Greater Self-Dual Solids

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Self-Dual Icosioctahedron #4 (canonical)
canonical form
Vertices:  28  (4[3] + 12[4] + 12[4])
Faces:28  (4 equilateral triangles + 12 kites + 12 isosceles trapezoids)
Edges:54  (4 different lengths)
Symmetry:  Full Tetrahedral  (Td)
(values below based on edge-scribed radius = 1)
Edge 1 (24):  (7*sqrt(34)−17*sqrt(2))/28    ≈0.599108310841945980946
Edge 2 (12):  2*sqrt(34)/17    ≈0.68599434057003534951
Edge 3 (6):  3*(7*sqrt(34)−17*sqrt(2))/68    ≈0.74007497221652150587
Edge 4 (12):  (sqrt(34)−3*sqrt(2))/2    ≈0.79415560386300766223
Max Vertex Radius:  sqrt(17−3*sqrt(17))/2    ≈1.0759511052026270341
Edge-scribed Radius:  1
Volume:8*(6783−920*sqrt(17))/6069    ≈3.9410022401473090053