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HSM COXETER

  • H.S.M. Coxeter
  • Canadian geometer (1907–2003)

    the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm. Coxeter was

    H.S.M. Coxeter

    H.S.M. Coxeter

    H.S.M._Coxeter

  • Coxeter element
  • Concept in geometry

    same order. This order is known as the Coxeter number. They are named after British-Canadian geometer H.S.M. Coxeter, who introduced the groups in 1934 as

    Coxeter element

    Coxeter_element

  • 5-cube
  • 5-dimensional hypercube

    5-cube or 5-orthoplex. Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter (1991), p. 117. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 1973

    5-cube

    5-cube

  • Regular skew apeirohedron
  • Infinite regular skew polyhedron

    Machine (Paper 2) H.S.M. Coxeter, "The Regular Sponges, or Skew Polyhedra", Scripta Mathematica 6 (1939) 240–244. (Paper 22) H.S.M. Coxeter, Regular and Semi

    Regular skew apeirohedron

    Regular skew apeirohedron

    Regular_skew_apeirohedron

  • 7-cube
  • 7-dimensional hypercube

    6-simplex 6-faces. Coxeter, Regular Polytopes, p. 12, Sec. 1.8 Configurations Coxeter (1991), p. 117. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes

    7-cube

    7-cube

    7-cube

  • Uniform 7-polytope
  • Seven-dimensional geometric object

    Müller. Archived from the original (PDF) on 29 April 2025. H.S.M. Coxeter: H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: Uniform Polyhedra,

    Uniform 7-polytope

    Uniform 7-polytope

    Uniform_7-polytope

  • Uniform 6-polytope
  • Uniform 6-dimensional polytope

    uniform polytopes: 1940: The search was expanded systematically by H.S.M. Coxeter in his publication Regular and Semi-Regular Polytopes. Nonregular uniform

    Uniform 6-polytope

    Uniform 6-polytope

    Uniform_6-polytope

  • 5-cell
  • Four-dimensional analogue of the tetrahedron

    of n Dimensions, Messenger of Mathematics, Macmillan, 1900 H.S.M. Coxeter: Coxeter, H.S.M. (1973). Regular Polytopes (3rd ed.). New York: Dover. p. 120

    5-cell

    5-cell

    5-cell

  • Coxeter–Dynkin diagram
  • Pictorial representation of symmetry

    a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group

    Coxeter–Dynkin diagram

    Coxeter–Dynkin diagram

    Coxeter–Dynkin_diagram

  • Coxeter notation
  • Classification system for symmetry groups in geometry

    Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter

    Coxeter notation

    Coxeter notation

    Coxeter_notation

  • Snub (geometry)
  • Geometric operation applied to a polyhedron

    [2] (Paper 17) Coxeter, The Evolution of Coxeter–Dynkin diagrams, [Nieuw Archief voor Wiskunde 9 (1991) 233–248] (Paper 22) H.S.M. Coxeter, Regular and

    Snub (geometry)

    Snub (geometry)

    Snub_(geometry)

  • List of F4 polytopes
  • (Chapter 26) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    List of F4 polytopes

    List of F4 polytopes

    List_of_F4_polytopes

  • Uniform 10-polytope
  • Type of geometrical object

    Müller. Archived from the original (PDF) on 29 April 2025. H.S.M. Coxeter: H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: Uniform Polyhedra,

    Uniform 10-polytope

    Uniform 10-polytope

    Uniform_10-polytope

  • 16-cell
  • Four-dimensional analog of the octahedron

    Mathematics, Macmillan, 1900 H.S.M. Coxeter: Coxeter, H.S.M. (1973). Regular Polytopes (3rd ed.). New York: Dover. Coxeter, H.S.M. (1991). Regular Complex

    16-cell

    16-cell

    16-cell

  • Goldberg–Coxeter construction
  • Graph operation

    capsids that applied and expanded upon concepts from Goldberg and Fuller. H.S.M. Coxeter published an article in 1971 covering much of the same information.

    Goldberg–Coxeter construction

    Goldberg–Coxeter construction

    Goldberg–Coxeter_construction

  • Pentellated 7-cubes
  • gotesa) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Pentellated 7-cubes

    Pentellated 7-cubes

    Pentellated_7-cubes

  • 8-cube
  • 8-dimensional hypercube

    hypercubes: Coxeter, Regular Polytopes, p. 12, Sec. 1.8 Configurations Coxeter (1991), p. 117. Klitzing, Richard. "o3o3o3o3o3o3o4x - octo". H.S.M. Coxeter: Coxeter

    8-cube

    8-cube

    8-cube

  • Uniform 4-polytope
  • Class of 4-dimensional polytopes

    uniform polytopes: 1940: The search was expanded systematically by H.S.M. Coxeter in his publication Regular and Semi-Regular Polytopes. Convex uniform

    Uniform 4-polytope

    Uniform 4-polytope

    Uniform_4-polytope

  • 24-cell
  • Regular object in four dimensional geometry

    New York: Dover. Coxeter, H.S.M. (1991), Regular Complex Polytopes (2nd ed.), Cambridge: Cambridge University Press Coxeter, H.S.M. (1995), Sherk, F

    24-cell

    24-cell

    24-cell

  • 4 21 polytope
  • Polytope in 8-dimensional geometry

    vertices) in his 1912 listing of semiregular polytopes. H.S.M. Coxeter called it 421 because its Coxeter-Dynkin diagram has three branches of length 4, 2, and

    4 21 polytope

    4 21 polytope

    4_21_polytope

  • Uniform 5-polytope
  • Five-dimensional geometric shape

    uniform polytopes: 1940-1988: The search was expanded systematically by H.S.M. Coxeter in his publication Regular and Semi-Regular Polytopes I, II, and III

    Uniform 5-polytope

    Uniform 5-polytope

    Uniform_5-polytope

  • 600-cell
  • Four-dimensional analog of the icosahedron

    Mathematics, 2: 55–65, 110–120 Coxeter, H.S.M. (1973) [1948]. Regular Polytopes (3rd ed.). New York: Dover. Coxeter, H.S.M. (1991). Regular Complex Polytopes

    600-cell

    600-cell

    600-cell

  • 10-cube
  • 10-dimensional hypercube

    enneazettonic facets. Klitzing, (o3o3o3o3o3o3o3o3o4x - deker). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 1973, 3rd edition, Dover, New York, pp.

    10-cube

    10-cube

    10-cube

  • Tetrahedral-octahedral honeycomb
  • Quasiregular space-filling tesselation

    H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (1.9 Uniform space-fillings) (Paper 24) H.S.M. Coxeter

    Tetrahedral-octahedral honeycomb

    Tetrahedral-octahedral honeycomb

    Tetrahedral-octahedral_honeycomb

  • Stericated 6-cubes
  • gocax). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Stericated 6-cubes

    Stericated 6-cubes

    Stericated_6-cubes

  • Uniform 9-polytope
  • Type of geometric object

    Müller. Archived from the original (PDF) on 29 April 2025. H.S.M. Coxeter: H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: Uniform Polyhedra,

    Uniform 9-polytope

    Uniform 9-polytope

    Uniform_9-polytope

  • Uniform 8-polytope
  • Polytope contained by 7-polytope facets

    Müller. Archived from the original (PDF) on 29 April 2025. H.S.M. Coxeter: H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: Uniform Polyhedra,

    Uniform 8-polytope

    Uniform 8-polytope

    Uniform_8-polytope

  • List of planar symmetry groups
  • [2] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular

    List of planar symmetry groups

    List_of_planar_symmetry_groups

  • E6 polytope
  • Klitzing. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    E6 polytope

    E6 polytope

    E6_polytope

  • Kepler–Poinsot polyhedron
  • Any of 4 regular star polyhedra

    Machine (Paper 1) H.S.M. Coxeter, The Nine Regular Solids [Proc. Can. Math. Congress 1 (1947), 252–264, MR 8, 482] (Paper 10) H.S.M. Coxeter, Star Polytopes

    Kepler–Poinsot polyhedron

    Kepler–Poinsot polyhedron

    Kepler–Poinsot_polyhedron

  • 5-demicube
  • Regular 5-polytope

    ISBN 978-0-471-01003-6 (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular

    5-demicube

    5-demicube

    5-demicube

  • Stericated 7-orthoplexes
  • gocaz) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Stericated 7-orthoplexes

    Stericated 7-orthoplexes

    Stericated_7-orthoplexes

  • Runcinated tesseracts
  • ISBN 978-0-471-01003-6 (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular

    Runcinated tesseracts

    Runcinated tesseracts

    Runcinated_tesseracts

  • Uniform 1 k2 polytope
  • Uniform polytope

    Toronto, 1966 H.S.M. Coxeter: Regular and Semi-Regular Polytopes, Part II, Mathematische Zeitschrift, Springer, Berlin, 1985 H.S.M. Coxeter: Regular and

    Uniform 1 k2 polytope

    Uniform_1_k2_polytope

  • 4-polytope
  • Four-dimensional geometric object with flat sides

    1845 cases in 2005 H.S.M. Coxeter: Coxeter, H.S.M. (1973) [1948]. Regular Polytopes (3rd ed.). New York: Dover. H.S.M. Coxeter, M.S. Longuet-Higgins

    4-polytope

    4-polytope

    4-polytope

  • Hexicated 7-simplexes
  • Type of 7-polytope

    guph). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Hexicated 7-simplexes

    Hexicated 7-simplexes

    Hexicated_7-simplexes

  • Pentellated 6-simplexes
  • Uniform 6-polytope

    gotaf). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Pentellated 6-simplexes

    Pentellated 6-simplexes

    Pentellated_6-simplexes

  • Hexic 7-cubes
  • guthesa) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Hexic 7-cubes

    Hexic 7-cubes

    Hexic_7-cubes

  • 5-orthoplex
  • Convex regular 5-polytope in geometry

    Coxeter (1991), p. 117. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Coxeter, H.S.M. (1991) [1974]. Regular Complex

    5-orthoplex

    5-orthoplex

    5-orthoplex

  • Runcinated 5-cell
  • Four-dimensional geometrical object

    "S3s3s3s". H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Runcinated 5-cell

    Runcinated 5-cell

    Runcinated_5-cell

  • Omnitruncated simplicial honeycomb
  • (1991) Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Omnitruncated simplicial honeycomb

    Omnitruncated_simplicial_honeycomb

  • H4 polytope
  • Four-dimensional geometric objects

    (Chapter 26) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    H4 polytope

    H4 polytope

    H4_polytope

  • Four-dimensional space
  • Geometric space with four dimensions

    posthumously in 1901, and remained largely unknown until publication of H.S.M. Coxeter's Regular Polytopes in 1947. During that interval many others also discovered

    Four-dimensional space

    Four-dimensional space

    Four-dimensional_space

  • Rectified 7-simplexes
  • Convex uniform 7-polytope in seven-dimensional geometry

    - he). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Rectified 7-simplexes

    Rectified 7-simplexes

    Rectified_7-simplexes

  • Regular 4-polytope
  • Four-dimensional analogues of the regular polyhedra in three dimensions

    The Schläfli-Hess polytopes Coxeter, H.S.M. (1973) [1948]. Regular Polytopes (3rd ed.). New York: Dover. Coxeter, H.S.M. (1969). Introduction to Geometry

    Regular 4-polytope

    Regular 4-polytope

    Regular_4-polytope

  • 8-orthoplex
  • Convex regular 8-polytope

    "x3o3o3o3o3o3o4o - ek". Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter (1991), p. 117. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd

    8-orthoplex

    8-orthoplex

    8-orthoplex

  • Point groups in four dimensions
  • of the four-dimensional crystal classes 1985 H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, Coxeter notation for 4D point groups 2003 John Conway

    Point groups in four dimensions

    Point groups in four dimensions

    Point_groups_in_four_dimensions

  • 2 31 polytope
  • Uniform Polytope

    Groningen H. S. M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur

    2 31 polytope

    2 31 polytope

    2_31_polytope

  • 16-cell honeycomb
  • D3*. Conway & Sloane (1998), p. 120. Conway & Sloane (1998), p. 466. Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover, ISBN 0-486-61480-8 pp

    16-cell honeycomb

    16-cell honeycomb

    16-cell_honeycomb

  • Stericated 5-simplexes
  • gocad). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Stericated 5-simplexes

    Stericated 5-simplexes

    Stericated_5-simplexes

  • Truncated 8-simplexes
  • - be). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Truncated 8-simplexes

    Truncated 8-simplexes

    Truncated_8-simplexes

  • Skew apeirohedron
  • Infinite polyhedron with non-planar faces

    340-344 Coxeter, Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Skew apeirohedron

    Skew_apeirohedron

  • Pentic 7-cubes
  • gochesa) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Pentic 7-cubes

    Pentic 7-cubes

    Pentic_7-cubes

  • Uniform polytope
  • Isogonal polytope with uniform facets

    Müller. Archived from the original (PDF) on 29 April 2025. H.S.M. Coxeter: H.S.M. Coxeter, M.S. Longuet-Higgins and J.C.P. Miller: Uniform Polyhedra,

    Uniform polytope

    Uniform polytope

    Uniform_polytope

  • Eight-dimensional space
  • Geometric space with eight dimensions

    16-dimensional.) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Eight-dimensional space

    Eight-dimensional_space

  • Cubic honeycomb
  • Only regular space-filling tessellation of the cube

    1263789 Williams (1979), p. 199, Figure 5-38. cantic snub cubic honeycomb Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover, ISBN 0-486-61480-8 p

    Cubic honeycomb

    Cubic honeycomb

    Cubic_honeycomb

  • 10-demicube
  • Uniform 10-polytope

    73–92[77]. doi:10.2969/aspm/02710073. ISBN 978-4-931469-77-8. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 1973, 3rd edition, Dover, New York, pp.

    10-demicube

    10-demicube

    10-demicube

  • A4 polytope
  • (Chapter 26) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    A4 polytope

    A4 polytope

    A4_polytope

  • 7-orthoplex
  • Regular 7- polytope

    (x3o3o3o3o3o4o - zee). Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter (1991), p. 117. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd

    7-orthoplex

    7-orthoplex

    7-orthoplex

  • 1 32 polytope
  • Uniform polytope

    Groningen H. S. M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur

    1 32 polytope

    1 32 polytope

    1_32_polytope

  • Truncated 24-cells
  • the polytope (0, 1, 1, 0)F4 = W(F4)(ω2+ω3) H.S.M. Coxeter: Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen

    Truncated 24-cells

    Truncated 24-cells

    Truncated_24-cells

  • D4 polytope
  • (Chapter 26) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    D4 polytope

    D4_polytope

  • Vish (game)
  • process of any standard dictionary. In his book, Projective Geometry, H.S.M. Coxeter cites Vish in his discussion of definitions in mathematics: Vish illustrates

    Vish (game)

    Vish_(game)

  • Runcinated 6-cubes
  • gobpoxog). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Runcinated 6-cubes

    Runcinated_6-cubes

  • Great icosahedron
  • Kepler–Poinsot polyhedron with 20 faces

    ISBN 978-1-899618-32-3. MR 0676126. (1st Edn University of Toronto (1938)) H.S.M. Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8

    Great icosahedron

    Great icosahedron

    Great_icosahedron

  • Stericated 5-cubes
  • gacnet). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Stericated 5-cubes

    Stericated 5-cubes

    Stericated_5-cubes

  • Cantic 8-cube
  • Uniform 8-polytope

    thocto). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Cantic 8-cube

    Cantic 8-cube

    Cantic_8-cube

  • Truncated 7-simplexes
  • Uniform 7-polytope

    tattoc). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Truncated 7-simplexes

    Truncated 7-simplexes

    Truncated_7-simplexes

  • Truncated tesseract
  • Type of tesseract

    ISBN 978-0-471-01003-6 (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular

    Truncated tesseract

    Truncated_tesseract

  • 5-simplex
  • Regular 5-polytope

    "5D uniform polytopes (polytera) x3o3o3o3o — hix". Coxeter 1973, §1.8 Configurations Coxeter, H.S.M. (1991). Regular Complex Polytopes (2nd ed.). Cambridge

    5-simplex

    5-simplex

  • 1 22 polytope
  • Uniform 6-polytope

    Groningen H. S. M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur

    1 22 polytope

    1 22 polytope

    1_22_polytope

  • 7-demicube
  • Uniform 7-polytope

    unique: Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter (1991), p. 117. Klitzing, Richard. "x3o3o *b3o3o3o3o - hesa". H.S.M. Coxeter: H.S.M. Coxeter

    7-demicube

    7-demicube

    7-demicube

  • Schläfli symbol
  • Notation for polytopes and tessellations

    Semi-regular Hyperbolic Coxeter (1973), p. 143. Coxeter (1973), p. 129. Coxeter (1973), p. 138. Coxeter (1973), p. 144. Coxeter, H.S.M. (1973). Regular Polytopes

    Schläfli symbol

    Schläfli symbol

    Schläfli_symbol

  • Rectified 9-cubes
  • nav). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Rectified 9-cubes

    Rectified 9-cubes

    Rectified_9-cubes

  • Bitruncated cubic honeycomb
  • Space-filling tessellation

    Geombinatorics 4(1994), 49 - 56. Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia

    Bitruncated cubic honeycomb

    Bitruncated cubic honeycomb

    Bitruncated_cubic_honeycomb

  • Pentagonal polytope
  • Regular polytope whose 2D form is a pentagon

    also be combined. Coxeter, H. S. M.: Regular Polytopes (third edition), p. 107, p. 266 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur

    Pentagonal polytope

    Pentagonal_polytope

  • Uniform k 21 polytope
  • Geometric object

    Toronto, 1966 H.S.M. Coxeter: Regular and Semi-Regular Polytopes, Part II, Mathematische Zeitschrift, Springer, Berlin, 1985 H.S.M. Coxeter: Regular and

    Uniform k 21 polytope

    Uniform_k_21_polytope

  • Pentic 6-cubes
  • gochax) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Pentic 6-cubes

    Pentic 6-cubes

    Pentic_6-cubes

  • Trinity Mathematical Society
  • Atiyah, A.Baker; B.Birch; C.Birkar; B.Bollobás; M.Born; J.H.Conway; H.S.M.Coxeter; H.Davenport; P.Dirac; F.W.Dyson; O.R.Frisch; W.T.Gowers; G.H.Hardy;

    Trinity Mathematical Society

    Trinity Mathematical Society

    Trinity_Mathematical_Society

  • Stericated 6-simplexes
  • gacal). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Stericated 6-simplexes

    Stericated 6-simplexes

    Stericated_6-simplexes

  • Uniform honeycombs in hyperbolic space
  • Tiling of hyperbolic 3-space by uniform polyhedra

    Humphreys (1990), Reflection Groups and Coxeter Groups, Cambridge studies in advanced mathematics, 29 H.S.M. Coxeter (1954), "Regular Honeycombs in Hyperbolic

    Uniform honeycombs in hyperbolic space

    Uniform honeycombs in hyperbolic space

    Uniform_honeycombs_in_hyperbolic_space

  • 120-cell
  • Four-dimensional analog of the dodecahedron

     18–20, 6. The Coxeter Plane. Denney et al. 2020. Coxeter, H.S.M. (1973) [1948]. Regular Polytopes (3rd ed.). New York: Dover. Coxeter, H.S.M. (1991). Regular

    120-cell

    120-cell

    120-cell

  • 6-demicube
  • Uniform 6-polytope

    H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 1973, 3rd edition, Dover, New York, p. 12, Section 1.8 Configurations, ISBN 0-486-61480-8 Coxeter,

    6-demicube

    6-demicube

    6-demicube

  • Synergetics (Fuller)
  • Empirical study of systems in transformation

    geometry or mathematics, as evidenced by the opening dedication to H.S.M. Coxeter, whom Fuller considered the greatest geometer of his era. Fuller acknowledges

    Synergetics (Fuller)

    Synergetics_(Fuller)

  • B4 polytope
  • (Chapter 26) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    B4 polytope

    B4 polytope

    B4_polytope

  • Convex uniform honeycomb
  • Spatial tiling of convex uniform polyhedra

    Viking Press. ISBN 0-500-34033-1. Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia

    Convex uniform honeycomb

    Convex uniform honeycomb

    Convex_uniform_honeycomb

  • Truncated 120-cells
  • Uniform 4-polytope

    ISBN 978-0-471-01003-6 (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular

    Truncated 120-cells

    Truncated 120-cells

    Truncated_120-cells

  • Truncated 5-cell
  • 3] Coxeter group. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter

    Truncated 5-cell

    Truncated 5-cell

    Truncated_5-cell

  • Rectified 10-simplexes
  • teru). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Rectified 10-simplexes

    Rectified 10-simplexes

    Rectified_10-simplexes

  • Complex polytope
  • Generalization of a polytope in real space

    4-polytopes. Coxeter, Kaleidoscopes — Selected Writings of H.S.M. Coxeter, Paper 25 Surprising relationships among unitary reflection groups, p. 431. Coxeter (1991)

    Complex polytope

    Complex_polytope

  • 10-orthoplex
  • Convex regular polytope in 10 dimensional geometry

    Klitzing. H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    10-orthoplex

    10-orthoplex

    10-orthoplex

  • Rectified 5-cell
  • Uniform polychoron

    1965 H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Rectified 5-cell

    Rectified 5-cell

    Rectified_5-cell

  • Pentellated 7-orthoplexes
  • gotaz) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Pentellated 7-orthoplexes

    Pentellated 7-orthoplexes

    Pentellated_7-orthoplexes

  • Runcinated 8-simplexes
  • gatpeb) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Runcinated 8-simplexes

    Runcinated 8-simplexes

    Runcinated_8-simplexes

  • Rectified 7-cubes
  • sez). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Rectified 7-cubes

    Rectified 7-cubes

    Rectified_7-cubes

  • 9-orthoplex
  • Convex regular 9 dimensional polytope

    vee). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    9-orthoplex

    9-orthoplex

    9-orthoplex

  • Stericated 7-simplexes
  • gabach). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Stericated 7-simplexes

    Stericated 7-simplexes

    Stericated_7-simplexes

  • Hexicated 7-orthoplexes
  • Convex uniform 7-polytope

    heptacross H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Hexicated 7-orthoplexes

    Hexicated 7-orthoplexes

    Hexicated_7-orthoplexes

  • 1 42 polytope
  • Uniform 8 dimensional polytope

    buffy). H. S. M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur

    1 42 polytope

    1 42 polytope

    1_42_polytope

  • Runcinated 6-simplexes
  • gibpof). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited

    Runcinated 6-simplexes

    Runcinated 6-simplexes

    Runcinated_6-simplexes

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