the original solid has v vertices and e edges, the truncated solid will have 2e vertices
and 3e edges. In symbols, (v,e) -> (2e,3e) with q= 3. [q is the number edges at each vertex]
Rectify: The midpoints of each edge are connected so that each original face and
vertex becomes a face. If the original solid has v vertices and e edges, the rectified
solid will have e vertices and 2e edges. In symbols, (v,e) -> (e,2e) with q= 4.
Snub: Each vertex becomes a triangle, faces are rotated slightly until each edge
becomes two triangles. In symbols, (v,e) -> (2v,5v) with q = 5.
Ödev
* First three pictures show how to make 9 circles of Oh symmetry
and 48 triangles in the dual solid of 4.6.8
* Escher's drawing (Ref 5) may help you visualise:
http://math.slu.edu/escher/upload/4/44/Concentric-rinds.jpg
* Fourth picture shows the other Catalan solids with Oh symmetry
http://en.wikipedia.org/wiki/Catalan_solid
* Show the effect of these transformations on the last picture
Truncate: (v,e,f) -> (2e,3e,e+2)
Rectify: (v,e,f) -> (e,2e,e+2)
Snub: (v,e,f) -> (e,5e/2,3e/2+2)
Referans
