| Acronym | n,n,k-tip |
| Name | n-gon - n-gon - k-gon - triprism |
| Circumradius | sqrt[1/(2 sin2(π/n))+1/(4 sin2(π/k))] |
| Face vector | n2k, 3n2k, 3n2k+n2+2nk, n2k+2n2+4nk, n2+2nk+2n+k, 2n+k |
| Especially | n,n,n-tip (k=n) n,n,4-tip (k=4) k,tes-dip (n=4) trittip (n=3, k=3) titstip (n=3, k=4) tithtip (n=3, k=6) tratess (n=4, k=3) ax (n=4, k=4) pettip (n=5, k=5) shihtip (n=6, k=4) hittip (n=6, k=6) |
| Confer |
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Incidence matrix according to Dynkin symbol
xno xno xko (n>2,k>2) . . . . . . | nnk | 2 2 2 | 1 4 4 1 4 1 | 2 2 2 8 2 2 2 | 1 4 1 4 4 1 | 2 2 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ x . . . . . | 2 | nnk * * | 1 2 2 0 0 0 | 2 2 1 4 1 0 0 | 1 4 1 2 2 0 | 2 2 1 . . x . . . | 2 | * nnk * | 0 2 0 1 2 0 | 1 0 2 4 0 2 1 | 1 2 0 4 2 1 | 2 1 2 . . . . x . | 2 | * * nnk | 0 0 2 0 2 1 | 0 1 0 4 2 1 2 | 0 2 1 2 4 1 | 1 2 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ xno . . . . | n | n 0 0 | nk * * * * * | 2 2 0 0 0 0 0 | 1 4 1 0 0 0 | 2 2 0 x . x . . . | 4 | 2 2 0 | * nnk * * * * | 1 0 1 2 0 0 0 | 1 2 0 2 1 0 | 2 1 1 x . . . x . | 4 | 2 0 2 | * * nnk * * * | 0 1 0 2 1 0 0 | 0 2 1 1 2 0 | 1 2 1 . . xno . . | n | 0 n 0 | * * * nk * * | 0 0 2 0 0 2 0 | 1 0 0 4 0 1 | 2 0 2 . . x . x . | 4 | 0 2 2 | * * * * nnk * | 0 0 0 2 0 1 1 | 0 1 0 2 2 1 | 1 1 2 . . . . xko | k | 0 0 k | * * * * * nn | 0 0 0 0 2 0 2 | 0 0 1 0 4 1 | 0 2 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ xno x . . . ♦ 2n | 2n n 0 | 2 n 0 0 0 0 | nk * * * * * * | 1 2 0 0 0 0 | 2 1 0 xno . . x . ♦ 2n | 2n 0 n | 2 0 n 0 0 0 | * nk * * * * * | 0 2 1 0 0 0 | 1 2 0 x . xno . . ♦ 2n | n 2n 0 | 0 n 0 2 0 0 | * * nk * * * * | 1 0 0 2 0 0 | 2 0 1 x . x . x . ♦ 8 | 4 4 4 | 0 2 2 0 2 0 | * * * nnk * * * | 0 1 0 1 1 0 | 1 1 1 x . . . xko ♦ 2k | k 0 2k | 0 0 k 0 0 2 | * * * * nn * * | 0 0 1 0 2 0 | 0 2 1 . . xno x . ♦ 2n | 0 2n n | 0 0 0 2 n 0 | * * * * * nk * | 0 0 0 2 0 1 | 1 0 2 . . x . xko ♦ 2k | 0 k 2k | 0 0 0 0 k 2 | * * * * * * nn | 0 0 0 0 2 1 | 0 1 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ xno xno . . ♦ nn | nn nn 0 | n nn 0 n 0 0 | n 0 n 0 0 0 0 | k * * * * * | 2 0 0 xno x . x . ♦ 4n | 4n 2n 2n | 4 2n 2n 0 n 0 | 2 2 0 n 0 0 0 | * nk * * * * | 1 1 0 xno . . xko ♦ nk | nk 0 nk | k 0 nk 0 0 n | 0 k 0 0 n 0 0 | * * n * * * | 0 2 0 x . xno x . ♦ 4n | 2n 4n 2n | 0 2n n 4 2n 0 | 0 0 2 n 0 2 0 | * * * nk * * | 1 0 1 x . x . xko ♦ 4k | 2k 2k 4k | 0 k 2k 0 2k 4 | 0 0 0 k 2 0 2 | * * * * nn * | 0 1 1 . . xno xko ♦ nk | 0 nk nk | 0 0 0 k nk n | 0 0 0 0 0 k n | * * * * * n | 0 0 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ xno xno x . ♦ 2nn | 2nn 2nn nn | 2n 2nn nn 2n nn 0 | 2n n 2n nn 0 n 0 | 2 n 0 n 0 0 | k * * xno x . xko ♦ 2nk | 2nk nk 2nk | 2k nk 2nk 0 nk 2n | k 2k 0 nk 2n 0 n | 0 k 2 0 n 0 | * n * x . xno xko ♦ 2nk | nk 2nk 2nk | 0 nk nk 2k 2nk 2n | 0 0 k nk n 2k 2n | 0 0 0 k n 2 | * * n
or . . . . . . | nnk | 4 2 | 2 4 8 1 | 4 4 8 4 | 1 8 2 4 | 2 4 ---------------+-----+----------+-----------------+-----------------+-------------+----- x . . . . . & | 2 | 2nnk * | 1 2 2 0 | 3 2 4 1 | 1 6 1 2 | 2 3 . . . . x . | 2 | * nnk | 0 0 4 1 | 0 2 4 4 | 0 4 2 4 | 1 4 ---------------+-----+----------+-----------------+-----------------+-------------+----- xno . . . . & | n | n 0 | 2nk * * * | 2 2 0 0 | 1 4 1 0 | 2 2 x . x . . . | 4 | 4 0 | * nnk * * | 2 0 2 0 | 1 4 0 1 | 2 2 x . . . x . & | 4 | 2 2 | * * 2nnk * | 0 1 2 1 | 0 3 1 2 | 1 3 . . . . xko | k | 0 k | * * * nn | 0 0 0 4 | 0 0 2 4 | 0 4 ---------------+-----+----------+-----------------+-----------------+-------------+----- xno x . . . & ♦ 2n | 3n 0 | 2 n 0 0 | 2nk * * * | 1 2 0 0 | 2 1 xno . . x . & ♦ 2n | 2n n | 2 0 n 0 | * 2nk * * | 0 2 1 0 | 1 2 x . x . x . ♦ 8 | 8 4 | 0 2 4 0 | * * nnk * | 0 2 0 1 | 1 2 x . . . xko & ♦ 2k | k 2k | 0 0 k 2 | * * * 2nn | 0 0 1 2 | 0 3 ---------------+-----+----------+-----------------+-----------------+-------------+----- xno xno . . ♦ nn | 2nn 0 | 2n nn 0 0 | 2n 0 0 0 | k * * * | 2 0 xno x . x . & ♦ 4n | 6n 2n | 4 2n 3n 0 | 2 2 n 0 | * 2nk * * | 1 1 xno . . xko & ♦ nk | nk nk | k 0 nk n | 0 k 0 n | * * 2n * | 0 2 x . x . xko ♦ 4k | 4k 4k | 0 k 4k 4 | 0 0 k 4 | * * * nn | 0 2 ---------------+-----+----------+-----------------+-----------------+-------------+----- xno xno x . ♦ 2nn | 4nn nn | 4n 2nn 2nn 0 | 4n 2n nn 0 | 2 2n 0 0 | k * xno x . xko & ♦ 2nk | 3nk 2nk | 2k nk 3nk 2n | k 2k nk 3n | 0 k 2 n | * 2n
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