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Pentagonal cupola information


Pentagonal cupola
TypeJohnson
J4J5J6
Faces5 triangles
5 squares
1 pentagon
1 decagon
Edges25
Vertices15
Vertex configuration10(3.4.10)
5(3.4.5.4)
Symmetry groupC5v, [5], (*55)
Rotation groupC5, [5]+, (55)
Dual polyhedron-
Propertiesconvex
Net
3D model a pentagonal cupola

In geometry, the pentagonal cupola is one of the Johnson solids (J5). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.

A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]

  1. ^ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.

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Pentagonal cupola

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geometry, the pentagonal cupola is one of the Johnson solids (J5). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists...

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Elongated pentagonal cupola

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solid can also be seen as an elongated pentagonal orthobicupola (J38) with its "lid" (another pentagonal cupola) removed. A Johnson solid is one of 92...

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Gyroelongated pentagonal cupola

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its base. It can also be seen as a gyroelongated pentagonal bicupola (J46) with one pentagonal cupola removed. A Johnson solid is one of 92 strictly convex...

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Pentagonal orthocupolarotunda

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the pentagonal orthocupolarotunda is one of the Johnson solids (J32). As the name suggests, it can be constructed by joining a pentagonal cupola (J5)...

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Johnson solid

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described as a gyroelongated pentagonal bipyramid. Augmented[+] indicates another polyhedron, namely a pyramid or cupola, is joined to one or more faces...

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Pentagonal gyrocupolarotunda

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In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids (J33). Like the pentagonal orthocupolarotunda (J32), it can be constructed by...

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Dodecahedron

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self-intersecting equilateral pentagonal faces. A tetartoid (also tetragonal pentagonal dodecahedron, pentagon-tritetrahedron, and tetrahedric pentagon dodecahedron)...

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Elongated pentagonal gyrocupolarotunda

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either the pentagonal cupola (J5) or the pentagonal rotunda (J6) through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda...

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Paragyrate diminished rhombicosidodecahedron

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a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and the opposing pentagonal cupola removed. A Johnson solid is one of...

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List of mathematical shapes

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rhombicosidodecahedron Pentagonal bipyramid Pentagonal cupola Pentagonal gyrobicupola Pentagonal gyrocupolarotunda Pentagonal orthobicupola Pentagonal orthobirotunda...

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Metagyrate diminished rhombicosidodecahedron

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rhombicosidodecahedron with one pentagonal cupola (J5) rotated through 36 degrees, and a non-opposing pentagonal cupola removed. (The cupolae cannot be...

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Diminished rhombicosidodecahedron

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(J76). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed. A Johnson solid is one of 92 strictly convex polyhedra that...

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Dodecahedral cupola

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dodecahedral cupola is a polychoron bounded by a rhombicosidodecahedron, a parallel dodecahedron, connected by 30 triangular prisms, 12 pentagonal prisms,...

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Bigyrate diminished rhombicosidodecahedron

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as a rhombicosidodecahedron with two pentagonal cupolae rotated through 36 degrees, and a third pentagonal cupola removed. (None of the cupolae can be...

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List of Johnson solids

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solids are the square pyramid, pentagonal pyramid, triangular cupola, square cupola, pentagonal cupola, and pentagonal rotunda. These solids may be applied...

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Augmented truncated dodecahedron

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solids (J68). As its name suggests, it is created by attaching a pentagonal cupola (J5) onto one decagonal face of a truncated dodecahedron. A Johnson...

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Pentagonal orthobicupola

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faces. A 36-degree rotation of one cupola before the joining yields a pentagonal gyrobicupola (J31). The pentagonal orthobicupola is the third in an infinite...

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J5

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after name changed to TVB Finance & Information Channel(無綫財經·資訊台) Pentagonal cupola, Johnson Solid number 5 and also: The Jackson 5, a Motown R&B/soul...

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Crossed pentagrammic cupola

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crossed pentagrammic cupola is one of the nonconvex Johnson solid isomorphs, being topologically identical to the convex pentagonal cupola. It can be obtained...

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Elongated pentagonal orthocupolarotunda

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elongated pentagonal orthocupolarotunda is one of the Johnson solids (J40). As the name suggests, it can be constructed by elongating a pentagonal orthocupolarotunda...

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Crossed pentagonal cuploid

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with a retrograde pentagonal base, so that the squares and triangles connect across the bases in the opposite way to the pentagonal cupola, hence intersecting...

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List of small polyhedra by vertex count

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bipyramid 6 Pentagonal pyramid Octahedron (regular) triangular antiprism square bipyramid Triangular prism wedge 7 Hexagonal pyramid Pentagonal bipyramid...

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J20

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protest the inauguration of Donald Trump in January 2017 Elongated pentagonal cupola, a Johnson solid (J20) January 20, 2005 counter-inaugural protest...

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Gyrate rhombicosidodecahedron

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squares, and 10 regular pentagons as its faces. The difference between those two polyhedrons is that one of two pentagonal cupolas from the gyrate rhombicosidodecahedron...

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Gyroelongated cupola

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cupola to an 2n-gonal antiprism. There are three gyroelongated cupolae that are Johnson solids made from regular triangles and square, and pentagons....

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Elongated cupola

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n-gonal cupola to an 2n-gonal prism. There are three elongated cupolae that are Johnson solids made from regular triangles and square, and pentagons. Higher...

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Parabiaugmented truncated dodecahedron

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solids (J69). As its name suggests, it is created by attaching two pentagonal cupolas (J5) onto two parallel decagonal faces of a truncated dodecahedron...

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Metabiaugmented truncated dodecahedron

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solids (J70). As its name suggests, it is created by attaching two pentagonal cupolas (J5) onto two nonadjacent, nonparallel decagonal faces of a truncated...

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