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Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...

A 4-sphere has positive curvature, with R^2=x^2+y^2+z^2+w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)+2w=0. (2) Since r=xx^^+yy^^+zz^^ (3) dw = -(xdx+ydy+zdz)/w (4) = ...

The surface of revolution obtained by cutting a conical "wedge" with vertex at the center of a sphere out of the sphere. It is therefore a cone plus a spherical cap, and is a ...

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 ...

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 ...

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 ...