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The spherical distance between two points P and Q on a sphere is the distance of the shortest path along the surface of the sphere (paths that cut through the interior of the ...

A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...

The radical circle of the Stammler circles has center at the nine-point center N, which is Kimberling center X_5. The radius is given by R_S = sqrt(R^2+ON^2) (1) = ...

The Stammler triangle is the triangle formed by the centers of the Stammler circles. It is an equilateral triangle. It circumscribes the circumcircle and homothetic to the ...

A tetrahedral ring is a term given in this work to a set of n regular tetrahedra joined face-to-face sharing a common edge (with internal conjoined faces removed). These ...

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 ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

The (not necessarily regular) tetrahedron of least volume circumscribed around a convex body B with volume V is not known. If B is a parallelepiped, then the smallest-volume ...

The third Morley triangle is made by rotating line BC toward vertex A about vertex B by angle (B+4pi)/3. It is an equilateral triangle. It has trilinear vertex matrix [1 ...