Leonardo da Vinci (1452-1519) made outstanding illustrations for Luca Pacioli's 1509 book "The Divine Proportion", in which they described "elevated" forms of many polyhedra. In the Bridges meeting held in Seoul this year, Rinus Roelofs presented a beautiful paper on the similarities and differences between Da Vinci's elevations and Kepler's stellations.
For details, check the following pdf file:
Elevations and Stellations,
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, 235-242.
Figure 1 and 2 in the paper are original illustrations made by Leonardo da Vinci:
It is interesting that bead models for the five elevated regular polyhedra can be built easily with great effects. Among them, elevated cube and dodecahedron are more flexible as expected.
Tuesday, October 21, 2014
Sunday, October 19, 2014
Saturday, October 18, 2014
I made another truss model of perovskite structure with octahedra constructed by yellow and blue bugle beads.