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We study the problem of acute triangulations of convex polyhedra and the space R^n.
A. D. Alexandrov, On partitions and tessellations of the plane (in Russian),
1937
Earlier work this paper cites.
Ju. D. Burago and V. A. Zalgaller, Polyhedral embedding of a net (in Russian),
1960
Earlier work this paper cites.
W. Manheimer, Solution to problem E1406: Dissecting an obtuse triangle into acute triangles,
1960
Earlier work this paper cites.
V. Klee, A combinatorial analogue of Poincaré‘s duality theorem,
1964
Earlier work this paper cites.
H. Lindgren,
1964
Earlier work this paper cites.
I. G. Macdonald, Polynomials associated with finite cell-complexes
1971
Earlier work this paper cites.
H. S. M. Coxeter,
1973
Earlier work this paper cites.
G. Strang and G. J. Fix,
1973
Earlier work this paper cites.
I. Niven, Convex polygons that cannot tile the plane,
1978
Earlier work this paper cites.
C. Cassidy and G. Lord, A square acutely triangulated,
1980
Earlier work this paper cites.
B. Grünbaum, P. Mani-Levitska and G. C. Shephard, Tiling three-dimensional space with polyhedral tiles of a given isomorphism type,
1984
Earlier work this paper cites.
E. Schulte, Tiling three-space by combinatorially equivalent convex polytopes,
1984
Earlier work this paper cites.
B. Grünbaum and G. C. Shephard,
1987
Cited alongside, same era.
B. S. Baker, E. Grosse, and C. S. Rafferty, Nonobtuse triangulations of polygons,
1988
Cited alongside, same era.
M. Bern and D. Eppstein, Polynomial-size nonobtuse triangulation of polygons
1992
Cited alongside, same era.
C. Fulton, Tessellations,
1992
Cited alongside, same era.
G. Kuperberg and O. Schramm, Average kissing numbers for noncongruent sphere packings,
1994
Cited alongside, same era.
R. P. Stanley, Flag
1994
Cited alongside, same era.
M. Bern, S. Mitchell and J. Ruppert, Linear-size nonobtuse triangulations of polygons,
T. Januszkiewicz and J. Świątkowski, Hyperbolic Coxeter groups of large dimension,
2003
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T. Zamfirescu, Acute triangulations: a short survey, in
2003
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D. Eppstein, J. M. Sullivan and A. Üngör, Tiling space and slabs with acute tetrahedra,
2004
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L. Yuan, Acute triangulations of polygons,
2005
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A. V. Akopyan, PL-analogue of the Nash–Kuiper theorem (in Russian), preprint (2007)
2007
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J. A. De Loera, J. Rambau and F. Santos,
2008
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1995
Cited alongside, same era.
J. C. Lagarias and D. Moews, Polytopes that fill
1995
Cited alongside, same era.
D. Eppstein, Acute square triangulation, 1997; available at
1997
Cited alongside, same era.
M. Bonk and B. Kleiner, Quasisymmetric parametrizations of two-dimensional metric spheres,
2002
Cited alongside, same era.
H. Maehara, Acute triangulations of polygons,
2002
Cited alongside, same era.
J. R. Shewchuk, What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures, preprint, 2002; available at
2002
Cited alongside, same era.
J. Brandts, S. Korotov, M. Křížek and J. Šolc, On Nonobtuse Simplicial Partitions,
2009
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I. Novik and E. Swartz, Applications of Klee‘s Dehn-Sommerville relations,
2009
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P. Przytycki and J. Świątkowski, Flag-no-square triangulations and Gromov boundaries in dimension
2009
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S. Saraf, Acute and nonobtuse triangulations of polyhedral surfaces,
2009
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M. Křížek, There is no face-to-face partition of
2010
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