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The square-triangle theorem states that any nonnegative integer can be represented as the sum of a square, an even square, and a triangular number (Sun 2005), i.e., ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

The common perpendicular to two opposite edges of a tetrahedron.

A line segment joining the midpoints of opposite sides of a quadrilateral or tetrahedron. Varignon's theorem states that the bimedians of a quadrilateral bisect each other ...

The four medians of a tetrahedron concur in a point which divides each tetrahedron median in the ratio 1:3, the longer segment being on the side of the vertex of the ...

A line making equal angles with the edges of a trihedron is called an isoclinal line of the trihedron.

A plane making equal angles with the three edges of a trihedron.

The Kepler-Poinsot polyhedra are four regular polyhedra which, unlike the Platonic solids, contain intersecting facial planes. In addition, two of the four Kepler-Poinsot ...

The four planes determined by the four altitudes of a tetrahedron and the orthocenters of the corresponding faces pass through the Monge point of the tetrahedron.

The 30-faced dual of the truncated dodecadodecahedron and Wenninger dual W_(98).