User:Tomruen/Rectified antiprism

Set of rectified antiprisms
Rectified pentagonal antiprism
Conway polyhedron notation	aAn
Faces	2 n-gons 2n trapezoids 2n triangles
Edges	8n
Vertices	4n
Symmetry group	Dnd, [2+,2n], (2*n), order 4n
Rotation group	Dn, [2,n]+, (22n), order 2n
Dual polyhedron	Elongated trapezohedron
Properties	convex

In geometry, a rectified antiprism (also rectified bipyramid) is one of an infinite set of polyhedra, constructed as a rectification of an n-gonal antiprism, truncating the vertices down to the midpoint of the original edges. In Conway polyhedron notation, it is represented as aAn, an ambo-antiprism. The lateral squares or rectangular faces of the antiprism become squares or rhombic faces, and new isosceles triangle faces are truncations of the original vertices. It can also be seen as two base-to-base cupola as gyrobicupolae

Elements

An n-gonal form has 3n vertices, 7n edges, and 3n faces: 2 regular n-gons, 2n trapezohedron, and 2n triangles.

Forms

The rectified triangular antiprism is the same as a semiregular cuboctahedron.

n	2	3	4	5	6	8	10	12	n
Image
Net
Faces	4 triangles 4 squares	2 triangle 6 triangles 6 squares	2 squares 8 triangles 8 squares	2 pentagons 10 triangles 10 squares	2 hexagons 12 triangles 12 squares	2 octagons 16 triangles 16 squares	2 decagons 20 triangles 20 squares	2 dodecagons 24 triangles 24 squares	2 n-gons 2n triangles 2n squares
Edges	16-2=14	24	32	40	48	64	80	96	8n
Vertices	8	12	16	20	24	32	40	48	4n
Related
Net
Related	Gyrobifastigium	Cuboctahedron	Square gyrobicupola	Pentagonal gyrobicupola

Star forms

Rectified star antiprisms also exist, like 5/2 and 5/3 forms:

Dual

Set of joined antiprisms
Conway polyhedron notation	jAn
Faces	4n
Edges	8n
Vertices	2+4n
Symmetry group	Dnd, [2+,2n], (2*n), order 4n
Rotation group	Dn, [2,n]+, (22n), order 2n
Dual polyhedron	Rectified antiprism Rectified bipyramid
Properties	convex

The dual of a rectified antiprism is an elongated trapezohedron. The degenerate n=2 case, is an elongated tetragonal disphenoid, with the polar axis vertices removed. It can also be constructed as a joined antiprism in Conway polyhedron notation. The elongated triangular antiprism is a rhombic dodecahedron. The topology also exists on a 2n-gonal prism with the top and bottom faces divided with alternate orientations top to bottom.

n	2	3	4	5	6	8	10	12	n
Image
Net
Faces	8	12	16	20	24	32	40	48	4n
Edges	16-2=14	24	32	40	48	64	80	96	8n
Vertices	10-2=8	14	18	22	26	34	42	50	2+4n
Related

See also

• Rectified prism

External links

• Conway Notation for Polyhedra Try: aAn and jAn, where n=3,4,5,6... example aA3 is a rectified triangular antiprism, and jA3 is an joined triangular antiprism or a elongated triangular trapezohedron.