Geodesic Cubes

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Geodesic Cube Pattern 5 [3,0]
Vertices:  56  (8[3] + 24[4] + 24[4])
Faces:54  (6 squares + 24 isosceles trapezoids + 24 kites)
Edges:108  (4 different lengths)
Symmetry:  Full Octahedral  (Oh)
(values below based on edge-scribed radius = 1)
Edge 1 (24):  sqrt(root[137288*(x^4)−3052860*(x^3)    
    +11742982*(x^2)−2439109*x+118098])    
≈0.37711709482093791581
Edge 2 (12):  sqrt(root[(x^4)−82*(x^3)    
    +528*(x^2)−384*x+64])    
≈0.49796048549336340816
Edge 3 (48):  sqrt(root[6728*(x^4)−164988*(x^3)    
    +566838*(x^2)−586845*x+118098])    
≈0.51282376974473566890
Edge 4 (24):  sqrt(root[841*(x^4)−3208*(x^3)    
    +1656*(x^2)−288*x+16])    
≈0.52768705399610792963
Edge-scribed Radius:  1
Volume:sqrt(root[10207763011681*(x^4)    
    −21990857255222048*(x^3)    
    +12098759338570264448*(x^2)    
    −1794252345306554615808*x    
    +26441159791106337181696])    
≈4.0647941303304973643