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Hexagonal prism

 

 
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Hexagonal prism
 
 
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In geometry
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....
, the hexagonal prism is a prism
Prism (geometry)

In geometry, an n-sided prism is a polyhedron made of an n-sided polygon base, a Translation copy, and n faces joining corresponding sides....
 with hexagon
Hexagon

In geometry, a hexagon is a polygon with six edges and six Vertex . A regular hexagon has Schl?fli symbol ....
al base.

It is an octahedron
Octahedron

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 wikt:vertex....
. However, the term octahedron is mainly used with "regular" in front or implied, hence not meaning a hexagonal prism; in the general meaning the term octahedron it is not much used because there are different types which have not much in common except having the same number of faces.

If faces are all regular, the hexagonal prism is a semiregular polyhedron
Semiregular polyhedron

A semiregular polyhedron is a polyhedron with regular polygon faces and a symmetry group which is transitive on its vertices. Or at least, that is what follows from Thorold Gosset's 1900 definition of the more general semiregular polytope....
.






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In geometry
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....
, the hexagonal prism is a prism
Prism (geometry)

In geometry, an n-sided prism is a polyhedron made of an n-sided polygon base, a Translation copy, and n faces joining corresponding sides....
 with hexagon
Hexagon

In geometry, a hexagon is a polygon with six edges and six Vertex . A regular hexagon has Schl?fli symbol ....
al base.

It is an octahedron
Octahedron

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 wikt:vertex....
. However, the term octahedron is mainly used with "regular" in front or implied, hence not meaning a hexagonal prism; in the general meaning the term octahedron it is not much used because there are different types which have not much in common except having the same number of faces.

If faces are all regular, the hexagonal prism is a semiregular polyhedron
Semiregular polyhedron

A semiregular polyhedron is a polyhedron with regular polygon faces and a symmetry group which is transitive on its vertices. Or at least, that is what follows from Thorold Gosset's 1900 definition of the more general semiregular polytope....
. This is the fourth in an infinite set of prisms formed by square sides and two regular polygon caps. The shape has eight faces, 18 edges, and 12 vertices. It can also be formed by truncating a hexagonal hosohedron
Hosohedron

An Polygon hosohedron is a tessellation of Lune s on a spherical surface, such that each lune shares the same two vertices. A regular n-gonal hosohedron has Schl?fli symbol ....
.

As in most prisms, the volume is found by taking the area of the base, with a side length of , and multiplying it by the height .

Other images



A transparent model

See also

  • Set of prisms
    Prism (geometry)

    In geometry, an n-sided prism is a polyhedron made of an n-sided polygon base, a Translation copy, and n faces joining corresponding sides....
  • Triangular prism
    Triangular prism

    In geometry, a triangular prism or three-sided prism is a type of Prism ; it is a polyhedron made of a triangle base, a Translation copy, and 3 faces joining corresponding sides....
  • Cube
    Cube

    A cube is a three-dimensional space solid object bounded by six square faces, facets or sides, with three meeting at each wikt:vertex. The cube can also be called a Regular polyhedron hexahedron and is one of the five Platonic solids....
     Square-capped prism
  • Pentagonal prism
    Pentagonal prism

    In geometry, the pentagonal prism is a Prism with a pentagonal base. It is a type of heptahedron.If faces are all regular, the pentagonal prism is a semiregular polyhedron, and the third in an infinite set of prisms formed by square sides and two regular polygon caps....
  • Hexagonal prismatic honeycomb
    Hexagonal prismatic honeycomb

    The hexagonal prismatic honeycomb is a space-filling tessellation in Euclidean 3-space made up of hexagonal prism.It is constructed from a hexagonal tiling extruded into prisms....
  • Triangular-hexagonal prismatic honeycomb
    Triangular-hexagonal prismatic honeycomb

    The triangular-hexagonal prismatic honeycomb is a space-filling tessellation in Euclidean 3-space. It is comprised of hexagonal prisms and triangular prisms in a ratio of 1:2....
  • Snub triangular-hexagonal prismatic honeycomb
    Snub triangular-hexagonal prismatic honeycomb

    The Snub triangular-hexagonal prismatic honeycomb is a space-filling tessellation in Euclidean 3-space. It is comprised of hexagonal prisms and triangular prisms in a ratio of 1:8....
  • Rhombitriangular-hexagonal prismatic honeycomb
    Rhombitriangular-hexagonal prismatic honeycomb

    The rhombitriangular-hexagonal prismatic honeycomb is a space-filling tessellation in Euclidean 3-space. It is comprised of hexagonal prisms, cubes, and triangular prisms in a ratio of 1:3:2....


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