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A number of attractive 12-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

The Wells graph, sometimes also called the Armanios-Wells graph, is a quintic graph on 32 nodes and 80 edges that is the unique distance-regular graph with intersection array ...

The Doro graph is a distance-transitive and Distance-Regular Graph on 68 vertices and with valency 12. It is the unique automorphic graph having intersection array ...

The Egawa graph with parameters (p,s) is a distance-regular but not distance-transitive graph on 16^p4^s nodes. These graphs generalize the Doob graphs and give (s,4)-Hamming ...

An asymptotic direction at a point p of a regular surface M in R^3 is a direction in which the normal curvature of M vanishes. 1. There are no asymptotic directions at an ...

Let p be an odd prime and F_n the cyclotomic field of p^(n+1)th roots of unity over the rational field. Now let p^(e(n)) be the power of p which divides the class number h_n ...

A ruled surface is called a generalized cone if it can be parameterized by x(u,v)=p+vy(u), where p is a fixed point which can be regarded as the vertex of the cone. A ...

Let each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces. Call the resulting polyhedron the local cell. Then the local density is ...

Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...