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# Centered prism numbers

## What are centered prism numbers?

Right and uniform ${\displaystyle \scriptstyle k\,}$-gonal centered prism numbers might be defined as ... (has yet to be determined...)

1. a prism volume: a stack of ${\displaystyle \scriptstyle n\,}$ layers of ${\displaystyle \scriptstyle n\,}$th centered ${\displaystyle \scriptstyle k\,}$-gonal numbers (so that every edge has ${\displaystyle \scriptstyle n\,}$ balls)
2. a prism surface: two end faces of ${\displaystyle \scriptstyle n\,}$th centered ${\displaystyle \scriptstyle k\,}$-gonal numbers, with the addition of ${\displaystyle \scriptstyle n-2\,}$ balls on the ${\displaystyle \scriptstyle n\,}$ joining edges (so that every edge has ${\displaystyle \scriptstyle n\,}$ balls)
3. a (better) prism surface: two end faces of ${\displaystyle \scriptstyle n\,}$th centered ${\displaystyle \scriptstyle k\,}$-gonal numbers, where each joining faces are ${\displaystyle \scriptstyle n\,}$th centered square numbers (with the addition of ${\displaystyle \scriptstyle n-2\,}$ balls on the ${\displaystyle \scriptstyle n\,}$ joining edges, and then adding the ${\displaystyle \scriptstyle (n-1)^{2}+(n)^{2}\,}$ internal balls (corresponding to the ${\displaystyle \scriptstyle (n-1)\,}$th centered square numbers) for each of the ${\displaystyle \scriptstyle n\,}$ joining faces)
4.  ?

Centered prism numbers:

• Centered trigonal prism numbers (centered triangular prism numbers)
• Centered tetragonal prism numbers (centered square prism numbers)
• Centered pentagonal prism numbers
• Centered hexagonal prism numbers
• Centered heptagonal prism numbers
• Centered octagonal prism numbers
• Centered enneagonal prism numbers
• Centered decagonal prism numbers
• Centered hendecagonal prism numbers
• Centered dodecagonal prism numbers
• ...