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Results tagged with polytopes
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user 10881
9
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0
answers
284
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Meaning of the Ehrhart polynomial at $-1/2$?
I am studying a large collection of lattice polytopes, all of them being simple and empty. The dimension can be any integer. The dilatation by $2$ gives non-empty polytopes. … For many of these polytopes but not all, the Ehrhart polynomial $E_P(t)$ vanishes at $t=-1/2$, sometimes with multiplicity. …
- 3,597
3
votes
Who knows this convex polytope?
It seems to ressemble the "Self-Dual Icosioctahedron #4" :
http://dmccooey.com/polyhedra/SelfDualIcosioctahedron4.html
Some code:
sage: P = polytopes.rhombic_dodecahedron()
sage: Q = polytopes.tetr …
- 3,597
1
vote
Do Bernoulli polynomials know about face vectors?
Explicitly, the polynomials are
sage: 12*(bernoulli_polynomial(x,5)-bernoulli(5))
12*x^5 - 30*x^4 + 20*x^3 - 2*x
sage: 24*(bernoulli_polynomial(x,7)-bernoulli(7)) …
- 3,597