There are no approved revisions of this page, so it may

**not** have been

reviewed.

With the exception of the

hyperpyramidal numbers (which include the

pyramidal numbers and the

centered pyramidal numbers, i.e. the

(centered polygons) pyramidal numbers, as

3-dimensional hyperpyramidal numbers), all the

figurate numbers considered are

regular polytope numbers corresponding to regular convex polytopes in a

-dimensional Euclidean space

Among the

hyperpyramidal numbers, the

-dimensional

square hyperpyramidal numbers, although not corresponding to

regular polytopes, are of particular interest since they are building blocks for the construction of the

hyperoctahedral numbers (

orthoplicial polytopic numbers), which are regular polytopes. For example, the

th octahedral number is the

th square dipyramidal number, i.e. it is the adjunction of the

th square pyramidal number to the

th square pyramidal number (corresponding to joined

square pyramids at their square bases), while for

hyperoctahedral numbers of dimension

we must do

successive adjunction operations.

Otherwise, considering nonconvex regular (e.g. stellated) polytopic numbers or considering nonregular (e.g. Archimedean solids) polytopic numbers would open the door to a humongous number of possibilities...