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.
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”)