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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 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 ...

Define a valid "coloring" to occur when no two faces with a common edge share the same color. Given two colors, there is a single way to color an octahedron (Ball and Coxeter ...

The term "Aristotle gap"' is introduced in this work to refer to the angle between the first and last member of a 5-tetrahedral ring. This gap has angle measure theta = ...

Geometric objects lying in a common plane are said to be coplanar. Three noncollinear points determine a plane and so are trivially coplanar. Four points are coplanar iff the ...

A (general) dodecahedron is a polyhedron having 12 faces. Examples include the Bilinski dodecahedron, decagonal prism, elongated square dipyramid (Johnson solid J_(15)), ...