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Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are decagons.

Decagonal Antiprism

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are decagons.

Decagonal Antiprism

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are dodecagons.

Dodecagonal Antiprism

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are dodecagons.

Dodecagonal Antiprism

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Heptagonal/Septagonal Antiprism

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by…

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Heptagonal/Septagonal Antiprism

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by…

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Hexagonal Antiprism

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Hexagonal Antiprism

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Nonagonal Antiprism

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Nonagonal Antiprism

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Octagonal Antiprism

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Octagonal Antiprism

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Skewed Heptagonal/Septagonal Antiprism

Illustration of a skewed (non-right) heptagonal, or sometimes known as a septagonal antiprism. An antiprism…

Illustration of a skewed (non-right) hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Skewed Hexagonal Antiprism

Illustration of a skewed (non-right) hexagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a skewed (non-right) nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Skewed Nonagonal Antiprism

Illustration of a skewed (non-right) nonagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a skewed (non-right) octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Skewed Octagonal Antiprism

Illustration of a skewed (non-right) octagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a skewed (non-right) pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Skewed Pentagonal Antiprism

Illustration of a skewed (non-right) pentagonal antiprism. An antiprism is formed by having two parallel…

Pattern that can be cut out and folded to construct a regular dodecahedron. Fold on the dotted lines, and keep the edges in contact by the glued strips of paper.

Pattern for Dodecahedron

Pattern that can be cut out and folded to construct a regular dodecahedron. Fold on the dotted lines,…

Illustration of a regular dodecahedron. A regular dodecahedron is a polyhedron with twelve equal pentagonal faces.

Regular Dodecahedron

Illustration of a regular dodecahedron. A regular dodecahedron is a polyhedron with twelve equal pentagonal…

Pattern that can be cut out and folded to construct a regular hexahedron. Fold on the dotted lines, and keep the edges in contact by the glued strips of paper.

Pattern for Hexahedron

Pattern that can be cut out and folded to construct a regular hexahedron. Fold on the dotted lines,…

Illustration of an icosahedron.

Icosahedron

Illustration of an icosahedron.

Illustration of the bottom part of an icosahedron. The base consists of a regular pyramid, upon which equilateral triangles are inserted to form the next section of the icosahedron.

Part of an Icosahedron

Illustration of the bottom part of an icosahedron. The base consists of a regular pyramid, upon which…

Illustration of the steps to a construction of an icosahedron. The base consists of a regular pyramid, upon which equilateral triangles are inserted to form the next section of the icosahedron, followed by another pyramid.

Partial Construction of an Icosahedron

Illustration of the steps to a construction of an icosahedron. The base consists of a regular pyramid,…

Pattern that can be cut out and folded to construct a regular icosahedron. Fold on the dotted lines, and keep the edges in contact by the glued strips of paper.

Pattern for Icosahedron

Pattern that can be cut out and folded to construct a regular icosahedron. Fold on the dotted lines,…

Pattern that can be cut out and folded to construct a regular octahedron. Fold on the dotted lines, and keep the edges in contact by the glued strips of paper.

Pattern for Octahedron

Pattern that can be cut out and folded to construct a regular octahedron. Fold on the dotted lines,…

Illustration of a regular octahedron. A polyhedron with eight equal faces.

Regular Octahedron

Illustration of a regular octahedron. A polyhedron with eight equal faces.

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

Illustration of regular polyhedrons: tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron.

Regular Polyhedrons

Illustration of regular polyhedrons: tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron.

Two similar polyhedrons may be decomposed into the same number of tetrahedrons similar, each to each, and similarly placed.

Similar Polyhedrons

Two similar polyhedrons may be decomposed into the same number of tetrahedrons similar, each to each,…

Diagram used to prove the theorem: "Two similar polyhedrons may be decomposed into the same number of tetrahedrons, similar each to each , and similarly placed."

Two Similar Polyhedrons

Diagram used to prove the theorem: "Two similar polyhedrons may be decomposed into the same number of…

Illustration of a right decagonal prism with regular decagons for bases and rectangular faces.

Decagonal Prism

Illustration of a right decagonal prism with regular decagons for bases and rectangular faces.

Illustration of a right decagonal prism with regular decagons for bases and rectangular faces. The prism is resting on its side, one of the faces.

Decagonal Prism Resting On Its Side

Illustration of a right decagonal prism with regular decagons for bases and rectangular faces. The prism…

Illustration of a hollow right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular faces.

Heptagonal/Septagonal Prism

Illustration of a hollow right heptagonal/septagonal prism with regular heptagons/septagons for bases…

Illustration of a regular right heptagonal/septagonal prism with regular heptagons/septagons for bases and square faces. The hidden edges are shown.

Heptagonal/Septagonal Prism

Illustration of a regular right heptagonal/septagonal prism with regular heptagons/septagons for bases…

Illustration of a right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular faces. The hidden edges are shown.

Heptagonal/Septagonal Prism

Illustration of a right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular…

Illustration of a right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular faces.

Heptagonal/Septagonal Prism

Illustration of a right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular…

Illustration of a right hexagonal prism.

Hexagonal Prism

Illustration of a right hexagonal prism.

Illustration of a right hexagonal prism with hidden edges shown.

Hexagonal Prism

Illustration of a right hexagonal prism with hidden edges shown.

Illustration of a right hexagonal prism with a height less than the length of the edge of the hexagon.

Hexagonal Prism

Illustration of a right hexagonal prism with a height less than the length of the edge of the hexagon.

Illustration of a right hexagonal prism with a height greater than the length of the edge of the hexagon.

Hexagonal Prism

Illustration of a right hexagonal prism with a height greater than the length of the edge of the hexagon.

Illustration of a right hexagonal prism with hexagons for bases and square faces.

Hexagonal Prism

Illustration of a right hexagonal prism with hexagons for bases and square faces.

Illustration of a right hexagonal prism with hexagons for bases and square faces. The hidden edges are shown.

Hexagonal Prism

Illustration of a right hexagonal prism with hexagons for bases and square faces. The hidden edges are…

Illustration of a right hexagonal prism with hexagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the hexagon. The hidden edges are shown.

Hexagonal Prism

Illustration of a right hexagonal prism with hexagons for bases and rectangular faces. The height of…

Illustration of a right nonagonal prism with regular nonagons for bases and rectangular faces. The hidden edges are shown.

Nonagonal Prism

Illustration of a right nonagonal prism with regular nonagons for bases and rectangular faces. The hidden…

Illustration of a right nonagonal prism with regular nonagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the nonagon. The hidden edges are shown.

Nonagonal Prism

Illustration of a right nonagonal prism with regular nonagons for bases and rectangular faces. The height…

Illustration of a right octagonal prism with regular octagons for bases and rectangular faces. The hidden edges are shown.

Octagonal Prism

Illustration of a right octagonal prism with regular octagons for bases and rectangular faces. The hidden…

Illustration of a right octagonal prism with regular octagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the octagon. The hidden edges are shown.

Octagonal Prism

Illustration of a right octagonal prism with regular octagons for bases and rectangular faces. The height…

Illustration of a right octagonal prism with octagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the octagon.

Octagonal Prism

Illustration of a right octagonal prism with octagons for bases and rectangular faces. The height of…

Illustration of a right octagonal prism, with octagons for bases and rectangular faces, that is resting on its side (an edge). The height of the prism is greater than the length of a side of the octagon.

Octagonal Prism Resting On Side

Illustration of a right octagonal prism, with octagons for bases and rectangular faces, that is resting…

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the pentagon. The hidden edges are shown.

Pentagonal Prism

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The…

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The height of the prism is slightly greater than the length of a side of the pentagon. The hidden edges are shown.

Pentagonal Prism

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The…

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The height of the prism is slightly greater than the length of a side of the pentagon.

Pentagonal Prism

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The…

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the pentagon.

Pentagonal Prism

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The…

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of the smaller prism is one half that of the larger.

2 Octagonal Prisms

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of…