. Have fun!