The Mobius configuration consists of two of these figures mutually inscribed, the projection of one 
The Mobius configuration consists of two of these figures mutually inscribed, the projection of one of which onto the plane gives a complete 4-graph. They have volume equal to one-sixth of a vector triple product, and, when one of these shapes is inscribed in the non-adjacent vertices of a unit (*) cube, it has volume one-third. Regular ones have volume equal to side- length-cubed over 6 times the square root of 2, and surface area root-three times side-length-squared. For ten points, identify this 3-dimensional figure whose regular variety is the simplest Platonic solid, consisting of 4 triangular faces.
The Mobius configuration consists of two of these figures mutually inscribed, the projection of one of which onto the plane gives a complete 4-graph.
regular {tetrahedron} (prompt on “triangular pyramid”)