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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 ${\displaystyle \alpha _{d}\,}$ 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 ${\displaystyle \alpha _{d}\,}$ 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 ${\displaystyle \beta _{d}\,}$ 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 ${\displaystyle \beta _{d}\,}$ 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 ${\displaystyle \gamma _{d}\,}$ 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 ${\displaystyle \gamma _{d}\,}$ 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
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
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)