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The elongated pentagonal orthobicupola is a convex equilateral solid that is Johnson solid J_(38). The unit elongated pentagonal orthobicupola has volume ...

The elongated pentagonal orthobirotunda is a convex equilateral orthobirotunda having regular pentagonal upper and lower rotundas arranged symmetrically with respect to each ...

The elongated triangular gyrobicupola is a convex equilateral solid that is Johnson solid J_(36). The unit elongated triangular gyrobicupola has volume ...

The elongated triangular orthobicupola is a convex equilateral solid that is Johnson solid J_(35). The unit longated triangular orthobicupola has volume ...

The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore ...

The gyrate bidiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(82). The unit gyrate bidiminished rhombicosidodecahedron has volume ...

The gyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating one of the pentagonal cupolas of a small rhombicosidodecahedron by 1/10 of a turn. It is ...

If p_1, ..., p_n are positive numbers which sum to 1 and f is a real continuous function that is convex, then f(sum_(i=1)^np_ix_i)<=sum_(i=1)^np_if(x_i). (1) If f is concave, ...

The metabiaugmented dodecahedron is a convex equilateral solid that is Johnson solid J_(60). The unit metabiaugmented dodecahedron has volume V=1/6(25+11sqrt(5)) (1) and Dehn ...

The metabiaugmented hexagonal prism is a convex equilateral solid that is Johnson solid J_(56). The metabiaugmented hexagonal prism has volume V=1/6(2sqrt(2)+9sqrt(3)) (1) ...