                       The Uniform Snub Polyhedra

These are the 12 polyhedra with Wenninger numbers 17, 18 and 110 to 119
which you can see on the sheet supplied with the paper manual.

All of the other models are made by combining either the tetrahedron, cube,
octahedron, and rhombic dodecahedron, or by combining the dodecahedron,
icosahedron and rhombic triacontahedron. The components of these two groups
are always oriented in the same way with respect to one another.

Model W17 (the snub cube) has 24 planes of snub triangles while the rest of
the snub polyhedra have 60 planes of additional triangles (or squares for
W119). These planes have different orientations for each polyhedron.

!Stellate calculates the angles of these snub planes from the definition of
the solid. It recognises a snub polyhedron since it contains a snub
component (types 8, 9 or 10 in the Components file). It then decides on
the particular polyhedron from its radius, computes the angles of all the
planes and revises the radius with its more accurate calculation.

Polyhedra W115 and W119 have the same radius of 2 but the latter is
recognized by being the only uniform solid with a component of type 8.

The polyhedra with higher Wenninger numbers are more complicated; selecting
the faces in the stellation diagrams for the later ones is not easy because
there are so many very small faces.

There is an additional problem in W114 and W116 in that it is not possible
to sort the faces for plotting the solid correctly. This problem has been
mostly solved by using split faces as described in Reference.Splits.


                Table of snub polyhedra parameters

Wenninger
number     Radius  Components*            Name

  17     2.687427   8{3} 24{3}  6{4}      snub cube
  18     4.311675  20{3} 60{3} 12{5}      snub dodecahedron
 110     2.916381  20{3} 60{3} 12{5/2}    small snub icosicosidodecahedron
 111     2.548880  12{5/2} 60{3} 12{5}    snub dodecadodecahedron
 112     2.253796  12{5/2} 20{3} 60{3} 12{5} snub icosidodecadodecahedron
 113     1.632161  20{3} 60{3} 12{5/2}    great inverted snub icosidodecahedron
 114     1.703260  12{5/2} 60{3} 12{5}    inverted snub dodecadodecahedron
 115     1.414214  20{3} 60{3} 12{5/2}   great snub dodecicosidodecahedron
 116     1.290040  20{3} 60{3} 12{5/2}    great snub icosidodecahedron
 117     1.160003  20{3} 60{3} 12{5/2}    great inverted retrosnub icosidodeca.
 118     1.161390  20{3} 60{3} 12{5/2}   small inverted retrosnub
                                                        icosicosidodecahedron
 119     1.414214  20{3} 60{4} 12{5/2} great dirhombicosidodecahedron

* The components are defined by: no. planes{no. face-sides}
  5/2 sides means a 5-pointed star; e.g. 8{3} means 8 triangles.
 These faces are doubled to make overlapped 5-pointed stars or triangles.
 This face is doubled but is also a hemi-face; it has 60 squares in total.
