Type (A): n/d-4-3-3-4, Type (B): 4-3-3-3-3, Type (C): 3-3-3-3, Type (D): 3-3-3-3-3, Type (E): n/d-3-3-3-3-3
The only n-gonal convex member of this family is the Johnson Solid sphenomegacorona or the "Digonal Spheno-mega-corona" with n=2. If n=3 then the resulting Triangular Spheno-mega-corona is clearly not convex.
Examination shows this family to be locally convex in the range 2 <= n/d < ~2.8. The local convexity is evident on this 7/3 spheno-mega-corona with only one rotation around the symmetry axis. The following models with only one rotation around the symmetry axis show that n/d=2.666 (8/3) is clearly convex, n/d=2.75 (11/4) appears to be marginally convex whilst n/d=2.8 (14/5) appears to contain coplanar faces. (Full 14/5). It must be stressed that the upper convexity limit has to date only been assessed from a visual examination of the VRML models and has not been explicitly determined.
Spheno-mega-coronas with d>1
and n<=12 for 2<n/d<3 are listed below. As with
the spheno-prisms, the solids have a number of internal vertices.
The type (B) vertices are not normally visible from the outside of the
Retrograde spheno-mega-coronas are also possible: for example this 7/4 spheno-mega-corona
Like the spheno-coronas, there are additional isomorphs to the spheno-mega-coronas, for example the above image is of a 7/3 spheno-mega-corona isomorph. These have not been classified, but a further 7/3 spheno-mega-corona isomorph is linked here:
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