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# User:Daniel Forgues/Contributions/Figurate numbers

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### In progress (Figurate numbers)

Category:Figurate numbers (by increasing number of vertices)
Figurate numbers
Category:Classifications of figurate numbers
Classifications of figurate numbers
Category:Regular polytope numbers (by increasing number of vertices)
Regular polytope numbers
 Category:Simplicial polytopic numbers Simplicial polytopic numbers or Regular simplex numbers or Simplex numbers or ${\displaystyle \alpha _{d}\,}$ numbers (dimensionality ${\displaystyle \scriptstyle d\,\geq \,0\,}$) Triangular numbers (3-sided Polygonal numbers or 2-D Simplicial polytopic numbers) Tetrahedral numbers (4-faced Platonic numbers or 3-D Simplicial polytopic numbers) Hypertetrahedral numbers (REDIRECT to Simplicial polytopic numbers)
 Category:Centered simplicial polytopic numbers Centered simplicial polytopic numbers or Centered regular simplex numbers or Centered simplex numbers or centered ${\displaystyle \alpha _{d}\,}$ numbers (dimensionality ${\displaystyle \scriptstyle d\,\geq \,0\,}$) Centered triangular numbers (3-sided Centered polygonal numbers or 2-D Centered simplicial polytopic numbers) Centered tetrahedral numbers (4-faced Centered Platonic numbers or 3-D Centered simplicial polytopic numbers) Centered hypertetrahedral numbers (REDIRECT to Centered simplicial polytopic numbers)
 Category:Orthoplicial polytopic numbers Orthoplicial polytopic numbers or Orthoplex numbers or Cross polytope numbers or ${\displaystyle \beta _{d}\,}$ numbers (dimensionality ${\displaystyle \scriptstyle d\,\geq \,0\,}$) Square numbers (4-sided Polygonal numbers, 2-D Regular orthotopic numbers or 2-D Orthoplicial polytopic numbers) Octahedral numbers or Square dipyramidal numbers (8-faced Platonic numbers or 3-D Orthoplicial polytopic numbers) Hyperoctahedral numbers (REDIRECT to Orthoplicial polytopic numbers)
 Category:Centered orthoplicial polytopic numbers Centered orthoplicial polytopic numbers or Centered orthoplex numbers or Centered cross polytope numbers or centered ${\displaystyle \beta _{d}\,}$ numbers (dimensionality ${\displaystyle \scriptstyle d\,\geq \,0\,}$) Centered square numbers (4-sided Centered polygonal numbers, 2-D Centered regular orthotopic numbers or 2-D Centered orthoplicial polytopic numbers) Centered octahedral numbers or (Centered squares) dipyramidal numbers (8-faced Centered Platonic numbers or 3-D Centered orthoplicial polytopic numbers) Centered hyperoctahedral numbers (REDIRECT to Centered orthoplicial polytopic numbers)
 Category:Regular orthotopic numbers Regular orthotopic numbers or Orthotope numbers or Measure polytope numbers or ${\displaystyle \gamma _{d}\,}$ numbers (dimensionality ${\displaystyle \scriptstyle d\,\geq \,0\,}$) Square numbers (4-sided Polygonal numbers, 2-D Regular orthotopic numbers or 2-D Orthoplicial polytopic numbers) Cube numbers (6-faced Platonic numbers or 3-D Regular orthotopic numbers) Hypercube numbers (REDIRECT to Regular orthotopic numbers)
 Category:Centered regular orthotopic numbers Centered regular orthotopic numbers or Centered orthotope numbers or Centered measure polytope numbers or centered ${\displaystyle \gamma _{d}\,}$ numbers (dimensionality ${\displaystyle \scriptstyle d\,\geq \,0\,}$) Centered square numbers (4-sided Centered polygonal numbers, 2-D Centered regular orthotopic numbers or 2-D Centered orthoplicial polytopic numbers) Centered cube numbers (6-faced Centered Platonic numbers or 3-D Centered regular orthotopic numbers) Centered hypercube numbers (REDIRECT to Centered regular orthotopic numbers)
Category:Nonregular polytope numbers (by increasing number of vertices)
Nonregular polytope numbers (created as stub)
Category:Hyperpyramidal numbers
 Category:(Centered squares) hyperpyramidal numbers 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) (Centered squares) hyperpyramidal numbers Centered square hyperpyramidal numbers REDIRECT to (Centered squares) hyperpyramidal numbers
Category:3-dimensional hyperpyramidal numbers
 Category:(Centered polygons) pyramidal numbers 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) (Centered polygons) pyramidal numbers Centered pyramidal numbers (REDIRECT to (Centered polygons) pyramidal numbers)
Category:Classification of figurate numbers by dimensionality
Classification of figurate numbers by dimensionality
Category:0-dimensional figurate numbers (by increasing number of vertices)
Category:0-dimensional regular polytope numbers
 Category:Point numbers Point numbers {0, 1} (The convention being that figurate numbers have the initial dot for n = 1.) 0-dimensional regular polytope numbers (REDIRECT to Point numbers)
 Category:Centered point numbers Centered point numbers {1} (The convention being that centered figurate numbers have the central dot for n = 0.) Centered 0-dimensional regular polytope numbers (REDIRECT to Centered point numbers)
 Category:1-dimensional figurate numbers (by increasing number of vertices)
Category:2-dimensional figurate numbers (by increasing number of vertices)
Category:2-dimensional regular polytope numbers
 Category:Polygonal numbers Polygonal numbers 2-dimensional regular polytope numbers (REDIRECT to Polygonal numbers) Triangular numbers (3-sided Polygonal numbers or 2-D Simplicial polytopic numbers) Square numbers (4-sided Polygonal numbers, 2-D Regular orthotopic numbers or 2-D Orthoplicial polytopic numbers) Pentagonal numbers (5-sided Polygonal numbers) Hexagonal numbers (6-sided Polygonal numbers) Heptagonal numbers (7-sided Polygonal numbers) Octagonal numbers (8-sided Polygonal numbers) Dodecagonal numbers (12-sided Polygonal numbers) Icosagonal numbers (20-sided Polygonal numbers)
 Category:Centered polygonal numbers Centered polygonal numbers Centered 2-dimensional regular polytope numbers (REDIRECT to Centered polygonal numbers) Centered triangular numbers (3-sided Centered polygonal numbers or 2-D Centered simplicial polytopic numbers) Centered square numbers (4-sided Centered polygonal numbers, 2-D Centered regular orthotopic numbers or 2-D Centered orthoplicial polytopic numbers) Centered pentagonal numbers (5-sided Centered polygonal numbers) Centered hexagonal numbers or Hex numbers (6-sided Centered polygonal numbers) Centered heptagonal numbers (7-sided Centered polygonal numbers) Centered octagonal numbers (8-sided Centered polygonal numbers) Centered dodecagonal numbers (12-sided Centered polygonal numbers) Centered icosagonal numbers (20-sided Centered polygonal numbers)
Category:3-dimensional figurate numbers (by increasing number of vertices)
Category:3-dimensional regular polytope numbers
Category:Platonic numbers
Platonic numbers
3-dimensional regular polytope numbers (REDIRECT to Platonic numbers)
 Tetrahedral numbers (4-faced Platonic numbers or 3-D Simplicial polytopic numbers)
 Octahedral/cube numbers (dual pair) Octahedral numbers or Square dipyramidal numbers (8-faced Platonic numbers or 3-D Orthoplicial polytopic numbers) Cube numbers (6-faced Platonic numbers or 3-D Regular orthotopic numbers)
 Icosahedral/dodecahedral numbers (dual pair) Icosahedral numbers (REDIRECT to 20-faced Platonic numbers) Dodecahedral numbers (REDIRECT to 12-faced Platonic numbers)
Category:Centered Platonic numbers
Centered Platonic numbers
Centered 3-dimensional regular polytope numbers (REDIRECT to Centered Platonic numbers)
 Centered octahedral/cube numbers (dual pair) Centered octahedral numbers or (Centered squares) dipyramidal numbers or (8-faced Centered Platonic numbers or 3-D Centered orthoplicial polytopic numbers) Centered cube numbers (6-faced Centered Platonic numbers or 3-D Centered regular orthotopic numbers)
 Centered icosahedral/dodecahedral numbers (dual pair) Centered icosahedral numbers (REDIRECT to 20-faced Centered Platonic numbers) Centered dodecahedral numbers (REDIRECT to 12-faced Centered Platonic numbers)
Category:3-dimensional nonregular polytope numbers
 Category:(Centered polygons) pyramidal numbers 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) (Centered polygons) pyramidal numbers Centered pyramidal numbers (REDIRECT to (Centered polygons) pyramidal numbers)
 Dipyramidal/prism numbers (dual pair)
 Centered dipyramidal/prism numbers (dual pair)
Category:4-dimensional figurate numbers (by increasing number of vertices)
Category:4-dimensional regular polytope numbers
Category:Regular polychoron numbers
Regular polychoron numbers
4-dimensional regular polytope numbers (REDIRECT to Regular polychoron numbers)
 Pentachoron numbers (5-celled Regular polychoron numbers or 4-D Simplicial polytopic numbers)
 Tetracross/tesseract numbers (dual pair) Tetracross numbers (16-celled Regular polychoron numbers or 4-D Orthoplicial polytopic numbers) Tesseract numbers (8-celled Regular polychoron numbers or 4-D Regular orthotopic numbers)
 24-cell numbers (REDIRECT to 24-celled Regular polychoron numbers)
 Hypericosahedral/hyperdodecahedral numbers (dual pair) Hypericosahedral numbers or 600-cell numbers (both REDIRECT to 600-celled Regular polychoron numbers) Hyperdodecahedral numbers or 120-cell numbers (both REDIRECT to 120-celled Regular polychoron numbers)
Category:Centered regular polychoron numbers
Centered regular polychoron numbers
Centered 4-dimensional regular polytope numbers (REDIRECT to Centered regular polychoron numbers)
 Centered tetracross/tesseract numbers (dual pair) Centered tetracross numbers (16-celled Centered regular polychoron numbers or 4-D Centered orthoplicial polytopic numbers) Centered tesseract numbers (8-celled Centered regular polychoron numbers or 4-D Centered regular orthotopic numbers)
 Centered 24-cell numbers (REDIRECT to 24-celled Centered regular polychoron numbers)
 Centered hypericosahedral/hyperdodecahedral numbers (dual pair) Centered hypericosahedral numbers or Centered 600-cell numbers (both REDIRECT to 600-celled Centered regular polychoron numbers) Centered hyperdodecahedral numbers or Centered 120-cell numbers (both REDIRECT to 120-celled Centered regular polychoron numbers)