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Dual
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Med
Lrg
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Description :
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Make the dual of a polyhedron. The dual of an icosahedron is a dodecahedron.
View this model with the command
pol_recip ico | antiview
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Dual pair
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Med
Lrg
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Description :
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Make the dual pair. Display an icosahedron with its dual. Notice that
the base vertex colours are used for the dual faces, and vice versa.
View this model with the command
pol_recip -a ico | antiview
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Dual infinite 1
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Med
Lrg
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Description :
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Make the dual of a polyhedron with faces going through the reciprocation
centre. The face becomes an ideal vertex 'at infinity'. The default
display shows that the vertex can lie either side of the original face
by connecting to it in both directions. This is simulated with two
vertices and the model is not a topological dual, it is for display
purposes only. It is not
possible to place vertices at infinity, so a distance is used that
helps with display. This distance can be overriden with option -I.
The example shows the dual of an octahemioctahedron, with the
'infinity' distance set to 100000, which helps draw the ray-traced
image correctly but is not needed for display with antiview.
View this model with the command
pol_recip -I 100000 u_octahemioctahedron | antiview
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Dual infinite 2
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Med
Lrg
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Description :
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Make the dual of a polyhedron with faces going through the reciprocation
centre. The face becomes an ideal vertex 'at infinity'. Using
option -x the model will be a topological dual. It is not
possible to place vertices at infinity, so a distance is used that
helps with display. This distance can be overriden with option -I.
The example shows the dual of an octahemioctahedron, with the
'infinity' distance set to 10 (to show a close distance can be used)
View this model with the command
pol_recip -x -I 10 u_octahemioctahedron | antiview
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Dual off-centre
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Med
Lrg
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Description :
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Make the dual of a polyhedron, specifing the reciprocation sphere
directly. The dual of an icosahedron here is a distorted dodecahedron.
View this model with the command
pol_recip -c 0.4,0,0 -r 1 ico | antiview
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Dual self
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Med
Lrg
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Description :
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Make the dual of a self-dual polyhedron. The special centres are experimental
and may not be successful, but the command in this example has found
the reciprocation sphere that makes a self-dual pair of uniform
square pyramids.
View this model with the command
off_color pyr4 -v red -f blue | pol_recip -c e -a -n 10000 | antiview
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Dual midcentre
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Med
Lrg
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Description :
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Make the dual of a polyhedron that is edge-line-tangent to a sphere. A
reguar pyramid typically has two midcentres on its axis. Find a
midcentre with -c M, and control the particular centre by starting
the search near the desired centre. In this example the non-default midcentre
is found.
View this model with the command
off_color pyr5 -v red -f blue | pol_recip -c M -C 0,0,-5 -a -n 100000 | antiview
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