This version of an expanded truncated icosahedron was made in a similar fashion to the one two posts ago — but with the augmentation-by-prisms step altered by using prisms of somewhat greater height, with the goal being to make the rectangular faces closer to “squareness.”

As a result, this polyhedron is closer than the others to being a near-miss to the Johnson Solids — a category of polyhedra which has been discussed on this blog before. “Near-misses” are almost Johnson solids, and must therefore have faces which are regular (as the hexagon and pentagons here are) are nearly-regular (as the rectangles and triangles come close to being).

Is this a near-miss, or is it not? That’s difficult to answer, for that set of polyhedra has no precise definition, and cannot have one — it only has a “fuzzy” definition.

In my opinion, it isn’t quite a near-miss, for the triangles are too non-equilateral to qualify, to my eye — but others might disagree. In the unlikely event that mathematicians wish to start talking about “near-near-misses,” I offer this as a member of that set.

(Software credit: see http://www.software3d.com/stella.php for a free trial download of the software used to make these polyhedral images.)

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