Virtual regular hole

Way way back, before there was a Mathematrec, on my other blog I posted about a book titled Adventures Among the Toroids: a study of Quasi-Convex, Aplanar, Tunneled Orientable Polyhedra of Positive Genus having Regular Faces with Disjoint Interiors, being an elaborate Description and Instructions for the Construction of an enormous number of new and fascinating Mathematical Models of interest to Students of Euclidean Geometry and Topology, both Secondary and Collegiate, to Designers, Engineers and Architects, to the Scientific Audience concerned with Molecular and other Structural Problems, and to Mathematicians, both professional and dilettante with hundreds of Exercises and Search Projects many completely outlined for Self-Instruction (Revised Second Edition), by B. M. Stewart, and I showed a picture of a paper model I’d made of one of Stewart’s toroidal polyhedra, designated Q32/S3S3. Today after much trial and even more error, I figured out how to draw that same polyhedron using the open source Antiprism software. The command is

off_align -F oct,0,0,0 oct | off_align -F J27,2,0,3 | \
off_util -D f19,8 | antiview

(which stacks and merges two octahedra, stacks them inside a triangular orthobicupola and subtracts them from it, removes the two additional coincident faces which off_align doesn’t, and then displays the result). If you don’t have Antiprism but you have something that’ll display OFF files, here it is: https://drive.google.com/open?id=1M_a474kL95XMdTl4qHHfH6AfCrm2Tnfw. And if you have neither, here’s a static image of it:And no, I am not planning on doing the same for J91/Z4 anytime soon. Feel free to take that on yourself.

 

 

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