Greater Self-Dual Solids

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

Self-Dual Icosioctahedron #3 (canonical)
Vertices:  28  (4[3] + 12[3] + 12[5])
Faces:28  (4 equilateral triangles + 12 isosceles triangles
    + 12 mirror-symmetric pentagons)
Edges:54  (4 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
(values below based on edge-scribed radius = 1)
Edge 1 (12):  2*sqrt(6*(cbrt(12*(27099+5725*sqrt(69)))    
    −cbrt(12*(5725*sqrt(69)−27099))−33))/15    
≈0.28965916191148478684
Edge 2 (12):  2*sqrt(6*(1175    
    −cbrt(4*(958374475+183294741*sqrt(69)))    
    +cbrt(4*(183294741*sqrt(69)−958374475))))/147    
≈0.61245753461283559803
Edge 3 (12):  2*sqrt(3*(86−cbrt(4*(17611+1425*sqrt(69)))    
    −cbrt(4*(17611−1425*sqrt(69)))))/15    
≈0.67337585517609205726
Edge 4 (18):  2*sqrt(6*(cbrt(4*(11+3*sqrt(69)))    
    −cbrt(4*(3*sqrt(69)−11))−1))/3    
≈1.0570925484406993277
Max Vertex Radius:  sqrt(3*(1+2*cbrt(4*(11+3*sqrt(69)))    
    −2*cbrt(4*(3*sqrt(69)−11))))/3    
≈1.1310884863670980997
Edge-scribed Radius:  1
Volume:root[3rd-order polynomial]    ≈3.7946854281952148493