Geometry Working Group

Rhombidodecahedron,
an augmented cube, the neglected polyhedron:

Derivation of r.d. from the cube

Why are pairs of faces coplanar? I.e., why do the triangles actually form rhombi?

Determine dimensions (lengths of edges, face diagonals, "space diagonals") of the cube and then of the r.d.

Determine volume of the r.d. and relate to the cube

What polygons are the intersections of the r.d. and planes?

Which Platonic solids can be inscribed in the r.d.?

What is the dual of the r.d.?

(Advanced) One can fill space with r.d.’s. Then the intersection with a plane will give a tiling of the plane, a la Philip’s course. What tilings arise this way?