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The augmented truncated dodecahedron is Johnson solid J_(68) constructed by affixing a pentagonal cupola to one of the decagonal faces of a truncated dodecahedron such that ...

Johnson solid J_(50).

A figurate number in which layers of polygons are drawn centered about a point instead of with the point at a polygon vertex.

The polyhedron compound consisting of the cuboctahedron and its dual, the rhombic dodecahedron, illustrated in the left figure above. The right figure shows the solid common ...

A diminished polyhedron is a polyhedron in which one or more groups of associated faces (such as those comprising the top of a pyramid or cupola in the case of a Johnson ...

A n-gonal cupola adjoined to a 2n-gonal prism.

A statement which is rigorously not true. Regular two-valued logic allows statements to be only true or false, but fuzzy logic treats "truth" as a continuum which can have a ...

Let G be a group and S be a set. Then S is called a left G-set if there exists a map phi:G×S->S such that phi(g_1,phi(g_2,s))=phi(g_1g_2,s) for all s in S and all g_1,g_2 in ...

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...

A polygonal number of the form n(5n-3)/2. The first few are 1, 7, 18, 34, 55, 81, 112, ... (OEIS A000566). The generating function for the heptagonal numbers is ...