Midpoint Augmentation
Midpoint augmentation, a term introduced here, is a variant of conventional augmentation in which each facial polygon is replaced by a triangular polygon joining vertices with the neighboring edge midpoints, and then constructing a pyramid with the base determined by the face's midpoints. Midpoint augmentation allows compounds of Archimedean solids and Archimedean duals to be easily constructed.
Archimedean solid dual face 1 face 2
cuboctahedron rhombic dodecahedron 3: 1/4sqrt(6) 4: 1/2sqrt(2)
icosidodecahedron rhombic triacontahedron 3: [画像:1/4sqrt(1/5(sqrt(7-3sqrt(5))))] 5: 1/4sqrt(1/5(5+2sqrt(5)))
small rhombicuboctahedron deltoidal icositetrahedron 3: 1/(42)sqrt(3)(3-sqrt(2)) 4: 1/2(sqrt(2)-1)
truncated cube small triakis octahedron 3: 1/6sqrt(3)(3-2sqrt(2)) 8: 1/2(1+sqrt(2))
truncated dodecahedron triakis icosahedron 3:
1/(372)sqrt(3)(1+5sqrt(5)) 10: 1/2sqrt(1/2(5+sqrt(5)))
truncated icosahedron pentakis dodecahedron 5: 1/(38)sqrt(1/(10)(305+131sqrt(5))) 6: 1/4sqrt(3)(sqrt(5)-3)
truncated octahedron tetrakis hexahedron 4:
1/8sqrt(2) 6: 1/4sqrt(6)
truncated tetrahedron triakis tetrahedron 3:
1/(30)sqrt(6) 6: 1/2sqrt(6)
See also
Archimedean Dual, Archimedean Solid, AugmentationExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Midpoint Augmentation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MidpointAugmentation.html