F4 Class I

Med
Lrg

Description :

A four frequency Class I icosahedral geodesic sphere.
This can be specified as the Class I pattern repeated
according to Fuller's stepping frequency
geodesic F 4 std_ico  antiview
as the Class I pattern repeated four times along an edge
geodesic f 4 std_ico  antiview
or as general pattern
geodesic c 4,0 std_ico  antiview
View this model with the command
geodesic f 4 std_ico  antiview





F4 Class II

Med
Lrg

Description :

A four frequency Class II icosahedral geodesic sphere.
This can be specified as the Class II pattern repeated
according to Fuller's stepping frequency
geodesic F 4 c 2 std_ico  antiview
as the Class II pattern repeated twice along an edge
geodesic f 2 c 2 std_ico  antiview
or using a general pattern
geodesic c 2,2 std_ico  antiview
View this model with the command
geodesic F 4 c 2 std_ico  antiview





F6 Class III

Med
Lrg

Description :

A six frequency Class III icosahedral geodesic sphere.
This can be specified as the particular Class III pattern repeated
according to Fuller's stepping frequency
geodesic F 6 c 2,1 std_ico  antiview
as the Class III pattern repeated
twice along an edge
geodesic f 2 c 2,1 std_ico  antiview
or using a general pattern
geodesic c 4,2 std_ico  antiview
View this model with the command
geodesic F 6 c 2,1 std_ico  antiview





Pretriangulate

Med
Lrg

Description :

The geodesic division is only carried out on polyhedra whose faces are all
triangles. When a polyhedron has faces with more than three sides these
are first converted to triangles by attaching the edges of the face to
its centre. The following example is a 'one frequency'
rhombicosidodecahedron. The square and pentagonal faces have been
converted to triangles. This would
be the base model used for any higher frequency subdivisions.
View this model with the command
off_color e white u_rhombicosi  geodesic  antiview v 0.015





Planar

Med
Lrg

Description :

The following example is a planar Class III 2,1 rhombicosidodecahedron. The
square and pentagonal faces are first converted to triangles by joining
a face's edges to its centre. The geodesic subdivision is applied to this
base model. In the planar models the subdivision is based on dividing the
original edges by equal length (as opposed to equal central angle in the
spherical models), and the models are not projected onto a sphere afterwards.
View this model with the command
geodesic M p c 2,1 u_rhombicosi  antiview v 0.01





Spherical Tiling

Med
Lrg

Description :

The elements of an icosahedron are coloured. It is converted to a geodesic
sphere. The new edges and vertices are not displayed (coloured invisible), the
subdivided faces and edges, and the original vertices, keep their original
colours. The result is an approximation of a spherical tiling of the
original polyhedron.
View this model with the command
off_color e white v red f P m map_darkred:tan:grey20 ico  geodesic f 8  antiview v 0.04 e 0.02 V x E x




