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The volume, as for all prisms, is the product of the area of the pentagonal base times the height or distance along any edge perpendicular to the base. For a uniform pentagonal prism with edges h the formula is
Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids. [2] Like many basic geometric terms, the word prism (from Greek πρίσμα (prisma) 'something sawed') was first used in Euclid's Elements. Euclid defined the term in Book XI as “a solid figure ...
In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected by an alternating band of 2n triangles. They are represented by the Conway notation An . Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron.
In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams . It is a special case of a right prism with a pentagram as base, which in general has rectangular non-base faces. Topologically it is the same as a convex pentagonal prism .
The volume of a symmetric bipyramid is , where B is the area of the base and h the height from the base plane to any apex. In the case of a regular n {\displaystyle n} - sided polygon with side length s {\displaystyle s} and whose altitude is h {\displaystyle h} , the volume of such bipyramid is: n 6 h s 2 cot π n . {\displaystyle {\frac ...
Dodecahedral prism. In geometry, a dodecahedral prism is a convex uniform 4-polytope. This 4-polytope has 14 polyhedral cells: 2 dodecahedra connected by 12 pentagonal prisms. It has 54 faces: 30 squares and 24 pentagons. It has 80 edges and 40 vertices. It can be constructed by creating two coinciding dodecahedra in 3-space, and translating ...
In geometry, a pentahedron ( pl.: pentahedra) is a polyhedron with five faces or sides. There are no face-transitive polyhedra with five sides and there are two distinct topological types. With regular polygon faces, the two topological forms are the square pyramid and triangular prism . The square pyramid can be seen as a triangular prism ...
An biaugmented pentagonal prism with edge length has a surface area, calculated by adding the area of four equilateral triangles, four squares, and two regular pentagons: [2] Its volume can be obtained by slicing it into a regular pentagonal prism and an equilateral square pyramid, and adding their volume subsequently: [2] The dihedral angle of ...