Pentakis Rotundae

This family of polyhedra can be generated by taking a pentagonal rotunda, and augmenting the lateral pentagonal faces with pyramids.  The triangular complexes have the flexibility to allow n-gonal variants to be generated for values of n other than the original pentagon.  As with the rotunda and the cupolae, the opposite polygon will be a 2n-gon.  The family can also be generated from the truncated tetrahedron by replacing three of the hexagonal faceds with complexes of 6 coplanar triangles.

Star polyhedra of the form {n/d} can also be used as the capping polygon.  If d is even then an family of semi-rotundae, similar in nature to the semicupolae can be generated with a virtual {2n/d} base.

I have concentrated my examples to date around n=7, although an example for n=9 has also been generated.  This is the upper limit for this family for convex polygons, a regular form for n=11 cannot be generated as the distance between the {11} and {22} faces is too great to be spanned by the lateral faces.  

In the images and linked files below, the blue triangles are those present in the original rotunda, the green triangles are those from the pentagonal prisms.

Pentakis Rotundae
 Pentakis Semi-Rotundae

n=7
n=7/2 (virtual {7})

n=7/3
n=7/4 (virtual {7/2})

n=7/5
n=7/6 (virtual {7/3})
 
A variant can also be generated with the pyramids facing inwards (example for n=7)

 These polyhedra were generated using Great Stella, Antiprism and HEDRON.