The Hebe-spheno-mega-coronas are a  family of locally convex polyhedra with cyclic symmetry. The polyhedra have parallel n/d and 2n/d faces and are thus related to the cupolas.  The hebe-spheno-mega-coronas are 5-uniform. Starting from the  n/d face (see left hand image of a 7/3 Hebe-spheno-mega-corona above) and running through to the 2n/d face (right hand image) the vertices are:

Type (A): n/d-3-3-3-3-3, Type (B): 3-3-3-3-3, Type (C): 4-3-3-3-3, Type (D): 3-3-3-3-3, Type (E): 2n/d-4-3-3

The only n-gonal convex member of this family is the Johnson Solid hebesphenomegacorona or the "Digonal Hebe-spheno-mega-corona" with n=2. If n=3 then in terms of convexity the resulting Triangular Hebe-spheno-mega-corona is the limiting case as it contains coplanar faces.  A regular and convex Diminished Triangular Hebe-spheno-mega-corona can be created by removing the pentagonal pyramids with Type(D) vertices at their apices and replacing them with pentagons, this Johnson Solid is more commonly known as the Hebesphenorotunda.

As was mentioned above, the family is locally convex in the range 2 <= n/d < 3. The local convexity is evident on this 7/3 hebe-spheno-mega-corona with only one rotation around the symmetry axis. In order for the hebe-spheno-mega-corona to exist then 2n/d must be coprime, this implies that d must be odd.  This means for d=3 the only locally convex members of the family are those with n/d=7/3 and n/d=8/3.

The solids have a number of internal vertices.  The type (C) vertices are not normally visible from the outside of the solid. 
7/3 8/3

Again in similar fashion to the cupolas a related family of what could be termed "hebe-spheno-mega-coronoids" exists where d is even. In these cases the 2n/d face becomes an n/(d/2) face which is circumscribed twice.  The face itself can thus be removed leaving a non-convex solid.   An example of this family is shown in the above images of the 5/2 Hebe-spheno-mega-coronoid which has a 'virtual' 5/1 face (right hand image).

A list of hebe-spheno-mega-coronoids generated to date is as follows:
5/2 9/4 11/4


Again there appear to be additional isomorphs to the hebe-spheno-mega-coronas and -coronoids.  These have not been classified but two examples of isomorphs to the 7/3 hebe-spheno-mega corona are isomorph1 and isomporph2.

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