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The truncated tetrahedral graph is the cubic Archimedean graph on 12 nodes and 18 edges that is the skeleton of the truncated tetrahedron. It is implemented in the Wolfram ...

An Enriques surface X is a smooth compact complex surface having irregularity q(X)=0 and nontrivial canonical sheaf K_X such that K_X^2=O_X (Endraß). Such surfaces cannot be ...

The pentagonal hexecontahedron is the 60-faced dual polyhedron of the snub dodecahedron A_8 (Holden 1971, p. 55). It is Wenninger dual W_(18). A tetrahedron 10-compound, cube ...

A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...

A symbol consisting of three rational numbers that can be used to describe uniform polyhedra based on how a point C in a spherical triangle can be selected so as to trace the ...

A figurate number Te_n of the form Te_n = sum_(k=1)^(n)T_k (1) = 1/6n(n+1)(n+2) (2) = (n+2; 3), (3) where T_k is the kth triangular number and (n; m) is a binomial ...

A space-filling polyhedron is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...

The Steinmetz solid is the solid common to two (or three) right circular cylinders of equal radii intersecting at right angles is called the Steinmetz solid. Two cylinders ...