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Programs: pol_recip 7 images
tree :: Antiprism Examples and Visual Reference > Program Examples > Programs: pol_recip
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    Example commands using the pol_recip program. This program makes duals by polar reciprocation in a sphere. The results depend on the particular sphere used, and there are options to find spheres that may produce interesting duals.
 
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Dual  Med    Lrg  
Description : 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  Med    Lrg  
Description : 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  Med    Lrg  
Description : 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  Med    Lrg  
Description : 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  Med    Lrg  
Description : 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  Med    Lrg  
Description : 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  Med    Lrg  
Description : 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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Contact: adrian@antiprism.com      -      Generated on vie 05 abr 2019 10:29:22 CEST