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Net In geometry , the gyroelongated pentagonal cupola is one of the Johnson solids ( J 24 ). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola ( J 5 ) by attaching a decagonal antiprism to its base.
Net In geometry , the elongated pentagonal cupola is one of the Johnson solids ( J 20 ). As the name suggests, it can be constructed by elongating a pentagonal cupola ( J 5 ) by attaching a decagonal prism to its base.
Nonagonal prism: Enneagonal antiprism: Gyroelongated triangular bicupola: Elongated triangular orthobicupola: Elongated triangular gyrobicupola: rhombocuboctohedron 19 20 Dodecahedron: Pentagonal rotunda: Elongated square cupola: Gyroelongated square cupola: Pentagonal orthobicupola: Pentagonal gyrobicupola: Decagonal prism: Decagonal antiprism ...
This family overlaps with the first: when one of the two "factor" polygons is a square, the product is equivalent to a hyperprism whose base is a three-dimensional prism. The symmetry number of a duoprism whose factors are a p -gon and a q -gon (a " p,q -duoprism") is 4 pq if p ≠ q ; if the factors are both p -gons, the symmetry number is 8 p 2 .
Coxeter, Longuet-Higgins & Miller (1954) define uniform polyhedra to be vertex-transitive polyhedra with regular faces. They define a polyhedron to be a finite set of polygons such that each side of a polygon is a side of just one other polygon, such that no non-empty proper subset of the polygons has the same property.
In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids (J 38). [1] As the name suggests, it can be constructed by elongating a pentagonal orthobicupola ( J 30 ) by inserting a decagonal prism between its two congruent halves.
Triangular antiprismatic prism, Square antiprismatic prism, Pentagonal antiprismatic prism, Hexagonal antiprismatic prism, Heptagonal antiprismatic prism, Octagonal antiprismatic prism, Enneagonal antiprismatic prism, Decagonal antiprismatic prism
As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola (J 31) by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal cupolae ( J 5 ) through 36 degrees before inserting the prism yields an elongated pentagonal orthobicupola ( J 38 ).