Derived Solids

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Tetrated Dodecahedron (canonical)
canonical form
Vertices:  28  (12[4] + 12[4] + 4[3])
Faces:28  (16 equilateral triangles + 12 mirror-symmetric pentagons)
Edges:54  (12 short + 42 long)
Symmetry:  Full Tetrahedral  (Td)
(values below based on edge-scribed radius = 1)
Short Edge (12):  sqrt(root[45369*(x^3)
   −170048*(x^2)+83200*x
   −8192])    
≈0.65057327723178783037
Long Edge (42):  sqrt(root[9*(x^3)−128*(x^2)
   +336*x−128])    
≈0.67707678700483726367
Edge-scribed Radius:  1
Volume:root[51759*(x^3)+1085112*(x^2)
   +3042816*x−29452288]    
≈3.7539533822341399411


References:[1]Jim McNeill: Tetrated Dodecahedron discovered
independently by Alex Doskey and Robert Austin