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Let a, b, and k be integers with k>=1. For j=0, 1, 2, let S_j=sum_(i=j (mod 3))(-1)^i(k; i)a^(k-i)b^i. Then 2(a^2+ab+b^2)^(2k)=(S_0-S_1)^4+(S_1-S_2)^4+(S_2-S_0)^4.

The gabled rhombohedra are a family of elongated gyrobifastigium that are space-filling. The equilateral elongated gyrobifastigium, illustrated above, is one such example.

The genesa is a mystical figure that correspond to a spherical cuboctahedron.

The dual of the uniform great rhombicosidodecahedron U_(67) and Wenninger dual W_(105).

The dual of the great truncated cuboctahedron U_(20) and Wenninger dual W_(93).

The dual of the great truncated icosidodecahedron U_(68) and Wenninger dual W_(108).

The dual of the great ditrigonal dodecicosidodecahedron U_(42) and Wenninger dual W_(81).

The dual of the great dodecicosidodecahedron U_(61) and Wenninger dual W_(99).

The dual of the great icosicosidodecahedron U_(48) and Wenninger dual W_(88).

The dual of the great snub icosidodecahedron U_(57) and Wenninger dual W_(113).