IBM Ponder This #190 · February 2014

If you juxtapose a regular hexagon to an equilateral triangle (where all the edges of both polygons are of the same unit length) on a common edge - you get a polygon with five vertices; five edges; and one face.

If you juxtapose a four-dimensional pyramid whose base is a right triangular prism to a four-dimensional pyramid whose base is a tetrahedron (again: all the edges of both polychora are of the same unit length) on a common tetrahedron - how many vertices, edges, faces, and cells would the resulting polychoron have?

Update 2/12: Hint: you may use Euler's formula to check your answer.

Solution

Best opened after a real attempt

To be added.