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