Geodesic Cubes

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Geodesic Cube Pattern 4 [2,2]
Vertices:  50  (8[3] + 6[4] + 12[4] + 24[4])
Faces:48  ({24 * 2} tri-equiangular kites)
Edges:96  (24 short + 48 medium + 24 long)
Symmetry:  Full Octahedral  (Oh)
(values below based on edge-scribed radius = 1)
Short Edge (24):  sqrt(root[576*(x^4)−12176*(x^3)    
    +57065*(x^2)−15296*x+1024])    
≈0.40644910357261897543
Medium Edge (48):  sqrt(root[(x^4)−54*(x^3)    
    +129*(x^2)−88*x+16])    
≈0.53917692400575247373
Long Edge (24):  sqrt(root[16*(x^4)−1608*(x^3)    
    +10073*(x^2)−4880*x+576])    
≈0.57088359480145441227
Edge-scribed Radius:  1
Volume:sqrt(root[12*(x^4)−95132*(x^3)    
    +165179027*(x^2)    
    −52653101056*x    
    +819200000000])    
≈4.0489004117868520143