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kiteohedron - kite-faced polyhedra

Usage    |    Examples    |    Notes

Usage



Usage: kiteohedron [options] frac_A frac_B [frac_C]

The three fractions A, B, C (default 2) specifying the Schwarz triangle
vertices, where n/d corresponds to an angle PI*d/n. The kite has vertices
along A, C, B, and C reflected in AB. The kite is repeated with the
symmetry corresponding to the base Schwarz triangle.

Options
  -h        this help message
  -l ht     height of kite vertex on OA (cannot use with -p))
  -p ht     height of pivot, midpoint of C and C reflected in AB (cannot
            use with -l))
  -k        output a single kite (colours not applied)
  -c type   colour the faces around each vertex of a type, from AaBbCc
            (colouring by value/index for upper/lower case) using a
            different colour for each set
  -o <file> write output to file (default: write to standard output)


Examples

General member of series including deltoidal hexacontahedron.
   kiteohedron 5 3 2 | antiview
General member of series including deltoidal icositetrahedron. The third vertex of the triangle uses the default of 2
   kiteohedron 3 4 | antiview
General member of series including deltoidal icositetrahedron. Set a height for the point along the first vertex (fixes the pivot)
   kiteohedron -l 2.5 3 4 | antiview
General member of series including deltoidal icositetrahedron. Set a height for the pivot, the midpoint of the line segment joining the kite's side vertices (fixes the vertex at A).
   kiteohedron -p 2.5 3 4 | antiview
General member of series including deltoidal icositetrahedron. The vertex order is significant
   kiteohedron -l 2.5 4 3 | antiview
Colour faces around vertices of type A (the first vertex, in this case with angle 4) in sets
   kiteohedron -c A -l 2.5 4 3 | antiview
Colour faces around vertices of type B (the second vertex, in this case with angle 3) in sets
   kiteohedron -c B -l 2.5 4 3 | antiview
Colour faces around vertices of type C (the third vertex, in this case with angle 3). With vertex C only half the faces around each vertex have the same colour
   kiteohedron -c C -l 2.5 4 3 | antiview
Output a single kite
   kiteohedron -k -l 2.5 4 3 | antiview
Negative heights are allowed
   kiteohedron -l -2.5 4 3 2 | antiview
Instead of using a negative height, B and C could be replaced with their supplements
   kiteohedron -l 2.5 4 3/2 2 | antiview
The duals can be attractive
   kiteohedron -l 0.3 5/4 5/2 2 | pol_recip | antiview
Models with A or B as 2 will be degenerate, and have triangles for kites
   kiteohedron 3 2 4| antiview

Notes

See the Wikipedia page on Schwarz triangles for a description and list of triangles.

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Next: conway - Conway Notation transformations

Antiprism Documentation 13.10.2012 - http://www.antiprism.com/