| Acronym | n,m,k-tippip |
| Name | n-gon - m-gon - m-gon - triprismatic prism |
| Circumradius | sqrt[1/4+1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/m))] |
| Face vector | 2nmk, 7nmk, 9nmk+2nm+2nk+2mk, 5nmk+5nm+5nk+5mk, nmk+4nm+4nk+4mk+2n+2m+2k, nm+nk+mk+3n+3m+3k, n+m+k+2 |
| Especially | tratratrip (n=m=k=3) hept (n=m=k=4) n,n,n-tippip (n=m=k) |
| Confer |
|
Incidence matrix according to Dynkin symbol
x xno xmo xko (n,m,k>2) . . . . . . . | 2nmk | 1 2 2 2 | 2 2 2 1 4 4 1 4 1 | 1 4 4 1 4 1 2 2 2 8 2 2 2 | 2 2 2 8 2 2 2 1 4 1 4 4 1 | 1 4 1 4 4 1 2 2 2 | 2 2 2 1 --------------+------+--------------------+----------------------------------------+---------------------------------------------------+--------------------------------------------+-------------------------+-------- x . . . . . . | 2 | nmk * * * | 2 2 2 0 0 0 0 0 0 | 1 4 4 1 4 1 0 0 0 0 0 0 0 | 2 2 2 8 2 2 2 0 0 0 0 0 0 | 1 4 1 4 4 1 0 0 0 | 2 2 2 0 . x . . . . . | 2 | * 2nmk * * | 1 0 0 1 2 2 0 0 0 | 1 2 2 0 0 0 2 2 1 4 1 0 0 | 2 2 1 4 1 0 0 1 4 1 2 2 0 | 1 4 1 2 2 0 2 2 1 | 2 2 1 1 . . . x . . . | 2 | * * 2nmk * | 0 1 0 0 2 0 1 2 0 | 0 2 0 1 2 0 1 0 2 4 0 2 1 | 1 0 2 4 0 2 1 1 2 0 4 2 1 | 1 2 0 4 2 1 2 1 2 | 2 1 2 1 . . . . . x . | 2 | * * * 2nmk | 0 0 1 0 0 2 0 2 1 | 0 0 2 0 2 1 0 1 0 4 2 1 2 | 0 1 0 4 2 1 2 0 2 1 2 4 1 | 0 2 1 2 4 1 1 2 2 | 1 2 2 1 --------------+------+--------------------+----------------------------------------+---------------------------------------------------+--------------------------------------------+-------------------------+-------- x x . . . . . | 4 | 2 2 0 0 | nmk * * * * * * * * | 1 2 2 0 0 0 0 0 0 0 0 0 0 | 2 2 1 4 1 0 0 0 0 0 0 0 0 | 1 4 1 2 2 0 0 0 0 | 2 2 1 0 x . . x . . . | 4 | 2 0 2 0 | * nmk * * * * * * * | 0 2 0 1 2 0 0 0 0 0 0 0 0 | 1 0 2 4 0 2 1 0 0 0 0 0 0 | 1 2 0 4 2 1 0 0 0 | 2 1 2 0 x . . . . x . | 4 | 2 0 0 2 | * * nmk * * * * * * | 0 0 2 0 2 1 0 0 0 0 0 0 0 | 0 1 0 4 2 1 2 0 0 0 0 0 0 | 0 2 1 2 4 1 0 0 0 | 1 2 2 0 . xno . . . . | n | 0 n 0 0 | * * * 2mk * * * * * | 1 0 0 0 0 0 2 2 0 0 0 0 0 | 2 2 0 0 0 0 0 1 4 1 0 0 0 | 1 4 1 0 0 0 2 2 0 | 2 2 0 1 . x . x . . . | 4 | 0 2 2 0 | * * * * 2nmk * * * * | 0 1 0 0 0 0 1 0 1 2 0 0 0 | 1 0 1 2 0 0 0 1 2 0 2 1 0 | 1 2 0 2 1 0 2 1 1 | 2 1 1 1 . x . . . x . | 4 | 0 2 0 2 | * * * * * 2nmk * * * | 0 0 1 0 0 0 0 1 0 2 1 0 0 | 0 1 0 2 1 0 0 0 2 1 1 2 0 | 0 2 1 1 2 0 1 2 1 | 1 2 1 1 . . . xmo . . | m | 0 0 m 0 | * * * * * * 2nk * * | 0 0 0 1 0 0 0 0 2 0 0 2 0 | 0 0 2 0 0 2 0 1 0 0 4 0 1 | 1 0 0 4 0 1 2 0 2 | 2 0 2 1 . . . x . x . | 4 | 0 0 2 2 | * * * * * * * 2nmk * | 0 0 0 0 1 0 0 0 0 2 0 1 1 | 0 0 0 2 0 1 1 0 1 0 2 2 1 | 0 1 0 2 2 1 1 1 2 | 1 1 2 1 . . . . . xko | k | 0 0 0 k | * * * * * * * * 2nm | 0 0 0 0 0 1 0 0 0 0 2 0 2 | 0 0 0 0 2 0 2 0 0 1 0 4 1 | 0 0 1 0 4 1 0 2 2 | 0 2 2 1 --------------+------+--------------------+----------------------------------------+---------------------------------------------------+--------------------------------------------+-------------------------+-------- x xno . . . . ♦ 2n | n 2n 0 0 | n 0 0 2 0 0 0 0 0 | mk * * * * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 0 | 1 4 1 0 0 0 0 0 0 | 2 2 0 0 x x . x . . . ♦ 8 | 4 4 4 0 | 2 2 0 0 2 0 0 0 0 | * nmk * * * * * * * * * * * | 1 0 1 2 0 0 0 0 0 0 0 0 0 | 1 2 0 2 1 0 0 0 0 | 2 1 1 0 x x . . . x . ♦ 8 | 4 4 0 4 | 2 0 2 0 0 2 0 0 0 | * * nmk * * * * * * * * * * | 0 1 0 2 1 0 0 0 0 0 0 0 0 | 0 2 1 1 2 0 0 0 0 | 1 2 1 0 x . . xmo . . ♦ 2m | m 0 2m 0 | 0 m 0 0 0 0 2 0 0 | * * * nk * * * * * * * * * | 0 0 2 0 0 2 0 0 0 0 0 0 0 | 1 0 0 4 0 1 0 0 0 | 2 0 2 0 x . . x . x . ♦ 8 | 4 0 4 4 | 0 2 2 0 0 0 0 2 0 | * * * * nmk * * * * * * * * | 0 0 0 2 0 1 1 0 0 0 0 0 0 | 0 1 0 2 2 1 0 0 0 | 1 1 2 0 x . . . . xko ♦ 2k | k 0 0 2k | 0 0 k 0 0 0 0 0 2 | * * * * * nm * * * * * * * | 0 0 0 0 2 0 2 0 0 0 0 0 0 | 0 0 1 0 4 1 0 0 0 | 0 2 2 0 . xno x . . . ♦ 2n | 0 2n n 0 | 0 0 0 2 n 0 0 0 0 | * * * * * * 2mk * * * * * * | 1 0 0 0 0 0 0 1 2 0 0 0 0 | 1 2 0 0 0 0 2 1 0 | 2 1 0 1 . xno . . x . ♦ 2n | 0 2n 0 n | 0 0 0 2 0 n 0 0 0 | * * * * * * * 2mk * * * * * | 0 1 0 0 0 0 0 0 2 1 0 0 0 | 0 2 1 0 0 0 1 2 0 | 1 2 0 1 . x . xmo . . ♦ 2m | 0 m 2m 0 | 0 0 0 0 m 0 2 0 0 | * * * * * * * * 2nk * * * * | 0 0 1 0 0 0 0 1 0 0 2 0 0 | 1 0 0 2 0 0 2 0 1 | 2 0 1 1 . x . x . x . ♦ 8 | 0 4 4 4 | 0 0 0 0 2 2 0 2 0 | * * * * * * * * * 2nmk * * * | 0 0 0 1 0 0 0 0 1 0 1 1 0 | 0 1 0 1 1 0 1 1 1 | 1 1 1 1 . x . . . xko ♦ 2k | 0 k 0 2k | 0 0 0 0 0 k 0 0 2 | * * * * * * * * * * 2nm * * | 0 0 0 0 1 0 0 0 0 1 0 2 0 | 0 0 1 0 2 0 0 2 1 | 0 2 1 1 . . . xmo x . ♦ 2m | 0 0 2m m | 0 0 0 0 0 0 2 m 0 | * * * * * * * * * * * 2nk * | 0 0 0 0 0 1 0 0 0 0 2 0 1 | 0 0 0 2 0 1 1 0 2 | 1 0 2 1 . . . x . xko ♦ 2k | 0 0 k 2k | 0 0 0 0 0 0 0 k 2 | * * * * * * * * * * * * 2nm | 0 0 0 0 0 0 1 0 0 0 0 2 1 | 0 0 0 0 2 1 0 1 2 | 0 1 2 1 --------------+------+--------------------+----------------------------------------+---------------------------------------------------+--------------------------------------------+-------------------------+-------- x xno x . . . ♦ 4n | 2n 4n 2n 0 | 2n n 0 4 2n 0 0 0 0 | 2 n 0 0 0 0 2 0 0 0 0 0 0 | mk * * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 | 2 1 0 0 x xno . . x . ♦ 4n | 2n 4n 0 2n | 2n 0 n 4 0 2n 0 0 0 | 2 0 n 0 0 0 0 2 0 0 0 0 0 | * mk * * * * * * * * * * * | 0 2 1 0 0 0 0 0 0 | 1 2 0 0 x x . xmo . . ♦ 4m | 2m 2m 4m 0 | m 2m 0 0 2m 0 4 0 0 | 0 m 0 2 0 0 0 0 2 0 0 0 0 | * * nk * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 | 2 0 1 0 x x . x . x . ♦ 16 | 8 8 8 8 | 4 4 4 0 4 4 0 4 0 | 0 2 2 0 2 0 0 0 0 2 0 0 0 | * * * nmk * * * * * * * * * | 0 1 0 1 1 0 0 0 0 | 1 1 1 0 x x . . . xko ♦ 4k | 2k 2k 0 4k | k 0 2k 0 0 2k 0 0 4 | 0 0 k 0 0 2 0 0 0 0 2 0 0 | * * * * nm * * * * * * * * | 0 0 1 0 2 0 0 0 0 | 0 2 1 0 x . . xmo x . ♦ 4m | 2m 0 4m 2m | 0 2m m 0 0 0 4 2m 0 | 0 0 0 2 m 0 0 0 0 0 0 2 0 | * * * * * nk * * * * * * * | 0 0 0 2 0 1 0 0 0 | 1 0 2 0 x . . x . xko ♦ 4k | 2k 0 2k 4k | 0 k 2k 0 0 0 0 2k 4 | 0 0 0 0 k 2 0 0 0 0 0 0 2 | * * * * * * nm * * * * * * | 0 0 0 0 2 1 0 0 0 | 0 1 2 0 . xno xmo . . ♦ nm | 0 nm nm 0 | 0 0 0 m nm 0 n 0 0 | 0 0 0 0 0 0 m 0 n 0 0 0 0 | * * * * * * * 2k * * * * * | 1 0 0 0 0 0 2 0 0 | 2 0 0 1 . xno x . x . ♦ 4n | 0 4n 2n 2n | 0 0 0 4 2n 2n 0 n 0 | 0 0 0 0 0 0 2 2 0 n 0 0 0 | * * * * * * * * 2mk * * * * | 0 1 0 0 0 0 1 1 0 | 1 1 0 1 . xno . . xko ♦ nk | 0 nk 0 nk | 0 0 0 k 0 nk 0 0 n | 0 0 0 0 0 0 0 k 0 0 n 0 0 | * * * * * * * * * 2m * * * | 0 0 1 0 0 0 0 2 0 | 0 2 0 1 . x . xmo x . ♦ 4m | 0 2m 4m 2m | 0 0 0 0 2m m 4 2m 0 | 0 0 0 0 0 0 0 0 2 m 0 2 0 | * * * * * * * * * * 2nk * * | 0 0 0 1 0 0 1 0 1 | 1 0 1 1 . x . x . xko ♦ 4k | 0 2k 2k 4k | 0 0 0 0 k 2k 0 2k 4 | 0 0 0 0 0 0 0 0 0 k 2 0 2 | * * * * * * * * * * * 2nm * | 0 0 0 0 1 0 0 1 1 | 0 1 1 1 . . . xmo xko ♦ mk | 0 0 mk mk | 0 0 0 0 0 0 k mk m | 0 0 0 0 0 0 0 0 0 0 0 k m | * * * * * * * * * * * * 2n | 0 0 0 0 0 1 0 0 2 | 0 0 2 1 --------------+------+--------------------+----------------------------------------+---------------------------------------------------+--------------------------------------------+-------------------------+-------- x xno xmo . . ♦ 2nm | nm 2nm 2nm 0 | nm nm 0 2m 2nm 0 2n 0 0 | m nm 0 n 0 0 2m 0 2n 0 0 0 0 | m 0 n 0 0 0 0 2 0 0 0 0 0 | k * * * * * * * * | 2 0 0 0 x xno x . x . ♦ 8n | 4n 8n 4n 4n | 4n 2n 2n 8 4n 4n 0 2n 0 | 4 2n 2n 0 n 0 4 4 0 2n 0 0 0 | 2 2 0 n 0 0 0 0 2 0 0 0 0 | * mk * * * * * * * | 1 1 0 0 x xno . . xko ♦ 2nk | nk 2nk 0 2nk | nk 0 nk 2k 0 2nk 0 0 2n | k 0 nk 0 0 n 0 2k 0 0 2n 0 0 | 0 k 0 0 n 0 0 0 0 2 0 0 0 | * * m * * * * * * | 0 2 0 0 x x . xmo x . ♦ 8m | 4m 4m 8m 4m | 2m 4m 2m 0 4m 2m 8 4m 0 | 0 2m m 4 2m 0 0 0 4 2m 0 4 0 | 0 0 2 m 0 2 0 0 0 0 2 0 0 | * * * nk * * * * * | 1 0 1 0 x x . x . xko ♦ 8k | 4k 4k 4k 8k | 2k 2k 4k 0 2k 4k 0 4k 8 | 0 k 2k 0 2k 4 0 0 0 2k 4 0 4 | 0 0 0 k 2 0 2 0 0 0 0 2 0 | * * * * nm * * * * | 0 1 1 0 x . . xmo xko ♦ 2mk | mk 0 2mk 2mk | 0 mk mk 0 0 0 2k 2mk 2m | 0 0 0 k mk m 0 0 0 0 0 2k 2m | 0 0 0 0 0 k m 0 0 0 0 0 2 | * * * * * n * * * | 0 0 2 0 . xno xmo x . ♦ 2nm | 0 2nm 2nm nm | 0 0 0 2m 2nm nm 2n nm 0 | 0 0 0 0 0 0 2m m 2n nm 0 n 0 | 0 0 0 0 0 0 0 2 m 0 n 0 0 | * * * * * * 2k * * | 1 0 0 1 . xno x . xko ♦ 2nk | 0 2nk nk 2nk | 0 0 0 2k nk 2nk 0 nk 2n | 0 0 0 0 0 0 k 2k 0 nk 2n 0 n | 0 0 0 0 0 0 0 0 k 2 0 n 0 | * * * * * * * 2m * | 0 1 0 1 . x . xmo xko ♦ 2mk | 0 mk 2mk 2mk | 0 0 0 0 mk mk 2k 2mk 2n | 0 0 0 0 0 0 0 0 k mk m 2k 2m | 0 0 0 0 0 0 0 0 0 0 k m 2 | * * * * * * * * 2n | 0 0 1 1 --------------+------+--------------------+----------------------------------------+---------------------------------------------------+--------------------------------------------+-------------------------+-------- x xno xmo x . ♦ 4nm | 2nm 4nm 4nm 2nm | 2nm 2nm nm 4m 4nm 2nm 4n 2nm 0 | 2m 2nm nm 2n nm 0 4m 2m 4n 2nm 0 2n 0 | 2m m 2n nm 0 n 0 4 2m 0 2n 0 0 | 2 m 0 n 0 0 2 0 0 | k * * * x xno x . xko ♦ 4nk | 2nk 4nk 2nk 4nk | 2nk nk 2nk 4k 2nk 4nk 0 2nk 4n | 2k nk 2nk 0 nk 2n 2k 4k 0 2nk 4n 0 2n | k 2k 0 nk 2n 0 n 0 2k 4 0 2n 0 | 0 k 2 0 n 0 0 2 0 | * m * * x x . xmo xko ♦ 4mk | 2mk 2mk 4mk 4mk | mk 2mk 2mk 0 2mk 2mk 4k 4mk 4m | 0 mk mk 2k 2mk 2m 0 0 2k 2mk 2m 4k 4m | 0 0 k mk m 2k 2m 0 0 0 2k 2m 4 | 0 0 0 k m 2 0 0 2 | * * n * . xno xmo xko ♦ nmk | 0 nmk nmk nmk | 0 0 0 mk nmk nmk nk nmk nm | 0 0 0 0 0 0 mk mk nk nmk nm nk nm | 0 0 0 0 0 0 0 k mk m nk nm n | 0 0 0 0 0 0 k m n | * * * 2
© 2004-2024 | top of page |