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User:Daniel Forgues/Backup/Figurate numbers

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Classifications of figurate numbers (via numbered lists)

  1. Category:Figurate numbers (by increasing number of vertices)
    1. Figurate numbers
    2. Category:Regular polytope numbers (by increasing number of vertices)
      1. Regular polytope numbers
      2. Category:Simplicial polytopic numbers
        1. Simplicial polytopic numbers or Regular simplex numbers or Simplex numbers or numbers, dimensionality d ≥ 0
        2. Triangular numbers (3-sided Polygonal numbers or 2-D Simplicial polytopic numbers)
        3. Tetrahedral numbers (4-faced Platonic numbers or 3-D Simplicial polytopic numbers)
        4. Hypertetrahedral numbers (REDIRECT to Simplicial polytopic numbers)
      3. Category:Centered simplicial polytopic numbers
        1. Centered simplicial polytopic numbers or Centered regular simplex numbers or Centered simplex numbers or centered numbers, dimensionality d ≥ 0
        2. Centered triangular numbers (3-sided Centered polygonal numbers or 2-D Centered simplicial polytopic numbers)
        3. Centered tetrahedral numbers (4-faced Centered Platonic numbers or 3-D Centered simplicial polytopic numbers)
        4. Centered hypertetrahedral numbers (REDIRECT to Centered simplicial polytopic numbers)
      4. Category:Orthoplicial polytopic numbers
        1. Orthoplicial polytopic numbers or Orthoplex numbers or Cross polytope numbers or numbers, dimensionality d ≥ 0
        2. Square numbers (4-sided Polygonal numbers, 2-D Regular orthotopic numbers or 2-D Orthoplicial polytopic numbers)
        3. Octahedral numbers or Square dipyramidal numbers (8-faced Platonic numbers or 3-D Orthoplicial polytopic numbers)
        4. Hyperoctahedral numbers (REDIRECT to Orthoplicial polytopic numbers)
      5. Category:Centered orthoplicial polytopic numbers
        1. Centered orthoplicial polytopic numbers or Centered orthoplex numbers or Centered cross polytope numbers or centered numbers, dimensionality d ≥ 0
        2. Centered square numbers (4-sided Centered polygonal numbers, 2-D Centered regular orthotopic numbers or 2-D Centered orthoplicial polytopic numbers)
        3. Centered octahedral numbers or (Centered squares) dipyramidal numbers (8-faced Centered Platonic numbers or 3-D Centered orthoplicial polytopic numbers)
        4. Centered hyperoctahedral numbers (REDIRECT to Centered orthoplicial polytopic numbers)
      6. Category:Regular orthotopic numbers
        1. Regular orthotopic numbers or Orthotope numbers or Measure polytope numbers or numbers, dimensionality d ≥ 0
        2. Square numbers (4-sided Polygonal numbers, 2-D Regular orthotopic numbers or 2-D Orthoplicial polytopic numbers)
        3. Cubic numbers (6-faced Platonic numbers or 3-D Regular orthotopic numbers)
        4. Hypercubic numbers (REDIRECT to Regular orthotopic numbers)
      7. Category:Centered regular orthotopic numbers
        1. Centered regular orthotopic numbers or Centered orthotope numbers or Centered measure polytope numbers or centered numbers, dimensionality d ≥ 0
        2. Centered square numbers (4-sided Centered polygonal numbers, 2-D Centered regular orthotopic numbers or 2-D Centered orthoplicial polytopic numbers)
        3. Centered cubic numbers (6-faced Centered Platonic numbers or 3-D Centered regular orthotopic numbers)
        4. Centered hypercubic numbers (REDIRECT to Centered regular orthotopic numbers)
    3. Category:Nonregular polytope numbers (by increasing number of vertices)
      1. Nonregular polytope numbers (created as stub)
      2. Category:Hyperpyramidal numbers
        1. Category:Square hyperpyramidal numbers
          1. Square hyperpyramidal numbers
        2. Category:Centered square hyperpyramidal numbers REDIRECT to Category:(Centered squares) hyperpyramidal numbers
          NOTE: The (centered squares) hyperpyramidal numbers ARE NOT GLOBALLY CENTERED (only the original squares are)
          1. Centered square hyperpyramidal numbers REDIRECT to (Centered squares) hyperpyramidal numbers
        3. Category:3-dimensional hyperpyramidal numbers
          1. Category:Pyramidal numbers
            1. Pyramidal numbers
          2. Category:Centered pyramidal numbers REDIRECT to Category:(Centered polygons) pyramidal numbers
            NOTE: The (centered polygons) pyramidal numbers ARE NOT GLOBALLY CENTERED (only the original polygons are)
            1. Centered pyramidal numbers REDIRECT to (Centered polygons) pyramidal numbers
    4. Category:0-dimensional figurate numbers (by increasing number of vertices)
      1. Category:0-dimensional regular polytope numbers
        1. Category:Point numbers
          1. Point numbers {0, 1} (The convention being that figurate numbers have the initial dot for n = 1.)
          2. 0-dimensional regular polytope numbers (REDIRECT to Point numbers)
        2. Category:Centered point numbers
          1. Centered point numbers {1} (The convention being that centered figurate numbers have the central dot for n = 0.)
          2. Centered 0-dimensional regular polytope numbers (REDIRECT to Centered point numbers)
    5. Category:1-dimensional figurate numbers (by increasing number of vertices)
      1. Category:1-dimensional regular polytope numbers
        1. Category:Gnomonic numbers
          1. Gnomonic numbers
          2. 1-dimensional regular polytope numbers (REDIRECT to Gnomonic numbers)
        2. Category:Centered gnomonic numbers
          1. Centered gnomonic numbers
          2. Centered 1-dimensional regular polytope numbers (REDIRECT to Centered gnomonic numbers)
    6. Category:2-dimensional figurate numbers (by increasing number of vertices)
      1. Category:2-dimensional regular polytope numbers
        1. Category:Polygonal numbers
          1. Polygonal numbers
          2. 2-dimensional regular polytope numbers (REDIRECT to Polygonal numbers)
          3. Triangular numbers (3-sided Polygonal numbers or 2-D Simplicial polytopic numbers)
          4. Square numbers (4-sided Polygonal numbers, 2-D Regular orthotopic numbers or 2-D Orthoplicial polytopic numbers)
          5. Pentagonal numbers (5-sided Polygonal numbers)
          6. Hexagonal numbers (6-sided Polygonal numbers)
          7. Heptagonal numbers (7-sided Polygonal numbers)
          8. Octagonal numbers (8-sided Polygonal numbers)
          9. Dodecagonal numbers (12-sided Polygonal numbers)
          10. Icosagonal numbers (20-sided Polygonal numbers)
        2. Category:Centered polygonal numbers
          1. Centered polygonal numbers
          2. Centered 2-dimensional regular polytope numbers (REDIRECT to Centered polygonal numbers)
          3. Centered triangular numbers (3-sided Centered polygonal numbers or 2-D Centered simplicial polytopic numbers)
          4. Centered square numbers (4-sided Centered polygonal numbers, 2-D Centered regular orthotopic numbers or 2-D Centered orthoplicial polytopic numbers)
          5. Centered pentagonal numbers (5-sided Centered polygonal numbers)
          6. Centered hexagonal numbers or Hex numbers (6-sided Centered polygonal numbers)
          7. Centered heptagonal numbers (7-sided Centered polygonal numbers)
          8. Centered octagonal numbers (8-sided Centered polygonal numbers)
          9. Centered dodecagonal numbers (12-sided Centered polygonal numbers)
          10. Centered icosagonal numbers (20-sided Centered polygonal numbers)
    7. Category:3-dimensional figurate numbers (by increasing number of vertices)
      1. Category:3-dimensional regular polytope numbers
        1. Category:Platonic numbers
          1. Platonic numbers
          2. 3-dimensional regular polytope numbers (REDIRECT to Platonic numbers)
          3. Tetrahedral numbers (4-faced Platonic numbers or 3-D Simplicial polytopic numbers)
          4. Octahedral numbers or Square dipyramidal numbers (8-faced Platonic numbers or 3-D Orthoplicial polytopic numbers)
          5. Cubic numbers (6-faced Platonic numbers or 3-D Regular orthotopic numbers)
          6. Icosahedral numbers (REDIRECT to 20-faced Platonic numbers)
          7. Dodecahedral numbers (REDIRECT to 12-faced Platonic numbers)
        2. Category:Centered Platonic numbers
          1. Centered Platonic numbers
          2. Centered 3-dimensional regular polytope numbers (REDIRECT to Centered Platonic numbers)
          3. Centered tetrahedral numbers (4-faced Centered Platonic numbers or 3-D Centered simplicial polytopic numbers)
          4. Centered octahedral numbers or (Centered squares) dipyramidal numbers or (8-faced Centered Platonic numbers or 3-D Centered orthoplicial polytopic numbers)
          5. Centered cubic numbers (6-faced Centered Platonic numbers or 3-D Centered regular orthotopic numbers)
          6. Centered icosahedral numbers (REDIRECT to 20-faced Centered Platonic numbers)
          7. Centered dodecahedral numbers (REDIRECT to 12-faced Centered Platonic numbers)
      2. Category:3-dimensional nonregular polytope numbers
        1. Category:Pyramidal numbers
          1. Pyramidal numbers
        2. Category:Centered pyramidal numbers REDIRECT to Category:(Centered polygons) pyramidal numbers
          NOTE: The (centered polygons) pyramidal numbers ARE NOT GLOBALLY CENTERED (only the original polygons are)
          1. Centered pyramidal numbers REDIRECT to (Centered polygons) pyramidal numbers
    8. Category:4-dimensional figurate numbers (by increasing number of vertices)
      1. Category:4-dimensional regular polytope numbers
        1. Category:Regular polychoron numbers
          1. Regular polychoron numbers
          2. 4-dimensional regular polytope numbers (REDIRECT to Regular polychoron numbers)
          3. Pentachoron numbers (5-celled Regular polychoron numbers or 4-D Simplicial polytopic numbers)
          4. Tetracross numbers (16-celled Regular polychoron numbers or 4-D Orthoplicial polytopic numbers)
          5. Tesseract numbers (8-celled Regular polychoron numbers or 4-D Regular orthotopic numbers)
          6. 24-cell numbers (REDIRECT to 24-celled Regular polychoron numbers)
          7. Hypericosahedral numbers or 600-cell numbers (both REDIRECT to 600-celled Regular polychoron numbers)
          8. Hyperdodecahedral numbers or 120-cell numbers (both REDIRECT to 120-celled Regular polychoron numbers)
        2. Category:Centered regular polychoron numbers
          1. Centered regular polychoron numbers
          2. Centered 4-dimensional regular polytope numbers (REDIRECT to Centered regular polychoron numbers)
          3. Centered pentachoron numbers (5-celled Centered regular polychoron numbers or 4-D Centered simplicial polytopic numbers)
          4. Centered tetracross numbers (16-celled Centered regular polychoron numbers or 4-D Centered orthoplicial polytopic numbers)
          5. Centered tesseract numbers (8-celled Centered regular polychoron numbers or 4-D Centered regular orthotopic numbers)
          6. Centered 24-cell numbers (REDIRECT to 24-celled Centered regular polychoron numbers)
          7. Centered hypericosahedral numbers or Centered 600-cell numbers (both REDIRECT to 600-celled Centered regular polychoron numbers)
          8. Centered hyperdodecahedral numbers or Centered 120-cell numbers (both REDIRECT to 120-celled Centered regular polychoron numbers)