Geometry

(define (geodesic g n)
  (if (= n 0)
      g
      (geodesic (dual (semi-truncate g)) (- n 1))))

(geodesic icosahedron 4)

Here is an example of what my geometry and topology software does.

(product cell1 cell2 coordinate-combiner) forms the product of two cells. The procedure coordinate-combiner is used to combine the coordinates of each vertex of cell1 with the coordinates of each vertex of cell2.

For example,

  (product (dilate tetra .1) (dilate cube .8) h+)

forms the product of a small tetrahedron with a large cube, combining coordinates using h+ (vector sum of homogeneous coordinates):