Greater Self-Dual Solids

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Self-Dual Tetracontahedron #6 (canonical)
Vertices:  40  (4[3] + 12[3] + 12[4] + 12[5])
Faces:40  (4 equilateral triangles + 12 acute triangles
    + 12 kites + 12 irregular pentagons)
Edges:78  (6 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
(values below based on edge-scribed radius = 1)
Edge 1 (12):  sqrt(root[11th-order polynomial])    ≈0.39641590158440770607
Edge 2 (12):  sqrt(root[11th-order polynomial])    ≈0.51725027433782932337
Edge 3 (24):  sqrt(root[11th-order polynomial])    ≈0.5721824132810306965499
Edge 4 (12):  sqrt(root[11th-order polynomial])    ≈0.58540186661096130894
Edge 5 (12):  sqrt(root[11th-order polynomial])    ≈0.693016786034452313846
Edge 6 (6):  sqrt(root[11th-order polynomial])    ≈0.86878329773107530433
Max Vertex Radius:  sqrt(root[11th-order polynomial])    ≈1.0902734081890287757
Edge-scribed Radius:  1
Volume:root[11th-order polynomial]    ≈3.9519976689184320507