
 Crossed Pentagonal Cuploid 
Cuploids are similar to cupolae, but the n/dgon at the top must have an
even value for d. This means that the base is a 2n/dgon, but
since the top and bottom are both even now, we get two coincident
n/(d/2)gons instead. Each coincident edge meets a triangle for one of
the polygons, and a square for the other, meaning a total of four faces meet at
these edges. Polyhedronists generally don't like polyhedra with more than two
faces at an edge. By removing the two coincident base polygons and letting the
triangles connect to the squares instead we get back to a more acceptable
twofaceperedge model.
The model presented here is a 5/4 cuploid. It's upsidedown in this
photo with respect to the description above (the 5/4gon is at the
bottom instead of the top). A 5/4gon is a retrograde pentagon,
ie a normal pentagon, but we visit the vertices in the opposite order. The
base would be a 10/4gon, which is two coincident 5/2gons.
These coincident base pentagrams have been removed as described above, but you
can see the outline still there, now with triangles meeting squares at these
edges instead.
