The zonohedron based on the ten directions of the dodecahedron's long diagonals is the rhombic enneacontahedron. Note that Zometool is the ideal material for making models of these structures because the ball design is constrained to maintain parallelism in space. Use just yellow for the rhombic dodecahedron or the rhombic enneacontahedron, just blue for the truncated icosidodecahedron, and just red for the rhombic triacontahedron. George http://georgehart.com On 5/14/2018 7:44 AM, Veit Elser wrote:
On May 13, 2018, at 12:43 PM, Scott Kim <scott@scottkim.com> wrote:
I haven't tried pushing this higher…I wonder what zonohedron one would get starting from 15 vectors that point out to half the vertices of a dodecahedron? That seems like the next thing to try. Does anyone know?
The dodecahedron has 20 vertices. Are you thinking about the 15 two-fold axes of the icosahedron/dodecahedron, i.e. vectors that point to the edge mid-points? If so, then the answer is:
https://en.wikipedia.org/wiki/Truncated_icosidodecahedron
-Veit
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