Archimedean-Catalan Hulls

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Joined Truncated Icosahedron
Vertices:  92  (60[3] + 12[5] + 20[6])
Faces:90  (60 kites + 30 rhombi)
Edges:180  (60 short + 120 long)
Symmetry:  Full Icosahedral  (Ih)
Long Edge Angle:  acos(−(9+sqrt(5))/12)    ≈159.445557343 degrees
Short Edge Angle:  acos(−17/18)    ≈160.811863546 degrees
(values below based on unit-edge-length Truncated Icosahedron)
Short Edge (60):  (5*sqrt(7)+9*sqrt(35))/76    ≈0.87465098162130917547
Long Edge (120):  sqrt(2*(29−9*sqrt(5)))/4    ≈1.0532917569755953386
Rhombus Length:  3*(sqrt(5)−1)/2    ≈1.8541019662496845446
Rhombus Width:  1
Kite Length:  9*(2*sqrt(5)−1)/19    ≈1.6446959786840112913
Kite Width:  1
[3]-Vertex Radius (60):  sqrt(2*(29+9*sqrt(5)))/4    ≈2.4780186590676155376
[5]-Vertex Radius (12):  9*sqrt(65+22*sqrt(5))/38    ≈2.53092686862706152146
[6]-Vertex Radius (20):  3*sqrt(3)/2    ≈2.5980762113533159403
Inscribed Radius:  3*(1+sqrt(5))/4    ≈2.4270509831248422723
Volume:45*(46+3*sqrt(5))/38    ≈62.417609920065042343


References:[1]Conway Notation for Polyhedra (George Hart)