Decahedron
Encyclopedia
In geometry
, a decahedron is a polyhedron
with 10
faces
. There are 32300 topologically
distinct decahedra and none are regular, so this name is ambiguous.
With regular faces:
With nonregular faces it can also be:
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a decahedron is a polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
with 10
10 (number)
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
faces
Face (geometry)
In geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube...
. There are 32300 topologically
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
distinct decahedra and none are regular, so this name is ambiguous.
With regular faces:
- Octagonal prismOctagonal prismIn geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :...
(uniform 8-prismPrism (geometry)In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...
) - Square antiprismSquare antiprismIn geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps...
(uniform 4-antiprismAntiprismIn geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles...
) - Square cupolaSquare cupolaIn geometry, the square cupola, sometimes called lesser dome, is one of the Johnson solids . It can be obtained as a slice of the rhombicuboctahedron...
(Johnson solidJohnson solidIn geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...
4) - Pentagonal dipyramidPentagonal dipyramidIn geometry, the pentagonal bipyramid is third of the infinite set of face-transitive bipyramids.Each bipyramid is the dual of a uniform prism.If the faces are equilateral triangles, it is a deltahedron and a Johnson solid...
(Johnson solid 13, 5-bipyramidBipyramidAn n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal pyramid and its mirror image base-to-base.The referenced n-gon in the name of the bipyramids is not an external face but an internal one, existing on the primary symmetry plane which connects the two pyramid halves.The...
) - Augmented pentagonal prismAugmented pentagonal prismIn geometry, the augmented pentagonal prism is one of the Johnson solids . As the name suggests, it can be constructed by augmenting a pentagonal prism by attaching a square pyramid to one of its equatorial faces....
(Johnson solid 52)
With nonregular faces it can also be:
- Pentagonal trapezohedronPentagonal trapezohedronThe pentagonal trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms. It has ten faces which are congruent kites....
(5-trapezohedronTrapezohedronThe n-gonal trapezohedron, antidipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism. Its 2n faces are congruent kites . The faces are symmetrically staggered.The n-gon part of the name does not reference the faces here but arrangement of vertices around an axis of symmetry...
, antiprism dual) — often used as a dieDiceA die is a small throwable object with multiple resting positions, used for generating random numbers...
in role playing games, known as d10 - EnneagonEnneagonIn geometry, a nonagon is a nine-sided polygon.The name "nonagon" is a prefix hybrid formation, from Latin , used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century...
al pyramid (9-pyramidPyramid (geometry)In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base....
)