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





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





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 raytraced
image correctly but is not needed for display with antiview.
View this model with the command
pol_recip I 100000 u_octahemioctahedron  antiview





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





Dual offcentre

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





Dual self

Med
Lrg

Description :

Make the dual of a selfdual 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 selfdual 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





Dual midcentre

Med
Lrg

Description :

Make the dual of a polyhedron that is edgelinetangent 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 nondefault 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




