Re: [math-fun] new(?) equilateral dodecahedron
APGoucher>Bill Gosper,
Another example, where all faces are identical, is the endo-dodecahedron. (The Symmetries of Things, p. 328)
Is this four tetrahedra clumped around one <http://gosper.org/endodo.png>? There's always the rhombic dodecahedron, no?
Which maths camp was this?
http://www.mathcamp.org/currentstudents/visitingspeakers.php, whereat Julian failed to show CNWH S. Silver's marvelous 1x1013783 breeder<http://pentadecathlon.com/lifeNews/2011/05/quadratic_population_growth_fr.html> because it was "just a stunt". Grr, I bet CNWH would have loved it.
Was Julian at IMO 2011, also?
No, Evan O'dorney<http://mathcircle.berkeley.edu/pictures2/BAMO09/bamo09_evan_julian.JPG>won the B(ay)A(rea)MO again this year.
Sincerely,
Adam P. Goucher
--rwg
APGoucher>Bill Gosper,
Another example, where all faces are identical, is the endo-dodecahedron. (The Symmetries of Things, p. 328)
Is this four tetrahedra clumped around one <http://gosper.org/endodo.png>?
No, it has five non-convex equilateral pentagonal faces and pyritohedral symmetry. Specifically, it is the shape of the 'holes' left behind when regular dodecahedra are packed together in a FCC lattice.
There's always the rhombic dodecahedron, no?
Again, not pentagonal. Although I was reading somewhere about the regular dodecahedron as being the limit of a set of pyritohedral dodecahedra with vertices in Q^3, where the points are determined by ratios of successive Fibonacci numbers. The rhombic dodecahedron is indeed the degenerate case when this ratio is zero.
Which maths camp was this?
http://www.mathcamp.org/currentstudents/visitingspeakers.php, whereat Julian failed to show CNWH S. Silver's marvelous 1x1013783 breeder<http://pentadecathlon.com/lifeNews/2011/05/quadratic_population_growth_fr.html> because it was "just a stunt". Grr, I bet CNWH would have loved it.
Agreed. Has the same fate befallen my pi calculator? Sincerely, Adam P. Goucher
participants (2)
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Adam P. Goucher -
Bill Gosper