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There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures), also known as Bakos' compound, ...

If perpendiculars A^', B^', and C^' are dropped on any line L from the vertices of a triangle DeltaABC, then the perpendiculars to the opposite sides from their perpendicular ...

The uniform polyhedra are polyhedra consisting of regular (possibly polygrammic) faces of equal edge length whose polyhedron vertices are all symmetrically equivalent. The ...

The point of concurrence of the joins of the vertices of a triangle and the points of contact of an inconic of the triangle (Veblen and Young 1938, p. 111; Eddy and Fritsch ...

Given a point P and a triangle DeltaABC, the Cevian triangle DeltaA^'B^'C^' is defined as the triangle composed of the endpoints of the cevians though the Cevian point P. A ...

The dodecadodecahedron is the uniform polyhedron with Maeder index 36 (Maeder 1997), Wenninger index 73 (Wenninger 1989), Coxeter index 45 (Coxeter et al. 1954), and Har'El ...

The Johnson triangle DeltaJ_AJ_BJ_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix ...

The triangle bounded by the polars of the vertices of a triangle DeltaABC with respect to a conic is called its polar triangle. The following table summarizes polar triangles ...

The snub dodecadodecahedron, not to be confused with the Archimdean snub dodecahedron, is the uniform polyhedron is the uniform polyhedron with Maeder index 40 (Maeder 1997), ...

A median A_1M_1 of a triangle DeltaA_1A_2A_3 is the Cevian from one of its vertices A_1 to the midpoint M_1 of the opposite side. The three medians of any triangle are ...