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A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux ...

The equilateral triaugmented triangular prism is the Johnson solid J_(51) constructed by erecting a regular tetrahedron on each square face of an equilateral triangular ...

The deltoidal hexecontahedron is the 60-faced dual polyhedron of the small rhombicosidodecahedron A_5. It is sometimes also called the trapezoidal hexecontahedron (Holden ...

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed. Similarly, the circumradius of a polyhedron is the radius of a ...

The triakis tetrahedral graph is Archimedean dual graph which is the skeleton of the triakis tetrahedron. It is implemented in the Wolfram Language as ...

A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...