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Elongated cupola information


Set of elongated cupolae

Example pentagonal form
Faces n triangles
3n squares
1 n-gon
1 2n-gon
Edges 9n
Vertices 5n
Symmetry group Cnv, [n], (*nn)
Rotational group Cn, [n]+, (nn)
Dual polyhedron
Properties convex

In geometry, the elongated cupolae are an infinite set of polyhedra, constructed by adjoining an 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 forms can be constructed with isosceles triangles. Adjoining a triangular prism to a cube also generates a polyhedron, but has adjacent parallel faces, so is not a Johnson solid. Higher forms can be constructed without regular faces.

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Elongated cupola

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the elongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to an 2n-gonal prism. There are three elongated cupolae...

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Elongated triangular cupola

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the elongated triangular cupola is one of the Johnson solids (J18). As the name suggests, it can be constructed by elongating a triangular cupola (J3)...

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Elongated square cupola

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geometry, the elongated square cupola is one of the Johnson solids (J19). As the name suggests, it can be constructed by elongating a square cupola (J4) by...

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Elongated pentagonal cupola

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the elongated pentagonal cupola is one of the Johnson solids (J20). As the name suggests, it can be constructed by elongating a pentagonal cupola (J5)...

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Triangular cupola

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constructed in such a way are elongated triangular cupola J 18 {\displaystyle J_{18}} , gyroelongated triangular cupola J 22 {\displaystyle J_{22}} ,...

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Elongated triangular orthobicupola

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In geometry, the elongated triangular orthobicupola is a polyhedron constructed by attaching two regular triangular cupola into the base of a regular...

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Square cupola

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Some of the other Johnson solids are elongated square cupola J 19 {\displaystyle J_{19}} , gyroelongated square cupola J 23 {\displaystyle J_{23}} , square...

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Elongated triangular gyrobicupola

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In geometry, the elongated triangular gyrobicupola is a polyhedron constructed by attaching two regular triangular cupolas to the base of a regular hexagonal...

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Elongated bicupola

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In geometry, the elongated bicupolae are two infinite sets of polyhedra, constructed by adjoining two n-gonal cupolas to an n-gonal prism. They have 2n...

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Johnson solid

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pyramid Triangular cupola Square cupola Pentagonal cupola Pentagonal rotunda Elongated triangular pyramid Elongated square pyramid Elongated pentagonal pyramid...

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Elongated pentagonal orthocupolarotunda

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its halves. Rotating either the cupola or the rotunda through 36 degrees before inserting the prism yields an elongated pentagonal gyrocupolarotunda (J41)...

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Elongated square gyrobicupola

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In geometry, the elongated square gyrobicupola is a polyhedron constructed by two square cupolas attaching onto the bases of octagonal prism, with one...

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Gyroelongated cupola

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but the cupola faces are all in the same plane. Topologically other forms can be constructed without regular faces. Elongated cupola Elongated bicupola...

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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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List of mathematical shapes

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rotunda Elongated square bipyramid Elongated square cupola Elongated square gyrobicupola Elongated square pyramid Elongated triangular bipyramid Elongated triangular...

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Square orthobicupola

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an irregular hexagonal prism to yield an elongated square dipyramid (J15), which itself is merely an elongated octahedron. It can be constructed from the...

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M60 tank

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design based on the M1 cupola of the M48A2's turret. This T9 cupola provided the commander with more headroom than the T6 cupola of the T95 tank, carrying...

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Rhombicuboctahedron

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needed] The elongated square gyrobicupola is the only polyhedron resembling the rhombicuboctahedron. The difference is that the elongated square gyrobicupola...

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Gyrobifastigium

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parallelograms corresponding to the valence-4 equatorial vertices. Elongated gyrobifastigium Elongated octahedron Darling, David (2004), The Universal Book of Mathematics:...

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Icosahedron

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J22 J35 J36 J59 J60 J92 Gyroelongated triangular cupola Elongated triangular orthobicupola Elongated triangular gyrobicupola Parabiaugmented dodecahedron...

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Enneahedron

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solids have enneahedral duals: the triangular cupola, gyroelongated square pyramid, self-dual elongated square pyramid, triaugmented triangular prism...

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Triangular prism

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with their construction involving the triangular prism: elongated triangular pyramid, elongated triangular bipyramid, gyrobifastigium, augmented triangular...

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Gyroelongated bicupola

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coplanar faces. Higher forms can be constructed without regular faces. Elongated cupola Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal...

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List of small polyhedra by vertex count

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pyramid Tridecagonal bipyramid Pentagonal cupola Elongated triangular cupola Gyroelongated triangular cupola 16 Octagonal prism Octagonal antiprism Triaugmented...

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Dodecahedron

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Pentagonal cupola – 5 triangles, 5 squares, 1 pentagon, 1 decagon, C5v symmetry, order 10 Snub disphenoid – 12 triangles, D2d, order 8 Elongated square dipyramid...

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Triangular orthobicupola

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one cupola before the joining yields a cuboctahedron. Hence, another name for the triangular orthobicupola is the anticuboctahedron. The elongated triangular...

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