| Acronym | 4,n,m-tip |
| Name | square - n-gon - m-gon - triprism |
| Circumradius | sqrt[1/2+1/(4 sin2(π/n))+1/(4 sin2(π/m))] |
| Face vector | 4nm, 12nm, 13nm+4n+4m, 6nm+8n+8m, nm+5n+5m+4, n+m+4 |
| Especially | 4,n,n-tip (m=n) n,tes-dip (m=4) 3,3,4-tip (n=m=3) tratess (n=3, m=4) ax (n=m=4) shihtip (n=m=6) |
| Confer |
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Incidence matrix according to Dynkin symbol
x4o xno xmo (n>2,m>2) . . . . . . | 4nm | 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 | 4nm * * | 1 2 2 0 0 0 | 2 2 1 4 1 0 0 | 1 4 1 2 2 0 | 2 2 1 . . x . . . | 2 | * 4nm * | 0 2 0 1 2 0 | 1 0 2 4 0 2 1 | 1 2 0 4 2 1 | 2 1 2 . . . . x . | 2 | * * 4nm | 0 0 2 0 2 1 | 0 1 0 4 2 1 2 | 0 2 1 2 4 1 | 1 2 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ x4o . . . . | 4 | 4 0 0 | nm * * * * * | 2 2 0 0 0 0 0 | 1 4 1 0 0 0 | 2 2 0 x . x . . . | 4 | 2 2 0 | * 4nm * * * * | 1 0 1 2 0 0 0 | 1 2 0 2 1 0 | 2 1 1 x . . . x . | 4 | 2 0 2 | * * 4nm * * * | 0 1 0 2 1 0 0 | 0 2 1 1 2 0 | 1 2 1 . . xno . . | n | 0 n 0 | * * * 4m * * | 0 0 2 0 0 2 0 | 1 0 0 4 0 1 | 2 0 2 . . x . x . | 4 | 0 2 2 | * * * * 4nm * | 0 0 0 2 0 1 1 | 0 1 0 2 2 1 | 1 1 2 . . . . xmo | m | 0 0 m | * * * * * 4n | 0 0 0 0 2 0 2 | 0 0 1 0 4 1 | 0 2 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ x4o x . . . ♦ 8 | 8 4 0 | 2 4 0 0 0 0 | nm * * * * * * | 1 2 0 0 0 0 | 2 1 0 x4o . . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * nm * * * * * | 0 2 1 0 0 0 | 1 2 0 x . xno . . ♦ 2n | n 2n 0 | 0 n 0 2 0 0 | * * 4m * * * * | 1 0 0 2 0 0 | 2 0 1 x . x . x . ♦ 8 | 4 4 4 | 0 2 2 0 2 0 | * * * 4nm * * * | 0 1 0 1 1 0 | 1 1 1 x . . . xmo ♦ 2m | m 0 2m | 0 0 m 0 0 2 | * * * * 4n * * | 0 0 1 0 2 0 | 0 2 1 . . xno x . ♦ 2n | 0 2n n | 0 0 0 2 n 0 | * * * * * 4m * | 0 0 0 2 0 1 | 1 0 2 . . x . xmo ♦ 2m | 0 m 2m | 0 0 0 0 m 2 | * * * * * * 4n | 0 0 0 0 2 1 | 0 1 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ x4o xno . . ♦ 4n | 4n 4n 0 | n 4n 0 4 0 0 | n 0 4 0 0 0 0 | m * * * * * | 2 0 0 x4o x . x . ♦ 16 | 16 8 8 | 4 8 8 0 4 0 | 2 2 0 4 0 0 0 | * nm * * * * | 1 1 0 x4o . . xmo ♦ 4m | 4m 0 4m | m 0 4m 0 0 4 | 0 m 0 0 4 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 | * * * 4m * * | 1 0 1 x . x . xmo ♦ 4m | 2m 2m 4m | 0 m 2m 0 2m 4 | 0 0 0 m 2 0 2 | * * * * 4n * | 0 1 1 . . xno xmo ♦ nm | 0 nm nm | 0 0 0 m nm n | 0 0 0 0 0 m n | * * * * * 4 | 0 0 2 ------------+-----+-------------+----------------------+-----------------------+----------------+------ x4o xno x . ♦ 8n | 8n 8n 4n | 2n 8n 4n 8 4n 0 | 2n n 8 4n 0 4 0 | 2 n 0 4 0 0 | m * * x4o x . xmo ♦ 8m | 8m 4m 8m | 2m 4m 8m 0 4m 8 | m 2m 0 4m 8 0 4 | 0 m 2 0 4 0 | * n * x . xno xmo ♦ 2nm | nm 2nm 2nm | 0 nm nm 2m 2nm 2n | 0 0 m nm n 2m 2n | 0 0 0 m n 2 | * * 4
x x xno xmo (n>2,m>2) . . . . . . | 4nm | 1 1 2 2 | 1 2 2 2 2 1 4 1 | 2 2 1 4 1 1 4 1 2 2 | 1 4 1 2 2 2 2 1 | 2 2 1 1 ------------+-----+-----------------+------------------------------+---------------------------------+----------------------+-------- x . . . . . | 2 | 2nm * * * | 1 2 2 0 0 0 0 0 | 2 2 1 4 1 0 0 0 0 0 | 1 4 1 2 2 0 0 0 | 2 2 1 0 . x . . . . | 2 | * 2nm * * | 1 0 0 2 2 0 0 0 | 2 2 0 0 0 1 4 1 0 0 | 1 4 1 0 0 2 2 0 | 2 2 0 1 . . x . . . | 2 | * * 4nm * | 0 1 0 1 0 1 2 0 | 1 0 1 2 0 1 2 0 2 1 | 1 2 0 2 1 2 1 1 | 2 1 1 1 . . . . x . | 2 | * * * 4nm | 0 0 1 0 1 0 2 1 | 0 1 0 2 1 0 2 1 1 2 | 0 2 1 1 2 1 2 1 | 1 2 1 1 ------------+-----+-----------------+------------------------------+---------------------------------+----------------------+-------- x x . . . . | 4 | 2 2 0 0 | nm * * * * * * * | 2 2 0 0 0 0 0 0 0 0 | 1 4 1 0 0 0 0 0 | 2 2 0 0 x . x . . . | 4 | 2 0 2 0 | * 2nm * * * * * * | 1 0 1 2 0 0 0 0 0 0 | 1 2 0 2 1 0 0 0 | 2 1 1 0 x . . . x . | 4 | 2 0 0 2 | * * 2nm * * * * * | 0 1 0 2 1 0 0 0 0 0 | 0 2 1 1 2 0 0 0 | 1 2 1 0 . x x . . . | 4 | 0 2 2 0 | * * * 2nm * * * * | 1 0 0 0 0 1 2 0 0 0 | 1 2 0 0 0 2 1 0 | 2 1 0 1 . x . . x . | 4 | 0 2 0 2 | * * * * 2nm * * * | 0 1 0 0 0 0 2 1 0 0 | 0 2 1 0 0 1 2 0 | 1 2 0 1 . . xno . . | n | 0 0 n 0 | * * * * * 4m * * | 0 0 1 0 0 1 0 0 2 0 | 1 0 0 2 0 2 0 1 | 2 0 1 1 . . x . x . | 4 | 0 0 2 2 | * * * * * * 4nm * | 0 0 0 1 0 0 1 0 1 1 | 0 1 0 1 1 1 1 1 | 1 1 1 1 . . . . xmo | m | 0 0 0 m | * * * * * * * 4n | 0 0 0 0 1 0 0 1 0 2 | 0 0 1 0 2 0 2 1 | 0 2 1 1 ------------+-----+-----------------+------------------------------+---------------------------------+----------------------+-------- x x x . . . ♦ 8 | 4 4 4 0 | 2 2 0 2 0 0 0 0 | nm * * * * * * * * * | 1 2 0 0 0 0 0 0 | 2 1 0 0 x x . . x . ♦ 8 | 4 4 0 4 | 2 0 2 0 2 0 0 0 | * nm * * * * * * * * | 0 2 1 0 0 0 0 0 | 1 2 0 0 x . xno . . ♦ 2n | n 0 2n 0 | 0 n 0 0 0 2 0 0 | * * 2m * * * * * * * | 1 0 0 2 0 0 0 0 | 2 0 1 0 x . x . x . ♦ 8 | 4 0 4 4 | 0 2 2 0 0 0 2 0 | * * * 2nm * * * * * * | 0 1 0 1 1 0 0 0 | 1 1 1 0 x . . . xmo ♦ 2m | m 0 0 2m | 0 0 m 0 0 0 0 2 | * * * * 2n * * * * * | 0 0 1 0 2 0 0 0 | 0 2 1 0 . x xno . . ♦ 2n | 0 n 2n 0 | 0 0 0 n 0 2 0 0 | * * * * * 2m * * * * | 1 0 0 0 0 2 0 0 | 2 0 0 1 . x x . x . ♦ 8 | 0 4 4 4 | 0 0 0 2 2 0 2 0 | * * * * * * 2nm * * * | 0 1 0 0 0 1 1 0 | 1 1 0 1 . x . . xmo ♦ 2m | 0 m 0 2m | 0 0 0 0 m 0 0 2 | * * * * * * * 2n * * | 0 0 1 0 0 0 2 0 | 0 2 0 1 . . xno x . ♦ 2n | 0 0 2n n | 0 0 0 0 0 2 n 0 | * * * * * * * * 4m * | 0 0 0 1 0 1 0 1 | 1 0 1 1 . . x . xmo ♦ 2m | 0 0 m 2m | 0 0 0 0 0 0 m 2 | * * * * * * * * * 4n | 0 0 0 0 1 0 1 1 | 0 1 1 1 ------------+-----+-----------------+------------------------------+---------------------------------+----------------------+-------- x x xno . . ♦ 4n | 2n 2n 4n 0 | n 2n 0 2n 0 4 0 0 | n 0 2 0 0 2 0 0 0 0 | m * * * * * * * | 2 0 0 0 x x x . x . ♦ 16 | 8 8 8 8 | 4 4 4 4 4 0 4 0 | 2 2 0 2 0 0 2 0 0 0 | * nm * * * * * * | 1 1 0 0 x x . . xmo ♦ 4m | 2m 2m 0 4m | m 0 2m 0 2m 0 0 4 | 0 m 0 0 2 0 0 2 0 0 | * * n * * * * * | 0 2 0 0 x . xno x . ♦ 4n | 2n 0 4n 2n | 0 2n n 0 0 4 2n 0 | 0 0 2 n 0 0 0 0 2 0 | * * * 2m * * * * | 1 0 1 0 x . x . xmo ♦ 4m | 2m 0 2m 4m | 0 m 2m 0 0 0 2m 4 | 0 0 0 m 2 0 0 0 0 2 | * * * * 2n * * * | 0 1 1 0 . x xno x . ♦ 4n | 0 2n 4n 2n | 0 0 0 2n n 4 2n 0 | 0 0 0 0 0 2 n 0 2 0 | * * * * * 2m * * | 1 0 0 1 . x x . xmo ♦ 4m | 0 2m 2m 4m | 0 0 0 m 2m 0 2m 4 | 0 0 0 0 0 0 m 2 0 2 | * * * * * * 2n * | 0 1 0 1 . . xno xmo ♦ nm | 0 0 nm nm | 0 0 0 0 0 m nm n | 0 0 0 0 0 0 0 0 m n | * * * * * * * 4 | 0 0 1 1 ------------+-----+-----------------+------------------------------+---------------------------------+----------------------+-------- x x xno x . ♦ 8n | 4n 4n 8n 4n | 2n 4n 2n 4n 2n 8 4n 0 | 2n n 4 2n 0 4 2n 0 4 0 | 2 n 0 2 0 2 0 0 | m * * * x x x . xmo ♦ 8m | 4m 4m 4m 8m | 2m 2m 4m 2m 4m 0 4m 8 | m 2m 0 2m 4 0 2m 4 0 4 | 0 m 2 0 2 0 2 0 | * n * * x . xno xmo ♦ 2nm | nm 0 2nm 2nm | 0 nm nm 0 0 2m 2nm 2n | 0 0 m nm n 0 0 0 2m 2n | 0 0 0 m n 0 0 2 | * * 2 * . x xno xmo ♦ 2nm | 0 nm 2nm 2nm | 0 0 0 nm nm 2m 2nm 2n | 0 0 0 0 0 m nm n 2m 2n | 0 0 0 0 0 m n 2 | * * * 2
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