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 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid and length of the side of the pentagon (base) on the smaller pentagonal pyramid are one half that of the larger.

Similar Pentagonal Pyramids

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid…

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Pentagonal Pyramids

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent,…

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Rectangular Pyramids

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent,…

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 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 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 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 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 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 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 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 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 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 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) 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…

An illustration of an octahedral crystal. An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.

Octahedral Crystal

An illustration of an octahedral crystal. An octahedron is a polyhedron with eight faces. A regular…

The rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. It is an Archimedean dual solid, or a Catalan solid. Its dual is the cuboctahedron.

Rhombic Dodecahedron

The rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. It is an Archimedean dual solid,…

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…

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to each other as the products of the including edges."

Two Proportional Tetrahedrons

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to…

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 the bottom half of a regular dodecahedron. A regular dodecahedron is a polyhedron with twelve equal pentagonal faces.

Bottom Half of a Regular Dodecahedron

Illustration of a the bottom half of a regular dodecahedron. A regular dodecahedron is a polyhedron…

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…

Illustration of an inverted pentagonal pyramid. It is pyramid with a regular pentagon for its base.

Inverted Pentagonal Pyramid

Illustration of an inverted pentagonal pyramid. It is pyramid with a regular pentagon for its base.

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,…

Illustration of an icosahedron.

Icosahedron

Illustration of an icosahedron.