[jnncohyy] Partially truncated cube

Slice two opposing corners off a cube so that face diagonals become edges.  This leaves an octahedron with 2 equilateral triangular faces and 6 isosceles right triangular faces.  It is an antiprism.

Slice off only one corner, and you have three orthogonal square faces.  To make it more stable than lying on its equilateral triangle base, extend the base so that it becomes a hexagon and has triangular sides orthogonal to the base.  The resulting dome shape has 1 regular hexagon, 3 squares, and 6 triangles.