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The deltoidal icositetrahedron is the 24-faced dual polyhedron of the small rhombicuboctahedron A_6 and Wenninger dual W_(13). It is also called the trapezoidal ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...

Let M be a compact n-dimensional manifold with injectivity radius inj(M). Then Vol(M)>=(c_ninj(M))/pi, with equality iff M is isometric to the standard round sphere S^n with ...

A random number generator produced by iterating X_(n+1)=|100lnX_n (mod 1)| for a seed X_0=0.1. This simple generator passes the noise sphere test for randomness by showing no ...

The real projective plane with elliptic metric where the distance between two points P and Q is defined as the radian angle between the projection of the points on the ...

The interior of a set is the union of all its open subsets. More informally, the interior of geometric structure is that portion of a region lying "inside" a specified ...

A set which is connected but not simply connected is called multiply connected. A space is n-multiply connected if it is (n-1)-connected and if every map from the n-sphere ...

A spherical polyhedron is set of arcs on the surface of a sphere corresponding to the projections of the edges of a polyhedron. The images above illustrate the spherical ...