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The augmented sphenocorona is Johnson solid J_(87), which is formed from augmentation of one of the square faces of the sphenocorona by an equilateral square pyramid. The ...

The augmented triangular prism is Johnson solid J_(49), which is formed from augmentation of one of the lateral faces of an equilateral triangular prism by an equilateral ...

The collapsoids are a class of non-convex collapsible polyhedra. They can be constructed by replacing each edge of a dodecahedron or icosahedron by the diagonal of a pyramid ...

For a quadrilateral which is not cyclic, Ptolemy's theorem becomes an inequality: AB×CD+BC×DA>AC×BD. The Ptolemy inequality is still valid when ABCD is a triangular pyramid ...

Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to ...

The vertex of an isosceles triangle having angle different from the two equal angles is called the apex of the isosceles triangle. The common polygon vertex at the top of a ...

The augmented tridiminished icosahedron is Johnson solid J_(64), which is formed from augmentation of the triangular face adjecent to all three hexagons of the tridiminished ...

The biaugmented pentagonal prism is Johnson solid J_(53), which is formed from double augmentation of two nonadjacent lateral faces of the equilateral pentagonal prism by an ...

A polyhedron that is dual to itself. For example, the tetrahedron is self-dual. Naturally, the skeleton of a self-dual polyhedron is a self-dual graph. Pyramids are ...

A triacontahedron is a 30-faced polyhedron. Examples include the 14-gonal antiprism, biaugmented truncated cube (Johnson solid J_(67)), 15-gonal dipyramid, 28-gonal prism, ...