Derived Solids

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6-Truncated Joined Truncated Tetrahedron
(canonical)
version 1
Vertices:  40  (4[3] + 36[3])
Faces:22  (12 mirror-symmetric pentagons + 4 regular hexagons
    + 6 bi-mirror-symmetric hexagons)
Edges:60  (12 short + 24 medium + 24 long)
Symmetry:  Full Tetrahedral  (Td)
(values below based on regular hexagon origin distance = sqrt(3))
Short Edge (12):  sqrt(root[33282*(x^3)−291489*(x^2)    
    +271784*x−51984])    
≈0.87584400573467397137
Medium Edge (24):  sqrt(root[18*(x^3)−609*(x^2)+1268*x−676])    ≈0.99540603829271099818
Long Edge (24):  sqrt(root[(x^3)−80*(x^2)+1104*x−1152])    ≈1.0656454119579876699
Edge-scribed Radius:  root[(x^3)+9*(x^2)+6*x−54]    ≈1.9625748668573976054
Volume:root[129*(x^3)−249336*(x^2)    
    +20950592*x−393872896]    
≈27.986830309852392838