| Acronym | n,oct-dippip |
| Name | n-gon - octahedron duoprismatic prism |
| Face vector | 12n, 42n, 58n+12, 38n+30, 11n+28, n+10 |
| Especially | trope (n=3) octcube (n=4) |
| Confer |
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Incidence matrix according to Dynkin symbol
x xno x3o4o (n>2) . . . . . . | 12n | 1 2 4 | 2 4 1 8 4 | 1 8 4 4 8 1 | 4 8 1 4 2 | 4 2 1 ------------+-----+------------+-------------------+--------------------+---------------+------ x . . . . . | 2 | 6n * * | 2 4 0 0 0 | 1 8 4 0 0 0 | 4 8 1 0 0 | 4 2 0 . x . . . . | 2 | * 12n * | 1 0 1 4 0 | 1 4 0 4 4 0 | 4 4 0 4 1 | 4 1 1 . . . x . . | 2 | * * 24n | 0 1 0 2 2 | 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1 ------------+-----+------------+-------------------+--------------------+---------------+------ x x . . . . | 4 | 2 2 0 | 6n * * * * | 1 4 0 0 0 0 | 4 4 0 0 0 | 4 1 0 x . . x . . | 4 | 2 0 2 | * 12n * * * | 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0 . xno . . . | n | 0 n 0 | * * 12 * * | 1 0 0 4 0 0 | 4 0 0 4 0 | 4 0 1 . x . x . . | 4 | 0 2 2 | * * * 24n * | 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1 . . . x3o . | 3 | 0 0 3 | * * * * 16n | 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1 ------------+-----+------------+-------------------+--------------------+---------------+------ x xno . . . ♦ 2n | n 2n 0 | n 0 2 0 0 | 6 * * * * * | 4 0 0 0 0 | 4 0 0 x x . x . . ♦ 8 | 4 4 4 | 2 2 0 2 0 | * 12n * * * * | 1 2 0 0 0 | 2 1 0 x . . x3o . ♦ 6 | 3 0 6 | 0 3 0 0 2 | * * 8n * * * | 0 2 1 0 0 | 1 2 0 . xno x . . ♦ 2n | 0 2n n | 0 0 2 n 0 | * * * 24 * * | 1 0 0 2 0 | 2 0 1 . x . x3o . ♦ 6 | 0 3 6 | 0 0 0 3 2 | * * * * 16n * | 0 1 0 1 1 | 1 1 1 . . . x3o4o ♦ 6 | 0 0 12 | 0 0 0 0 8 | * * * * * 2n | 0 0 1 0 2 | 0 2 1 ------------+-----+------------+-------------------+--------------------+---------------+------ x xno x . . ♦ 4n | 2n 4n 2n | 2n n 4 2n 0 | 2 n 0 2 0 0 | 12 * * * * | 2 0 0 x x . x3o . ♦ 12 | 6 6 12 | 3 6 0 6 4 | 0 3 2 0 2 0 | * 8n * * * | 1 1 0 x . . x3o4o ♦ 12 | 6 0 24 | 0 12 0 0 16 | 0 0 8 0 0 2 | * * n * * | 0 2 0 . xno x3o . ♦ 3n | 0 3n 3n | 0 0 3 3n n | 0 0 0 3 n 0 | * * * 16 * | 1 0 1 . x . x3o4o ♦ 12 | 0 6 24 | 0 0 0 12 16 | 0 0 0 0 8 2 | * * * * 2n | 0 1 1 ------------+-----+------------+-------------------+--------------------+---------------+------ x xno x3o . ♦ 6n | 3n 6n 6n | 3n 3n 6 6n 2n | 3 3n n 6 2n 0 | 3 n 0 2 0 | 8 * * x x . x3o4o ♦ 24 | 12 12 48 | 6 24 0 24 32 | 0 12 16 0 16 4 | 0 8 2 0 2 | * n * . xno x3o4o ♦ 6n | 0 6n 12n | 0 0 6 12n 8n | 0 0 0 12 8n n | 0 0 0 8 n | * * 2
x xno o3x3o (n>2) . . . . . . | 12n | 1 2 4 | 2 4 1 8 2 2 | 1 8 2 2 4 4 4 1 | 4 4 4 1 2 2 2 | 2 2 2 1 ------------+-----+------------+---------------------+-------------------------+-------------------+-------- x . . . . . | 2 | 6n * * | 2 4 0 0 0 0 | 1 8 2 2 0 0 0 0 | 4 4 4 1 0 0 0 | 2 2 2 0 . x . . . . | 2 | * 12n * | 1 0 1 4 0 0 | 1 4 0 0 4 2 2 0 | 4 2 2 0 2 2 1 | 2 2 1 1 . . . . x . | 2 | * * 24n | 0 1 0 2 1 1 | 0 2 1 1 1 2 2 1 | 1 2 2 1 1 1 2 | 1 1 2 1 ------------+-----+------------+---------------------+-------------------------+-------------------+-------- x x . . . . | 4 | 2 2 0 | 6n * * * * * | 1 4 0 0 0 0 0 0 | 4 2 2 0 0 0 0 | 2 2 1 0 x . . . x . | 4 | 2 0 2 | * 12n * * * * | 0 2 1 1 0 0 0 0 | 1 2 2 1 0 0 0 | 1 1 2 0 . xno . . . | n | 0 n 0 | * * 12 * * * | 1 0 0 0 4 0 0 0 | 4 0 0 0 2 2 0 | 2 2 0 1 . x . . x . | 4 | 0 2 2 | * * * 24n * * | 0 1 0 0 1 1 1 0 | 1 1 1 0 1 1 1 | 1 1 1 1 . . . o3x . | 3 | 0 0 3 | * * * * 8n * | 0 0 1 0 0 2 0 1 | 0 2 0 1 1 0 2 | 1 0 2 1 . . . . x3o | 3 | 0 0 3 | * * * * * 8n | 0 0 0 1 0 0 2 1 | 0 0 2 1 0 1 2 | 0 1 2 1 ------------+-----+------------+---------------------+-------------------------+-------------------+-------- x xno . . . ♦ 2n | n 2n 0 | n 0 2 0 0 0 | 6 * * * * * * * | 4 0 0 0 0 0 0 | 2 2 0 0 x x . . x . ♦ 8 | 4 4 4 | 2 2 0 2 0 0 | * 12n * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 x . . o3x . ♦ 6 | 3 0 6 | 0 3 0 0 2 0 | * * 4n * * * * * | 0 2 0 1 0 0 0 | 1 0 2 0 x . . . x3o ♦ 6 | 3 0 6 | 0 3 0 0 0 2 | * * * 4n * * * * | 0 0 2 1 0 0 0 | 0 1 2 0 . xno . x . ♦ 2n | 0 2n n | 0 0 2 n 0 0 | * * * * 24 * * * | 1 0 0 0 1 1 0 | 1 1 0 1 . x . o3x . ♦ 6 | 0 3 6 | 0 0 0 3 2 0 | * * * * * 8n * * | 0 1 0 0 1 0 1 | 1 0 1 1 . x . . x3o ♦ 6 | 0 3 6 | 0 0 0 3 0 2 | * * * * * * 8n * | 0 0 1 0 0 1 1 | 0 1 1 1 . . . o3x3o ♦ 6 | 0 0 12 | 0 0 0 0 4 4 | * * * * * * * 2n | 0 0 0 1 0 0 2 | 0 0 2 1 ------------+-----+------------+---------------------+-------------------------+-------------------+-------- x xno . x . ♦ 4n | 2n 4n 2n | 2n n 4 2n 0 0 | 2 n 0 0 2 0 0 0 | 12 * * * * * * | 1 1 0 0 x x . o3x . ♦ 12 | 6 6 12 | 3 6 0 6 4 0 | 0 3 2 0 0 2 0 0 | * 4n * * * * * | 1 0 1 0 x x . . x3o ♦ 12 | 6 6 12 | 3 6 0 6 0 4 | 0 3 0 2 0 0 2 0 | * * 4n * * * * | 0 1 1 0 x . . o3x3o ♦ 12 | 6 0 24 | 0 12 0 0 8 8 | 0 0 4 4 0 0 0 2 | * * * n * * * | 0 0 2 0 . xno o3x . ♦ 3n | 0 3n 3n | 0 0 3 3n n 0 | 0 0 0 0 3 n 0 0 | * * * * 8 * * | 1 0 0 1 . xno . x3o ♦ 3n | 0 3n 3n | 0 0 3 3n 0 n | 0 0 0 0 3 0 n 0 | * * * * * 8 * | 0 1 0 1 . x . o3x3o ♦ 12 | 0 6 24 | 0 0 0 12 8 8 | 0 0 0 0 0 4 4 2 | * * * * * * 2n | 0 0 1 1 ------------+-----+------------+---------------------+-------------------------+-------------------+-------- x xno o3x . ♦ 6n | 3n 6n 6n | 3n 3n 6 6n 2n 0 | 3 3n n 0 6 2n 0 0 | 3 n 0 0 2 0 0 | 4 * * * x xno . x3o ♦ 6n | 3n 6n 6n | 3n 3n 6 6n 0 2n | 3 3n 0 n 6 0 2n 0 | 3 0 n 0 2 0 0 | * 4 * * x x . o3x3o ♦ 24 | 12 12 48 | 6 24 0 24 16 16 | 0 12 8 8 0 8 8 4 | 0 4 4 2 0 0 2 | * * n * . xno o3x3o ♦ 6n | 0 6n 12n | 0 0 6 12n 4n 4n | 0 0 0 0 12 4n 4n n | 0 0 0 0 4 4 n | * * * 2
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