Peter Mcmullen
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Peter Mcmullenmathematics Degrees
Mathematics
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Geometry
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Measure Theory
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Mathematics
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(Suggest an Edit or Addition)Peter Mcmullen's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- The maximum numbers of faces of a convex polytope (1970) (662)
- INTRODUCTION TO GEOMETRIC PROBABILITY (1999) (339)
- Convex Polytopes and the Upper Bound Conjecture (1971) (327)
- Convex Sets and Their Applications (1982) (289)
- Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes (1977) (225)
- Abstract Regular Polytopes (2003) (214)
- The numbers of faces of simplicial polytopes (1971) (193)
- On simple polytopes (1993) (186)
- Valuations on convex bodies (1983) (178)
- Non-linear angle-sum relations for polyhedral cones and polytopes (1975) (175)
- Valuations and Dissections (1993) (146)
- Lattice points in lattice polytopes (1985) (132)
- A generalized lower-bound conjecture for simplicial polytopes (1971) (123)
- Convex bodies which tile space by translation (1980) (114)
- GEOMETRIC TOMOGRAPHY (Encyclopedia of Mathematics and its Applications 58) (1997) (113)
- The polytope algebra (1989) (111)
- Lattice invariant valuations on rational polytopes (1978) (102)
- Polytopes: Abstract, Convex and Computational (1994) (91)
- On Hammer's X-Ray Problem (1980) (91)
- A COURSE IN CONVEXITY (Graduate Studies in Mathematics 54) By ALEXANDER BARVINOK: 366 pp., US$59.00, ISBN 0-8218-2968-8 (American Mathematical Society, Providence, RI, 2002) (2003) (76)
- AN INTRODUCTION TO CONVEX POLYTOPES (Graduate Texts in Mathematics, 90) (1984) (69)
- Continuous translation invariant valuations on the space of compact convex sets (1980) (66)
- Weights on polytopes (1996) (63)
- Isometry covariant valuations on convex bodies (1997) (61)
- Polyhedral 2-manifolds inE3 with unusually large genus (1983) (60)
- Diagrams for centrally symmetric polytopes (1968) (57)
- Representations of polytopes and polyhedral sets (1973) (54)
- Combinatorially regular polytopes (1967) (52)
- THE LINEAR ORDERING PROBLEM: ALGORITHMS AND APPLICATIONS (Research and Exposition in Mathematics 8) (1987) (52)
- SPACE TILING ZONOTOPES (1975) (50)
- On the upper-bound conjecture for convex polytopes (1971) (50)
- Regular Polytopes in Ordinary Space (1997) (49)
- Transforms, Diagrams and Representations (1979) (48)
- Realizations of regular polytopes (1988) (46)
- Equivelar polyhedral manifolds inE3 (1982) (42)
- Estimating the Sizes of Convex Bodies from Projections (1983) (41)
- Regular Polytopes of Full Rank (2004) (40)
- Constructions for regular polytopes (1990) (40)
- Volumes of Projections of unit Cubes (1984) (38)
- Infinite series of combinatorially regular polyhedra in three-space (1988) (37)
- Inequalities between intrinsic volumes (1991) (35)
- Constructions for projectively unique polytopes (1976) (33)
- Weakly continuous valuations on convex polytopes (1983) (32)
- Polytopes with centrally symmetric facets (1970) (31)
- Hermitian Forms and Locally Toroidal Regular Polytopes (1990) (30)
- Monotypic polytopes and their intersection properties (1974) (30)
- Regular polytopes from twisted Coxeter groups and unitary reflexion groups (1990) (28)
- Simplices with Equiareal Faces (2000) (26)
- Abstract Regular Polytopes: Regular Polytopes (2002) (26)
- Triangulations of Simplicial Polytopes (2004) (25)
- Valuations on lattice polytopes (2009) (25)
- Higher Toroidal Regular Polytopes (1996) (25)
- Regular polytopes from twisted Coxeter groups (1989) (24)
- Mixed Fibre Polytopes (2004) (22)
- Indecomposable convex polytopes (1987) (22)
- Duality, sections and projections of certain Euclidean tilings (1994) (21)
- Four-Dimensional Regular Polyhedra (2007) (21)
- Angle-sum relations for polyhedral sets (1986) (20)
- On a problem of klee concerning convex polytopes (1970) (19)
- The number of simplicial neighbourly d-polytopes with d+3 vertices (1973) (17)
- Separation in the polytope algebra. (1993) (17)
- A dice probability problem (1974) (17)
- Regular and chiral polytopes in low dimensions (2005) (16)
- On the inner parallel body of a convex body (1974) (16)
- MODERN DEVELOPMENTS IN REGULAR POLYTOPES (1994) (15)
- Regular polyhedra related to projective linear groups (1991) (14)
- Regular Star‐Polytopes, and a Theorem of Hess (1968) (14)
- Symmetric Tessellations on Euclidean Space-Forms (1999) (14)
- The number of neighbourly d -polytopes with d +3 vertices (1974) (13)
- Convex bodies which tile space by translation: Acknowledgement of priority (1981) (13)
- Realizations of regular polytopes, III (2003) (13)
- Realizations of regular polytopes (1988) (13)
- Arcs with increasing chords (1972) (12)
- Realizations of regular polytopes, II (2003) (12)
- Regular Maps Constructed from Linear Groups (1993) (12)
- Regular Polytopes of Nearly Full Rank (2011) (11)
- Regular Apeirotopes of Dimension and Rank 4 (2009) (11)
- HILBERT'S THIRD PROBLEM: SCISSORS CONGRUENCE (1980) (11)
- Self-Dual Regular 4-Polytopes and Their Petrie-Coxeter-Polyhedra (1987) (11)
- The Minimum Number of Facets of a Convex Polytope (1971) (10)
- The volume of certain convex sets (1982) (10)
- Locally Projective Regular Polytopes (1994) (10)
- Regular polytopes of type {4,4,3} and {4,4,4} (1992) (9)
- Quotients of polytopes and C-groups (1994) (9)
- Polytopes with an Axis Of Symmetry (1970) (9)
- Locally toroidal regular polytopes of rank 4 (1992) (9)
- The Groups of the Regular Star-Polytopes (1998) (9)
- Monotone translation invariant valuations on convex bodies (1990) (8)
- NONDIFFERENTIABLE OPTIMIZATION (Translation Series in Mathematics and Engineering) (1987) (8)
- Realizations of regular apeirotopes (1994) (7)
- Twisted Groups and Locally Toroidal Regular Polytopes (1996) (7)
- Determinants of Lattices induced by Rational Subspaces (1984) (7)
- Affinely and Projectively Regular Polytopes (1968) (7)
- POLYTOPES AND SYMMETRY: (London Mathematical Society Lecture Note Series, 90). (1984) (7)
- Finite Quotients of Infinite Universal Polytopes (1990) (6)
- Regular Polytopes of Nearly Full Rank: Addendum (2013) (6)
- Realizations of regular polytopes, IV (2014) (6)
- Volumes of complementary projections of convex polytopes (1987) (5)
- New Combinations of Convex Sets (1999) (5)
- Complete subgraphs of the graphs of convex polytopes (1981) (5)
- Minimal width and diameter of lattice-point-free convex bodies (1981) (5)
- Linearly Stable Polytopes (1969) (5)
- Two remarks on equivelar manifolds (1985) (4)
- Facets with fewest vertices (1990) (4)
- Polytope algebras, tensor weights and piecewise polynomials (1997) (4)
- Flat regular polytopes (1997) (4)
- Geometric Regular Polytopes (2020) (4)
- Locally unitary groups and regular polytopes (2002) (3)
- The Mix of a Regular Polytype with a Face (2002) (3)
- The Hausdorff distance between compact convex sets (1984) (3)
- Valuations and Tensor Weights on Polytopes (2006) (3)
- New Regular Compounds of 4-Polytopes (2018) (3)
- Sets homothetic to intersections of their translates (1978) (2)
- INTRODUCTION TO GEOMETRIC PROBABILITY By D ANIEL A. K LAIN and G IAN -C ARLO R OTA : 178 pp., £12.95 (US$19.95), ISBN 0 521 59654 8 (Cambridge University Press, 1997). (1999) (2)
- Mathematical programming : an introduction to optimization (1987) (2)
- The order of a finite Coxeter group. (1991) (2)
- Convex Bodies which Tile Space (1981) (2)
- The regular polyhedra of type {p, 3} with 2p vertices (1992) (2)
- Polytopes with centrally symmetric faces (1970) (1)
- The Brunn-Minkowski theorem for polytopes (2002) (1)
- POLYTOPES, GRAPHS AND OPTIMISATION By V. A. Yemelichev , M. M. Kovalev and M. K. Kravtsov : pp. 243. £25.00; US$49.50. (Cambridge University Press, 1984.) (1985) (1)
- QUASI-PERIODIC TILINGS OF ORDINARY SPACE (1993) (1)
- G. M. Ziegler Lectures on polytopes (Graduate Texts in Mathematics, Vol. 152, Springer-Verlag, Berlin-Heidelberg-New York-London-Paris-Tokyo-Hong Kong 1995), ix + 370 pp., softcover: 3 540 94365 X, £21, hardcover: 3 540 94329 3, £47. (1996) (1)
- Polytopes with parathetic faces (2006) (1)
- Quasi-Regular Polytopes of Full Rank (2021) (1)
- Higher Toroidal Polytopes (2002) (1)
- Polyhedra and Polytopes: Algebra and Combinatorics (2005) (1)
- Regular Polytopes of Nearly Full Rank: Addendum (2013) (0)
- THE GROUPS OF THE REGULAR STAR-POLYTOPES With best wishes to H. S. M. (Donald) Coxeter for his 90th birt hday (1998) (0)
- Locally Toroidal 4-Polytopes: II (2002) (0)
- Rigidity of Regular Polytopes (2014) (0)
- Abstract Regular Polytopes: Miscellaneous Classes of Regular Polytopes (2002) (0)
- Unitary Groups and Hermitian Forms (2002) (0)
- Associated polyhedra and dual linear programs (2010) (0)
- Regular compounds of honeycombs in H3 and H4 (2019) (0)
- Self-inscribed Regular Hyperbolic Honeycombs (2015) (0)
- Abstract Regular Polytopes: Classical Regular Polytopes (2002) (0)
- Identifying a polytope by its fibre polytopes (2020) (0)
- ( 1907 – 2003 ) (2003) (0)
- ALGORITHMIC GEOMETRY By J EAN -D ANIEL B OISSONNAT and M ARIETTE Y VINEC (translated by H ERVÉ B RÖNNIMANN ): 519 pp., £24.95 (US$39.95), ISBN 0 521 56529 4 (Cambridge University Press, 1998). (1999) (0)
- Realizations of the 120-cell (2021) (0)
- Abstract Regular Polytopes: Twisting (2002) (0)
- LATTICE POINT NUMBER ON BOUNDARY OF CONVEX BODIES (1973) (0)
- Lattices compatible with regular polytopes (2008) (0)
- Realizations of regular polytopes, IV (2013) (0)
- Polytopes and polyhedra: algebra and combinatorics. (2007) (0)
- Regular Polytopes on Space-Forms (2002) (0)
- Regular Polytopes Related to Linear Groups (2002) (0)
- Identifying a polytope by its fibre polytopes (2020) (0)
- Gosset–Elte Polytopes (2020) (0)
- Abstract Regular Polytopes: Amalgamation (2002) (0)
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