Geoffrey Colin Shephard

Geoffrey Colin Shephard's AcademicInfluence.com Rankings

Mathematics

#1367

World Rank

#2270

Historical Rank

Measure Theory

#959

World Rank

#1248

Historical Rank

mathematics Degrees

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Mathematics

Why Is Geoffrey Colin Shephard Influential?

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According to Wikipedia, Geoffrey Colin Shephard is a mathematician who works on convex geometry and reflection groups. He asked Shephard's problem on the volumes of projected convex bodies, posed another problem on polyhedral nets, proved the Shephard–Todd theorem in invariant theory of finite groups, began the study of complex polytopes, and classified the complex reflection groups.

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Geoffrey Colin Shephard'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

Tilings and Patterns (1990) (1982)
Finite Unitary Reflection Groups (1954) (1276)
Convex Polytopes and the Upper Bound Conjecture (1971) (327)
The difference body of a convex body (1957) (261)
Combinatorial Properties of Associated Zonotopes (1974) (165)
Aperiodic tiles (1992) (143)
Convex Bodies Associated with a Given Convex Body (1958) (135)
Tilings by Regular Polygons (1977) (114)
Convex polytopes with convex nets (1975) (96)
Tilings with congruent tiles (1980) (94)
Some extremal problems for convex bodies (1958) (92)
Shadow systems of convex sets (1964) (81)
Decomposable convex polyhedra (1963) (80)
Unitary Groups Generated by Reflections (1953) (74)
Interlace Patterns in Islamic and Moorish Art (1993) (72)
Metrics for sets of convex bodies (1965) (67)
The eighty-one types of isohedral tilings in the plane (1977) (62)
Satins and Twills: An Introduction to the Geometry of Fabrics (1980) (62)
Diagrams for centrally symmetric polytopes (1968) (57)
The Steiner Point of a Convex Polytope (1966) (52)
Convex bodies and convexity on Grassmann cones (1962) (48)
Stellar subdivisions of boundary complexes of convex polytopes (1974) (47)
Inequalities between mixed volumes of convex sets (1960) (46)
A Uniqueness Theorem for the Steiner Point of a Convex Region (1968) (42)
An Elementary Proof of Gram's Theorem for Convex Polytopes (1967) (42)
Polytopes with Centrally Symmetric Faces (1967) (37)
Regular 3-complexes with toroidal cells (1977) (35)
Tilings and patterns. W. H. Freeman and Co. Ltd., Oxford 1987. IX + 700 p., 1395 figs., price £ 54.95, ISBN 0–7167–1193–1 (1991) (34)
Diagrams for Positive Bases (1971) (34)
Spherical complexes and radial projections of polytopes (1971) (34)
Rotation and winding numbers for planar polygons and curves (1990) (33)
Spherical Tilings with Transitivity Properties (1981) (33)
FACETS AND NONFACETS OF CONVEX POLYTOPES (1967) (32)
Normed vector spaces consisting of classes of convex sets (1965) (32)
Regular Complex Polytopes (1952) (31)
Monotypic polytopes and their intersection properties (1974) (30)
Pick's theorem (1993) (30)
Analogues for Tilings of Kotzig'S Theorem on Minimal Weights of Edges* (1982) (30)
Space‐filling zonotopes (1974) (29)
Ceva, Menelaus, and the Area Principle (1995) (29)
Combinatorics: The geometry of planar graphs (1981) (28)
Edge-transitive planar graphs (1987) (28)
Approximation problems for convex polyhedra (1964) (27)
Facets and nofacets of convex polytopes (1967) (26)
A Polygon Problem (1996) (26)
Euler‐Type Relations for Convex Polytopes (1968) (25)
Angle Deficiencies of Convex Polytopes (1968) (25)
Isohedral tilings of the plane by polygons (1978) (25)
A New Look at Euler's Theorem for Polyhedra (1994) (24)
Is Selfduality Involutory (1988) (22)
Isonemal fabrics (1988) (21)
Sections and projections of convex polytopes (1972) (21)
The ninety-one types of isogonal tilings in the plane (1978) (21)
A theorem on cyclic polytopes (1968) (21)
Tiling three-dimensional space with polyhedral tiles of a given isomorphism type (1984) (19)
Some Problems on Plane Tilings (1981) (19)
Convex bodies and convexity on Grassmann cones (1962) (19)
A CATALOGUE OF ISONEMAL FABRICS (1985) (18)
Self-duality Groups and Ranks of Self-dualities (1990) (18)
Subpolytopes of stack polytopes (1974) (17)
Some problems on polyhedra (1987) (16)
A hierarchy of classification methods for patterns (1981) (16)
An extension to the catalogue of isonemal fabrics (1986) (16)
The enumeration of normal 2-homeohedral tilings (1985) (15)
Perfect colorings of transitive tilings and patterns in the plane (1977) (14)
Symmetry Groups of Knots (1985) (13)
Some New Transversality Properties (1998) (13)
Vector spaces of finite dimension (1967) (13)
The Mean Width of a Convex Polytope (1968) (12)
Reducible convex sets (1966) (12)
Determination of All Tessellation Polyhedra with Regular Polygonal Faces (2010) (12)
Neighbourliness and Radon's theorem (1969) (11)
Patterns on the 2-Sphere (1981) (11)
Portraits of a Family of Complex Polytopes (1993) (10)
Twenty Problems on Convex Polyhedra Part II (1968) (10)
Approximations by polytopes with projectively regular facets (1966) (10)
Abstract Definitions for Reflection Groups (1957) (10)
Polytopes with an Axis Of Symmetry (1970) (9)
A pre-hilbert space consisting of classes of convex sets (1966) (9)
Patch-determined tilings (1977) (9)
The 2-homeotoxal tilings of the plane and the 2-sphere (1983) (8)
A new Ceva-type theorem (1996) (8)
Can all Tiles of a Tiling have Five-Fold Symmetry? (1982) (8)
A Sphere in a Crate (1965) (8)
ISOHEDRAL DELTAHEDRA (2000) (7)
A construction for projectively unique polytopes (1974) (7)
The theorems of Euler and Eberhard for tilings of the plane (1982) (7)
Convex Bodies and Convexity on Grassmann Cones (VIII): Projection Functions of Vector Sums of Convex Sets (1964) (6)
The perpendicular bisector construction (1995) (6)
Convex Bodies and Convexity on Grassmann Cones (VI) the Projection Functions of a Simplex (1964) (6)
Euler ' s Triangle Theorem (1999) (6)
Isohedra with nonconvex faces (1998) (6)
Sequences of Smoothed Polygons (2003) (5)
Polyhedral diagrams for sections of the non-negative orthant (1971) (5)
Additive frieze patterns and multiplication tables (1976) (5)
Isomorphism Invariants for Projective Configurations (1999) (4)
Uniform Tilings with Hollow Tiles (1981) (3)
Is there an all-purpose tile? (1986) (3)
Dense sequences of convex polytopes (1970) (3)
CYCLIC SUMS FOR POLYGONS (1999) (3)
Cyclic Product Theorems for Polygons (I) Constructions using Circles (2000) (3)
POINCARÉ DUALITY ALGEBRAS AND RINGS OF COINVARIANTS (2006) (3)
Approximation problems for combinatorial isomorphism classes of convex polytopes (1974) (3)
The enumeration of stack polytopes and simplical clusters (1982) (3)
69.14 Space filling with identical symmetrical solids (1985) (3)
A Construction for Wythoffian Polytopes (1954) (3)
A dual for Descartes’ theorem on polyhedra (1987) (2)
Some Properties of Coronas (1998) (2)
Equitransitive Tilings, or How to Discover New Mathematics* (1987) (2)
Twenty Problems on Convex Polyhedra Part I (1968) (2)
Equifacetted 4-polytopes (2008) (2)
Pratt sequences and n-gons (2000) (1)
Isohedra with dart-shaped faces (2001) (1)
Incidence Numbers of Complexes and Polytopes (1976) (1)
Some remarks on Fedotov's paper on discrete chronogeometry (1981) (1)
Some Regular Maps and Their Polyhedral Realizations (1990) (1)
A Property of Projection Functions of Parallel Convex Bodies (1966) (1)
Convex bodies and convexity on grassmann cones (X): Projection functions of parallel convex bodies (1965) (1)
Some Comments on “Juxtapositions” (1979) (1)
Erratum to "The Ninety-One Types of Isogonal Tilings in the Plane" (1979) (1)
Finite edge-to-edge tilings by convex polygons (2001) (1)
Consulting the Miners (1974) (1)
Erratum to: “The ninety-one types of isogonal tilings in the plane” (Trans. Amer. Math. Soc. 242 (1978), 335–353) (1979) (0)
How to turn a tetrahedron into a cube and similar transformations (2013) (0)
Duality of Polyhedra (2013) (0)
More interlinked loops (2009) (0)
Mathematical Proceedings of the Cambridge Philosophical Society Glasses of unipotent elements in simple algebraic groups. II (2007) (0)
Convex polygons as carriers (2016) (0)
PLANE PROJECTIONS OF REGULAR POLYTOPES WITH FIVEFOLD SYMMETRIES (1992) (0)
Do Maximal Line-Generated Triangulations of the Plane Exist? (1978) (0)
Interlinked loops (2006) (0)
Erratum to: Correction/Addendum (1999) (0)
Families of polyhedra (2013) (0)
Idiot-proof tiles (1991) (0)
Cyclic Product Theorems for Polygons (II) Constructions using Conic Sections (2001) (0)
On a Conjecture of Melzak (1964) (0)
Another generalisation of Napoleon's theorem (2009) (0)
A jigsaw problem (2009) (0)
Super and superb colouring of tilings (1988) (0)
The mathematics of a mechanical puzzle (1977) (0)
The Compleat Ceva (1999) (0)
Regular Polyhedral Clones (2013) (0)
74.2 Centroids of polygons and polyhedra (1990) (0)
Patterns in the plane from Kepler to the present, including recent results and unsolved problems. (2016) (0)

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