Harold Scott MacDonald Coxeter

Harold Scott MacDonald Coxeter's AcademicInfluence.com Rankings

Mathematics

#82

World Rank

#230

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Measure Theory

#107

World Rank

#169

Historical Rank

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Mathematics

Why Is Harold Scott MacDonald Coxeter Influential?

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According to Wikipedia, Harold Scott MacDonald "Donald" Coxeter was a British-Canadian geometer and mathematician. He is regarded as one of the greatest geometers of the 20th century. Biography Coxeter was born in Kensington, England, to Harold Samuel Coxeter and Lucy . His father had taken over the family business of Coxeter & Son, manufacturers of surgical instruments and compressed gases , but was able to retire early and focus on sculpting and baritone singing; Lucy Coxeter was a portrait and landscape painter who had attended the Royal Academy of Arts. A maternal cousin was the architect Sir Giles Gilbert Scott.

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Harold Scott MacDonald Coxeter's Published Works

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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

Generators and relations for discrete groups (1957) (1946)
Introduction to Geometry (1961) (1401)
Regular Complex Polytopes (1991) (378)
Self-dual configurations and regular graphs (1950) (351)
Discrete Groups Generated by Reflections (1934) (263)
Triangulated polygons and frieze patterns (1973) (188)
The product of the generators of a finite group generated by reflections (1951) (174)
A practical method for enumerating cosets of a finite abstract group (1936) (159)
The Real Projective Plane (1992) (156)
The Complete Enumeration of Finite Groups of the Form Ri2=(RiRj)kij=1 (1935) (148)
Regular Skew Polyhedra in Three and Four Dimension, and their Topological Analogues (1938) (142)
Integral Cayley numbers (1946) (142)
Non-Euclidean geometry (1961) (140)
The Geometric vein : the Coxeter Festschrift (1981) (140)
The abstract groups (1939) (109)
The Problem of Apollonius (1968) (102)
Twelve Geometric Essays (1968) (92)
Close-Packing and Froth (1958) (90)
REGULAR HONEYCOMBS IN HYPERBOLIC SPACE (1956) (89)
THE FUNCTIONS OF SCHLÄFLI AND LOBATSCHEFSKY (1935) (87)
Geometry Revisited (New Mathematical Library) (1967) (86)
Quaternions and Reflections (1946) (84)
Geometry and Algebra in Ancient Civilizations (1985) (82)
Regular and semi-regular polytopes. II (1940) (77)
Twelve points in PG(5, 3) with 95040 self-transformations (1958) (76)
The Non-Euclidean Symmetry of Escher’s Picture ‘Circle Limit III’ (1979) (71)
A Problem of Collinear Points (1948) (60)
Covering space with equal spheres (1959) (59)
Extreme Forms (1951) (58)
Beyond The Third Dimension (1990) (55)
World-structure and non-Euclidean honeycombs (1950) (55)
Finite groups generated by unitary reflections (1967) (54)
A Geometrical Background for De Sitter's World (1943) (53)
The Polytope 2 21 Whose Twenty-Seven Vertices Correspond to the Lines to the General Cubic Surface (1940) (52)
The problem of packing a number of equal nonoverlapping circles on a sphere (1962) (52)
Wythoff's Construction for Uniform Polytopes (1935) (52)
Regular and semi-regular polytopes. I (1940) (50)
The Role of intermediate convergents in Tait's explanation for phyllotaxis (1972) (48)
Geometry Revisited: Preface (1967) (48)
An Extreme Duodenary Form (1953) (46)
Groups Generated by Unitary Reflections of Period Two (1957) (40)
Angels and Devils (1981) (37)
Triangulated polygons and frieze patterns (1973) (37)
The Polytopes with Regular‐Prismatic Vertex Figures (1932) (36)
Regular 3-complexes with toroidal cells (1977) (35)
Mathematical recreations & essays (1960) (34)
Ten toroids and fifty-seven hemi-dodecahedra (1982) (34)
Geometry Revisited by H.S.M. Coxeter (1967) (34)
The binary polyhedral groups, and other generalizations of the quaternion group (1940) (34)
A Symmetrical Arrangement of Eleven Hemi-Icosahedra (1984) (34)
The Fifty-Nine Icosahedra (1938) (34)
The trigonometry of escher’s woodcut “circle limit III“ (1996) (32)
Affinely regular polygons (1969) (31)
Finite groups generated by reflections, and their subgroups generated by reflections (1934) (31)
Foundations of Geometry (1962) (30)
Loxodromic sequences of tangent spheres (1968) (30)
The Optimal Ball and Horoball Packings of the Coxeter Tilings in the Hyperbolic 3-space (2005) (28)
Desargues configurations and their collineation groups (1975) (28)
The Coxeter legacy : reflections and projections (2006) (28)
Non-Euclidean Geometry: Fifth Edition (1965) (26)
The Pure Archimedean Polytopes in Six and Seven Dimensions (1928) (25)
The Beauty Of Geometry (1999) (25)
SOME APPLICATIONS OF TRILINEAR COORDINATES (1995) (24)
Some families of finite groups having two generators and two relations (1977) (24)
Generalized Clifford Parallelism (1971) (24)
Arrangements of equal spheres in non-Euclidean spaces (1954) (23)
On Laves' Graph Of Girth Ten (1955) (23)
The inversive plane and hyperbolic space (1966) (21)
Regular compound tessellations of the hyperbolic plane (1964) (20)
The Simplicial Helix and the Equation tan nθ = n tan θ (1985) (19)
Zero-symmetric graphs: Trivalent graphical regular representations of groups (1981) (19)
M.C. Escher: Art and Science (1987) (18)
Regular and semi-regular polytopes. III (1988) (18)
Trisecting an orthoscheme (1989) (18)
The pappus configuration and the self-inscribed octagon. III (1977) (18)
Groups Whose Fundamental Regions Are Simplexes (1931) (17)
Uniform polyhedra (1954) (16)
The Polytopes with Regular-Prismatic Vertex Figures (16)
Problems for Solution: 4603-4607 (1954) (16)
Regular Compound Polytopes in More Than Four Dimensions (1933) (15)
Frieze Patterns, Triangulated Polygons and Dichromatic Symmetry (1994) (15)
Non-euclidean geometries : the Cayley-Klein approach (2010) (15)
The Evolution of Coxeter-Dynkin Diagrams (1994) (15)
Twisted honeycombs {3, 5, 3}t and their groups (1984) (14)
Inversive distance (1966) (13)
Parallel lines (1978) (12)
The total length of the edges of a non-Euclidean polyhedron with triangular faces (1963) (12)
The Abstract Group G3, 7, 16 (1962) (12)
A simple introduction to colored symmetry (1987) (12)
The beauty of geometry : twelve essays (1999) (12)
Regular Honeycombs in Elliptic Space (1954) (11)
A NEW TRIVALENT SYMMETRICAL GRAPH WITH 110 VERTICES (1979) (11)
The Circumradius of the General Simplex (1930) (11)
1142. An n-dimensional extension of Pythagoras' Theorem (1935) (11)
Gauss as a geometer (1977) (10)
The space-time continuum (1975) (10)
The Trigonometry of Hyperbolic Tessellations (1997) (10)
Symmetrical combinations of three or four hollow triangles (1994) (10)
The symmetry groups of the regular complex polygons (1962) (10)
Portraits of a Family of Complex Polytopes (1993) (10)
The map-coloring of unorientable surfaces (1943) (9)
The lehmus inequality (1985) (9)
Numerical distances among the spheres in a loxodromic sequence (1997) (9)
The groups determined by the relations $S^l=T^m=(S^{-1}T^{-1}ST)^p=1$. Part I (1936) (9)
ZERO-SYMMETRIC GRAPHS OF GIRTH 3 (1981) (9)
Non-Euclidean Geometry by H. S. M. Coxeter (1998) (9)
The Representation of Conformal Space on a Quadric (1936) (9)
Mathmatical Recreations & Essays: 12th Edition (1974) (8)
The equianharmonic surface and the Hessian polyhedron (1974) (8)
Review: W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry. Vol. 2 (1952) (8)
Groups Generated by Reflections (1957) (8)
The Twenty-Seven Lines on the Cubic Surface (1983) (8)
The Abstract Groups Rm = Sm = (RiSi)Pi = 1, Sm = T2 = (SiT)2Pi = 1, AND Sm = T2 = (S−iTSiT)Pi = 1 (1936) (8)
Abstract definitions for the symmetry groups of the regular polytopes, in terms of two generators. Part II: the rotation groups (1936) (7)
The Densities of the Regular Polytopes (1931) (7)
Affine regularity (1992) (7)
THE FCC LATTICE AND THE CUSPED HYPERBOLIC 4-ORBIFOLD OF MINIMAL VOLUME THIERRY HILD (2007) (7)
The Chords of the Non-Ruled Quadric In PG(3, 3) (1958) (7)
A method for proving certain abstract groups to be infinite (1940) (7)
On points with arbitrarily assigned mutual distances (1934) (6)
The Derivation of Schoenberg's Star-Polytopes from Schoute's Simplex Nets (1981) (6)
THE GENERALIZED PETERSEN GRAPH G(24, 5) (1986) (6)
Non-Euclidean Geometry: AREA (1998) (6)
The Erlangen Program (1977) (5)
An Absolute Property of Four Mutually Tangent Circles (2006) (5)
Notes on the Plates (1982) (5)
Review: A. F. Wells, Three-dimensional nets and polyhedra (1978) (5)
Cyclotomic integers, nondiscrete tessellations, and quasicrystals (1993) (5)
Geometry Revisited: Contents (1967) (5)
Face-transitive polyhedra with rectangular faces and icosahedral symmetry (2001) (4)
Star polytopes and the Schläfli function f(... (1989) (4)
Loxodromic sequences of tangent spheres (1968) (4)
N‐DIMENSIONAL CRYSTALLOGRAPHY (Pitman Research Notes in Mathematics, 41) (1981) (4)
11.3. Kepler and mathematics (1975) (4)
Geometry Revisited: Collinearity and Concurrence (1967) (4)
Philon lines in non-Euclidean planes (1993) (4)
Mid-Circles and Loxodromes (1968) (4)
The dirac matrix group and other generalizations of the quaternion group (1973) (4)
Polytopes Over GF(2) and their Relevance for the Cubic Surface Group (1959) (3)
The product of three reflections (1947) (3)
Problems for Solution: E711-E715 (1946) (3)
On Simple Isomorphism between Abstract Groups (1934) (3)
Surprising relationships among unitary reflection groups (1984) (3)
Beyond the Third Dimension. By Thomas F. Banchoff (1991) (2)
Geometry Revisited: Some Properties of Circles (1967) (2)
An Abstract Definition for the Alternating Group in Terms of Two Generators (1936) (2)
Problems for Solution: 3882-3887 (1938) (2)
Cayley Diagrams and Regular Complex Polygons (1973) (2)
The densities of the regular polytopes, Part 2 (1932) (2)
Coordinates for the Regular Complex Polygons (1997) (2)
A Finite Projective Plane (1974) (2)
Inversive geometry (1971) (2)
Orthogonal trees (1991) (2)
Five Spheres in Mutual Contact (2000) (2)
An Easy Method for Constructing Polyhedral Group-Pictures (1938) (2)
FRIEZE PATTERNS FOR REGULAR STAR POLYTOPES AND STATISTICAL HONEYCOMBS (2000) (2)
The Mathematics of Map Coloring (1971) (1)
The Trigonometry of Escher’s Woodcut Circle Limit III (2003) (1)
Sphere Packings, Lattices and Groups. By J. H. Conway and N. J. A. Sloane (1989) (1)
An Ancient Tragedy (1971) (1)
Some Regular Maps and Their Polyhedral Realizations (1990) (1)
Packing and Covering (C. A. Rogers) (1965) (1)
Numerical Distances among the Circles in a Loxodromic Sequence (1999) (1)
THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY (1998) (1)
Abstract Definitions for the Symmetry Groups of the Regular Polytopes, in Terms of Two Generators. Part I: The Complete Groups (1936) (1)
Problems for Solution: 4523-4527 (1953) (1)
Quaternions and Reflections (Postscript) (1946) (1)
A Challenging Definite Integral (1988) (1)
M.C. Escher : art and science : proceedings of the International Congress on M.C. Escher, Rome, Italy, 26-28 March, 1985 (1986) (1)
Geometry Revisited: An Introduction to Inversive Geometry (1967) (1)
Elementary Problems: E2581-E2586 (1976) (1)
Reciprocating the Regular Polytopes (1997) (1)
The Introduction of Coordinates (1993) (0)
Problems for Solution: 4176-4180 (1945) (0)
Analytical Geometry: Analytical Geometry of Three Dimensions . By W. H. McCrea. (University Mathematical Texts, No. 7.) vii + 144 pp. Edinburgh: Oliver and Boyd. New York: Interscience Publishers. 1942. $1.75. (1945) (0)
TRIVALENT CAYLEY GRAPHS; THE LCF AND FRUCHT NOTATIONS (1981) (0)
III. Geometrical Recreations (1974) (0)
Index to the Mathematical Gazette (1975) (0)
Letter to the Editor (1976) (0)
Non-Euclidean Geometry: APPENDIX: ANGLES AND ARCS IN THE HYPERBOLIC PLANE (1998) (0)
I. Arithmetical Recreations (1974) (0)
Geometry Revisited: Hints and Answers to Exercises (1967) (0)
Problems for Solution: 4061-4064 (1942) (0)
Report on the Canadian Journal of Mathematics (1956-1957) (1958) (0)
Geometry Revisited: Glossary (1967) (0)
MORE 0-SYMMETRIC GRAPHS OF GIRTH 4 WITH 96 OR 120 VERTICES (1981) (0)
On Wigner’s problem of reflected light signals in de Sitter space (1961) (0)
Geometry Revisited: Transformations (1967) (0)
XIII. Calculating Prodigies (1974) (0)
Letters to the editor (1995) (0)
Graphs, Maps and Cayley Diagrams (1957) (0)
GENERAL REMARKS ON GRAPHS OF TYPE 1 Z (1981) (0)
Hyperbolic Tessellations and Fundamental Groups (1957) (0)
Cyclic, Dicyclic and Metacyclic Groups (1957) (0)
Rational spherical triangles (1982) (0)
Regular Figures. L. Fejes Tóth. Pergamon, London; Macmillan, New York, 1964. xii + 339 pp. Illus. $12 (1964) (0)
IX. Unicursal Problems (1974) (0)
CAYLEY GRAPHS OF DIRECT PRODUCTS OF DIHEDRAL GROUPS (1981) (0)
Problems for Solution: 4136-4140 (1944) (0)
An Alternative Enumeration, by Considering Solid Cells (1982) (0)
Non-Euclidean Geometry: ELLIPTIC GEOMETRY IN THREE DIMENSIONS (1998) (0)
Problems for Solution: E436-E440 (1940) (0)
Errata to “Crystallographic groups of four-dimensional space” (1980) (0)
Seven Cubes and Ten 24-Cells (1998) (0)
PRELIMINARIES ON CAYLEY GRAPHS OF GIRTH 6 FOR DIHEDRAL AND RELATED GROUPS (1981) (0)
A PROCEDURE FOR OBTAINING BIPARTITE CAYLEY GRAPHS OF GIRTH 4 (1981) (0)
Problems for Solution: E626-E630 (1944) (0)
Problems for Solution: 4141-4144 (1944) (0)
and Tony Bomford ’ s Colored Hyperbolic Rugs (0)
Complete Enumeration of Stellated Icosahedra, by Considering the Possible Faces (1982) (0)
Problems for Solution: 4161-4165 (1945) (0)
GRAPHS OF TYPE 1 Z THAT ARE CAYLEY GRAPHS OF GROUPS Z(m,n,k), n > 2 (1981) (0)
GRAPHS OF TYPE 1 Z AND GIRTH 4 THAT ARE CAYLEY GRAPHS OF GROUPS Z(m,2,k) (1981) (0)
THE CAYLEY GRAPHS OF COXETER'S GROUPS G p,q,r (1981) (0)
Geometry Revisited: Dedication (1967) (0)
Reflections of a Mathematician, by L. J. Mordell. Canadian Mathematical Congress, 1959. vii + 50 pages, $1.00. (1960) (0)
YET ANOTHER 0-SYMMETRIC GRAPH WITH 96 VERTICES (1981) (0)
Book Review (1985) (0)
Preface to the Twelfth Edition (1974) (0)
Corrigendum: Abstract Groups of the Form Vik=Vj3=(ViVj)2=1* (1934) (0)
II. Arithmetical Recreations (Continued) (1974) (0)
The Generalized Kaleidoscope (1940) (0)
Elementary Problems: E1915-E1924 (1966) (0)
Book Review:The Secrets of Ancient Geometry--And Its Uses Tons Brunes, Charles M. Napier (1973) (0)
IV. Geometrical Recreations (Continued) (1974) (0)
A Comparison of Various Kinds of Geometry (1993) (0)
THE CAYLEY GRAPHS OF THE GROUPS F 3,2,-1 AND F 4,2,1 ; THE EXTENDED LCF NOTATION (1981) (0)
CAYLEY GRAPHS (IN GENERAL) (1981) (0)
CAYLEY GRAPHS OF GENERALIZED DIHEDRAL GROUPS (1981) (0)
The Erlangen Program (1977) (0)
Systematic Enumeration of Cosets (1957) (0)
Triangles and Quadrangles (1974) (0)
Geometry Revisited: Note to the Reader (1967) (0)
Geometry Revisited: Points and Lines Connected with a Triangle (1967) (0)
Review: Harold Brown, Rolf Bülow, Joachim Neubüser, Hans Wondratschek and Hans Zassenhaus, Crystallographic groups of four-dimensional space (1979) (0)
Erratum to: Numerical Distances Among the Spheres in a Loxodromic Sequence (1998) (0)
The Use of Coordinates (1993) (0)
THE COMPANION GRAPHS OF CAYLEY GRAPHS OF GIRTH 4 (1981) (0)
Modular and Linear Fractional Groups (1957) (0)
The Principle of Duality (1974) (0)
A Modern View of Geometry, by L. M. Blumenthal. Freeman, San Francisco, 1961. xii + 191 pages. $2.25. (1962) (0)
Review: W. V. D. Hodge and Daniel Pedoe, Methods of algebraic geometry (1949) (0)
Geometry Revisited: An Introduction to Projective Geometry (1967) (0)
Elementary Problems: E1739-E1747 (1964) (0)
VIII. Map-Colouring Problems (1974) (0)
Escher's lizards (1988) (0)
Non-Euclidean Geometry: DESCRIPTIVE GEOMETRY (1998) (0)
The Symmetric, Alternating, and other Special Groups (1957) (0)
Preface to the Eleventh Edition (1974) (0)
Order and Continuity (1993) (0)
VI. Chess-Board Recreations (1974) (0)
XI. Miscellaneous Problems (1974) (0)
Problems for Solution: 4082-4085 (1943) (0)
Problems for Solution (1961) (0)
X. Combinatorial Designs (1974) (0)
XII. Three Classical Geometrical Problems (1974) (0)
Geometry Revisited: References (1967) (0)
Abstract Groups of the Form V1k = Vi3 = (ViVi)2 = 1 (1934) (0)
CAYLEY GRAPHS OF DIHEDRAL GROUPS WITH ONE REDUNDANT GENERATOR (1981) (0)
THE PARAMETERS OF CAYLEY GRAPHS OF GROUPS WITH THREE INVOLUTORY GENERATORS (1981) (0)
THE GROUPS Z(m,n,k) (1981) (0)
ENUMERATION OF FINITE GROUPS OF THE FORM (2006) (0)
The Abstract Group G3,7,16: A Correction (1962) (0)
MORE 0-SYMMETRIC CAYLEY GRAPHS OF Z(m,n,k) OBTAINED BY CHANGE OF GENERATORS (1981) (0)
2581. The Area of a Hyperbolic Sector (1955) (0)
REFLECTED LIGHT SIGNALS. (1967) (0)
THE JUXTAPOSITION PROCEDURE (1981) (0)
XIV. Cryptography and Cryptanalysis (1974) (0)
Problems Dedicated to Emory P. Starke: S1-S3 (1979) (0)
ELLIPTIC GEOMETRY IN TWO DIMENSIONS (1998) (0)
Escher’s Fondness for Animals (2003) (0)
Projectivities on a Conic (1993) (0)
VII. Magic Squares (1974) (0)
Harold Coxeter Interview October 1978 (1978) (0)
THE CAYLEY GRAPHS OF THE GROUPS B(m,k) (1981) (0)
TECHNICAL NOTES AND SHORT PAPERS A Method for the Numerical Evaluation of Certain Infinite Integrals (1957) (0)
One-Dimensional Projectivities (1993) (0)
GENERAL REMARKS ON 0-SYMMETRIC GRAPHS (1981) (0)
The Fundamental Theorem and Pappus’s Theorem (1974) (0)
The Problem of Apollonius1 (1968) (0)
Preface to the Tenth Edition (1974) (0)
Problems for Solution: E396-E400 (1939) (0)
Discussions and Notes (1946) (0)
The Conic, Continued (1974) (0)
COMPANION GRAPHS OF HIGHER GIRTH (1981) (0)

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