The inclination of each triangular face of the pyramid versus the cube face is arctan(), approximately 26.565° . One edge of the isosceles triangles has length a, the other two have length , which follows by applying the Pythagorean theorem to height and base length. This yields an altitude of in the triangle (). Its area is , and the internal angles are arccos() (approximately 48.1897°) and the complementary 180° − 2 arccos() (approximately 83.6206°). The volume of the pyramid is ; so the total volume of the six pyramids and the cube in the hexahedron is . Kleetope It can be seen as a cube with square pyramids covering each square face; that is, it is the Kleetope of the cube. Cubic pyramid It is very similar to the 3D net for a 4D cubic pyramid, as the net for a square based is a square with triangles attached to each edge, the net for a cubic pyramid is a cube with square pyramids attached to each face. Related polyhedra and tilings It is a polyhedra in a sequence defined by the face configuration V4.6.2n. This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and continuing into the hyperbolic plane for any n ≥ 7. With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors. Each face on these domains also corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex. See also Disdyakis triacontahedron Disdyakis dodecahedron Kisrhombille tiling Compound of three octahedra Deltoidal icositetrahedron, another 24-face Catalan solid. References (Section 3-9) (The thirteen semiregular convex polyhedra and their duals, Page 14, Tetrakishexahedron) The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, page 284, Tetrakis hexahedron) External links Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra VRML model Conway Notation for Polyhedra Try: "dtO" or "kC" Tetrakis Hexahedron – Interactive Polyhedron model The Uniform Polyhedra Catalan solids