Acronym | test | ||||||||||||||||||||||||||||||||
Name |
tesseractic tetracomb, 4D hypercubical honeycomb (δ4), Voronoi complex of C4 lattice, Delone complex of C4 lattice | ||||||||||||||||||||||||||||||||
Vertex layers
(first ones only) |
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Coordinates | (i, j, k, l) i.e. all integer touples | ||||||||||||||||||||||||||||||||
Dual | (selfdual) | ||||||||||||||||||||||||||||||||
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x4o3o3o4o (N → ∞) . . . . . | N ♦ 8 | 24 | 32 | 16 ----------+----+----+----+----+--- x . . . . | 2 | 4N ♦ 6 | 12 | 8 ----------+----+----+----+----+--- x4o . . . | 4 | 4 | 6N | 4 | 4 ----------+----+----+----+----+--- x4o3o . . ♦ 8 | 12 | 6 | 4N | 2 ----------+----+----+----+----+--- x4o3o3o . ♦ 16 | 32 | 24 | 8 | N snubbed forms: s4o3o3o4o
x4o3o3o4x (N → ∞) . . . . . | 16N ♦ 4 4 | 6 12 6 | 4 12 12 4 | 1 4 6 4 1 ----------+-----+---------+-------------+---------------+------------- x . . . . | 2 | 32N * ♦ 3 3 0 | 3 6 3 0 | 1 3 3 1 0 . . . . x | 2 | * 32N ♦ 0 3 3 | 0 3 6 3 | 0 1 3 3 1 ----------+-----+---------+-------------+---------------+------------- x4o . . . | 4 | 4 0 | 24N * * | 2 2 0 0 | 1 2 1 0 0 x . . . x | 4 | 2 2 | * 48N * | 0 2 2 0 | 0 1 2 1 0 . . . o4x | 4 | 0 4 | * * 24N | 0 0 2 2 | 0 0 1 2 1 ----------+-----+---------+-------------+---------------+------------- x4o3o . . ♦ 8 | 12 0 | 6 0 0 | 8N * * * | 1 1 0 0 0 x4o . . x ♦ 8 | 8 4 | 2 4 0 | * 24N * * | 0 1 1 0 0 x . . o4x ♦ 8 | 4 8 | 0 4 2 | * * 24N * | 0 0 1 1 0 . . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * * 8N | 0 0 0 1 1 ----------+-----+---------+-------------+---------------+------------- x4o3o3o . ♦ 16 | 32 0 | 24 0 0 | 8 0 0 0 | N * * * * x4o3o . x ♦ 16 | 24 8 | 12 12 0 | 2 6 0 0 | * 4N * * * x4o . o4x ♦ 16 | 16 16 | 4 16 4 | 0 4 4 0 | * * 6N * * x . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 0 6 2 | * * * 4N * . o3o3o4x ♦ 16 | 0 32 | 0 0 24 | 0 0 0 8 | * * * * N snubbed forms: s4o3o3o4x, s4o3o3o4s
o3o3o *b3o4x (N → ∞) . . . . . | 2N ♦ 8 | 24 | 32 | 8 8 -------------+----+----+-----+----+---- . . . . x | 2 | 8N ♦ 6 | 12 | 4 4 -------------+----+----+-----+----+---- . . . o4x | 4 | 4 | 12N | 4 | 2 2 -------------+----+----+-----+----+---- . o . *b3o4x ♦ 8 | 12 | 6 | 8N | 1 1 -------------+----+----+-----+----+---- o3o . *b3o4x ♦ 16 | 32 | 24 | 8 | N * . o3o *b3o4x ♦ 16 | 32 | 24 | 8 | * N
x∞o x4o3o4o (N → ∞) . . . . . . | N ♦ 2 6 | 12 12 | 24 8 | 16 ------------+----+------+-------+------+--- x . . . . . | 2 | N * ♦ 6 0 | 12 0 | 8 . . x . . . | 2 | * 3N ♦ 2 4 | 8 4 | 8 ------------+----+------+-------+------+--- x . x . . . | 4 | 2 2 | 3N * | 4 0 | 4 . . x4o . . | 4 | 0 4 | * 3N | 2 2 | 4 ------------+----+------+-------+------+--- x . x4o . . ♦ 8 | 4 8 | 4 2 | 3N * | 2 . . x4o3o . ♦ 8 | 0 12 | 0 6 | * N | 2 ------------+----+------+-------+------+--- x . x4o3o . ♦ 16 | 8 24 | 12 12 | 6 2 | N
x∞x x4o3o4o (N → ∞) . . . . . . | 2N ♦ 1 1 6 | 6 6 12 | 12 12 8 | 8 8 ------------+----+--------+----------+----------+---- x . . . . . | 2 | N * * ♦ 6 0 0 | 12 0 0 | 8 0 . x . . . . | 2 | * N * ♦ 0 6 0 | 0 12 0 | 0 8 . . x . . . | 2 | * * 6N ♦ 1 1 4 | 4 4 4 | 4 4 ------------+----+--------+----------+----------+---- x . x . . . | 4 | 2 0 2 | 3N * * | 4 0 0 | 4 0 . x x . . . | 4 | 0 2 2 | * 3N * | 0 4 0 | 0 4 . . x4o . . | 4 | 0 0 4 | * * 6N | 1 1 2 | 2 2 ------------+----+--------+----------+----------+---- x . x4o . . ♦ 8 | 4 0 8 | 4 0 2 | 3N * * | 2 0 . x x4o . . ♦ 8 | 0 4 8 | 0 4 2 | * 3N * | 0 2 . . x4o3o . ♦ 8 | 0 0 12 | 0 0 6 | * * 2N | 1 1 ------------+----+--------+----------+----------+---- x . x4o3o . ♦ 16 | 8 0 24 | 12 0 12 | 6 0 2 | N * . x x4o3o . ♦ 16 | 0 8 24 | 0 12 12 | 0 6 2 | * N
x∞o x4o3o4x (N → ∞) . . . . . . | 8N ♦ 2 3 3 | 6 6 3 6 3 | 6 12 6 1 3 3 1 | 2 6 6 2 ------------+----+------------+-------------------+---------------------+---------- x . . . . . | 2 | 8N * * ♦ 3 3 0 0 0 | 3 6 3 0 0 0 0 | 1 3 3 1 . . x . . . | 2 | * 12N * ♦ 2 0 2 2 0 | 4 4 0 1 2 1 0 | 2 4 2 0 . . . . . x | 2 | * * 12N ♦ 0 2 0 2 2 | 0 4 4 0 1 2 1 | 0 2 4 2 ------------+----+------------+-------------------+---------------------+---------- x . x . . . | 4 | 2 2 0 | 12N * * * * | 2 2 0 0 0 0 0 | 1 2 1 0 x . . . . x | 4 | 2 0 2 | * 12N * * * | 0 2 2 0 0 0 0 | 0 1 2 1 . . x4o . . | 4 | 0 4 0 | * * 6N * * | 2 0 0 1 1 0 0 | 2 2 0 0 . . x . . x | 4 | 0 2 2 | * * * 12N * | 0 2 0 0 1 1 0 | 0 2 2 0 . . . . o4x | 4 | 0 0 4 | * * * * 6N | 0 0 2 0 0 1 1 | 0 0 2 2 ------------+----+------------+-------------------+---------------------+---------- x . x4o . . ♦ 8 | 4 8 0 | 4 0 2 0 0 | 6N * * * * * * | 1 1 0 0 x . x . . x ♦ 8 | 4 4 4 | 2 2 0 2 0 | * 12N * * * * * | 0 1 1 0 x . . . o4x ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 6N * * * * | 0 0 1 1 . . x4o3o . ♦ 8 | 0 12 0 | 0 0 6 0 0 | * * * N * * * | 2 0 0 0 . . x4o . x ♦ 8 | 0 8 4 | 0 0 2 4 0 | * * * * 3N * * | 0 2 0 0 . . x . o4x ♦ 8 | 0 4 8 | 0 0 0 4 2 | * * * * * 3N * | 0 0 2 0 . . . o3o4x ♦ 8 | 0 0 12 | 0 0 0 0 6 | * * * * * * N | 0 0 0 2 ------------+----+------------+-------------------+---------------------+---------- x . x4o3o . ♦ 16 | 8 24 0 | 12 0 12 0 0 | 6 0 0 2 0 0 0 | N * * * x . x4o . x ♦ 16 | 8 16 8 | 8 4 4 8 0 | 2 4 0 0 2 0 0 | * 3N * * x . x . o4x ♦ 16 | 8 8 16 | 4 8 0 8 4 | 0 4 2 0 0 2 0 | * * 3N * x . . o3o4x ♦ 16 | 8 0 24 | 0 12 0 0 12 | 0 0 6 0 0 0 2 | * * * N
x∞x x4o3o4x (N → ∞) . . . . . . | 16N ♦ 1 1 3 3 | 3 3 3 3 3 6 3 | 3 6 3 3 6 3 1 3 3 1 | 1 3 3 1 1 3 3 1 ------------+-----+---------------+-----------------------------+---------------------------------+-------------------- x . . . . . | 2 | 8N * * * ♦ 3 3 0 0 0 0 0 | 3 6 3 0 0 0 0 0 0 0 | 1 3 3 1 0 0 0 0 . x . . . . | 2 | * 8N * * ♦ 0 0 3 3 0 0 0 | 0 0 0 3 6 3 0 0 0 0 | 0 0 0 0 1 3 3 1 . . x . . . | 2 | * * 24N * ♦ 1 0 1 0 2 2 0 | 2 2 0 2 2 0 1 2 1 0 | 1 2 1 0 1 2 1 0 . . . . . x | 2 | * * * 24N ♦ 0 1 0 1 0 2 2 | 0 2 2 0 2 2 0 1 2 1 | 0 1 2 1 0 1 2 1 ------------+-----+---------------+-----------------------------+---------------------------------+-------------------- x . x . . . | 4 | 2 0 2 0 | 12N * * * * * * | 2 2 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 x . . . . x | 4 | 2 0 0 2 | * 12N * * * * * | 0 2 2 0 0 0 0 0 0 0 | 0 1 2 1 0 0 0 0 . x x . . . | 4 | 0 2 2 0 | * * 12N * * * * | 0 0 0 2 2 0 0 0 0 0 | 0 0 0 0 1 2 1 0 . x . . . x | 4 | 0 2 0 2 | * * * 12N * * * | 0 0 0 0 2 2 0 0 0 0 | 0 0 0 0 0 1 2 1 . . x4o . . | 4 | 0 0 4 0 | * * * * 12N * * | 1 0 0 1 0 0 1 1 0 0 | 1 1 0 0 1 1 0 0 . . x . . x | 4 | 0 0 2 2 | * * * * * 24N * | 0 1 0 0 1 0 0 1 1 0 | 0 1 1 0 0 1 1 0 . . . . o4x | 4 | 0 0 0 4 | * * * * * * 12N | 0 0 1 0 0 1 0 0 1 1 | 0 0 1 1 0 0 1 1 ------------+-----+---------------+-----------------------------+---------------------------------+-------------------- x . x4o . . ♦ 8 | 4 0 8 0 | 4 0 0 0 2 0 0 | 6N * * * * * * * * * | 1 1 0 0 0 0 0 0 x . x . . x ♦ 8 | 4 0 4 4 | 2 2 0 0 0 2 0 | * 12N * * * * * * * * | 0 1 1 0 0 0 0 0 x . . . o4x ♦ 8 | 4 0 0 8 | 0 4 0 0 0 0 2 | * * 6N * * * * * * * | 0 0 1 1 0 0 0 0 . x x4o . . ♦ 8 | 0 4 8 0 | 0 0 4 0 2 0 0 | * * * 6N * * * * * * | 0 0 0 0 1 1 0 0 . x x . . x ♦ 8 | 0 4 4 4 | 0 0 2 2 0 2 0 | * * * * 12N * * * * * | 0 0 0 0 0 1 1 0 . x . . o4x ♦ 8 | 0 4 0 8 | 0 0 0 4 0 0 2 | * * * * * 6N * * * * | 0 0 0 0 0 0 1 1 . . x4o3o . ♦ 8 | 0 0 12 0 | 0 0 0 0 6 0 0 | * * * * * * 2N * * * | 1 0 0 0 1 0 0 0 . . x4o . x ♦ 8 | 0 0 8 4 | 0 0 0 0 2 4 0 | * * * * * * * 6N * * | 0 1 0 0 0 1 0 0 . . x . o4x ♦ 8 | 0 0 4 8 | 0 0 0 0 0 4 2 | * * * * * * * * 6N * | 0 0 1 0 0 0 1 0 . . . o3o4x ♦ 8 | 0 0 0 12 | 0 0 0 0 0 0 6 | * * * * * * * * * 2N | 0 0 0 1 0 0 0 1 ------------+-----+---------------+-----------------------------+---------------------------------+-------------------- x . x4o3o . ♦ 16 | 8 0 24 0 | 12 0 0 0 12 0 0 | 6 0 0 0 0 0 2 0 0 0 | N * * * * * * * x . x4o . x ♦ 16 | 8 0 16 8 | 8 4 0 0 4 8 0 | 2 4 0 0 0 0 0 2 0 0 | * 3N * * * * * * x . x . o4x ♦ 16 | 8 0 8 16 | 4 8 0 0 0 8 4 | 0 4 2 0 0 0 0 0 2 0 | * * 3N * * * * * x . . o3o4x ♦ 16 | 8 0 0 24 | 0 12 0 0 0 0 12 | 0 0 6 0 0 0 0 0 0 2 | * * * N * * * * . x x4o3o . ♦ 16 | 0 8 24 0 | 0 0 12 0 12 0 0 | 0 0 0 6 0 0 2 0 0 0 | * * * * N * * * . x x4o . x ♦ 16 | 0 8 16 8 | 0 0 8 4 4 8 0 | 0 0 0 2 4 0 0 2 0 0 | * * * * * 3N * * . x x . o4x ♦ 16 | 0 8 8 16 | 0 0 4 8 0 8 4 | 0 0 0 0 4 2 0 0 2 0 | * * * * * * 3N * . x . o3o4x ♦ 16 | 0 8 0 24 | 0 0 0 12 0 0 12 | 0 0 0 0 0 6 0 0 0 2 | * * * * * * * N
x∞o o3o3o *d4x (N → ∞) . . . . . . | 2N ♦ 2 6 | 12 12 | 24 4 4 | 8 8 ---------------+----+-------+-------+--------+---- x . . . . . | 2 | 2N * ♦ 6 0 | 12 0 0 | 4 4 . . . . . x | 2 | * 6N ♦ 2 4 | 8 2 2 | 4 4 ---------------+----+-------+-------+--------+---- x . . . . x | 4 | 2 2 | 6N * | 4 0 0 | 2 2 . . . o . *d4x | 4 | 0 4 | * 6N | 2 1 1 | 2 2 ---------------+----+-------+-------+--------+---- x . . o . *d4x ♦ 8 | 4 8 | 4 2 | 6N * * | 1 1 . . o3o . *d4x ♦ 8 | 0 12 | 0 6 | * N * | 2 0 . . . o3o *d4x ♦ 8 | 0 12 | 0 6 | * * N | 0 2 ---------------+----+-------+-------+--------+---- x . o3o . *d4x ♦ 16 | 8 24 | 12 12 | 6 2 0 | N * x . . o3o *d4x ♦ 16 | 8 24 | 12 12 | 6 0 2 | * N
x∞x o3o3o *d4x (N → ∞) . . . . . . | 4N ♦ 1 1 6 | 6 6 12 | 12 12 4 4 | 4 4 4 4 ---------------+----+-----------+-----------+-------------+-------- x . . . . . | 2 | 2N * * ♦ 6 0 0 | 12 0 0 0 | 4 4 0 0 . x . . . . | 2 | * 2N * ♦ 0 6 0 | 0 12 0 0 | 0 0 4 4 . . . . . x | 2 | * * 12N ♦ 1 1 4 | 4 4 2 2 | 2 2 2 2 ---------------+----+-----------+-----------+-------------+-------- x . . . . x | 4 | 2 0 2 | 6N * * | 4 0 0 0 | 2 2 0 0 . x . . . x | 4 | 0 2 2 | * 6N * | 0 4 0 0 | 0 0 2 2 . . . o . *d4x | 4 | 0 0 4 | * * 12N | 1 1 1 1 | 1 1 1 1 ---------------+----+-----------+-----------+-------------+-------- x . . o . *d4x ♦ 8 | 4 0 8 | 4 0 2 | 6N * * * | 1 1 0 0 . x . o . *d4x ♦ 8 | 0 4 8 | 0 4 2 | * 6N * * | 0 0 1 1 . . o3o . *d4x ♦ 8 | 0 0 12 | 0 0 6 | * * 2N * | 1 0 1 0 . . . o3o *d4x ♦ 8 | 0 0 12 | 0 0 6 | * * * 2N | 0 1 0 1 ---------------+----+-----------+-----------+-------------+-------- x . o3o . *d4x ♦ 16 | 8 0 24 | 12 0 12 | 6 0 2 0 | N * * * x . . o3o *d4x ♦ 16 | 8 0 24 | 12 0 12 | 6 0 0 2 | * N * * . x o3o . *d4x ♦ 16 | 0 8 24 | 0 12 12 | 0 6 2 0 | * * N * . x . o3o *d4x ♦ 16 | 0 8 24 | 0 12 12 | 0 6 0 2 | * * * N
x4o4o x4o4o (N → ∞) . . . . . . | N ♦ 4 4 | 4 16 4 | 16 16 | 16 ------------+----+-------+--------+-------+--- x . . . . . | 2 | 2N * ♦ 2 4 0 | 8 4 | 8 . . . x . . | 2 | * 2N ♦ 0 4 2 | 4 8 | 8 ------------+----+-------+--------+-------+--- x4o . . . . | 4 | 4 0 | N * * | 4 0 | 4 x . . x . . | 4 | 2 2 | * 4N * | 2 2 | 4 . . . x4o . | 4 | 0 4 | * * N | 0 4 | 4 ------------+----+-------+--------+-------+--- x4o . x . . ♦ 8 | 8 4 | 2 4 0 | 2N * | 2 x . . x4o . ♦ 8 | 4 8 | 0 4 2 | * 2N | 2 ------------+----+-------+--------+-------+--- x4o . x4o . ♦ 16 | 16 16 | 4 16 4 | 4 4 | N
x4o4o o4x4o (N → ∞) . . . . . . | 2N ♦ 4 4 | 4 16 2 2 | 16 8 8 | 8 8 ------------+----+-------+-----------+----------+---- x . . . . . | 2 | 4N * ♦ 2 4 0 0 | 8 2 2 | 4 4 . . . . x . | 2 | * 4N ♦ 0 4 1 1 | 4 4 4 | 4 4 ------------+----+-------+-----------+----------+---- x4o . . . . | 4 | 4 0 | 2N * * * | 4 0 0 | 2 2 x . . . x . | 4 | 2 2 | * 8N * * | 2 1 1 | 2 2 . . . o4x . | 4 | 0 4 | * * N * | 0 4 0 | 4 0 . . . . x4o | 4 | 0 4 | * * * N | 0 0 4 | 0 4 ------------+----+-------+-----------+----------+---- x4o . . x . ♦ 8 | 8 4 | 2 4 0 0 | 4N * * | 1 1 x . . o4x . ♦ 8 | 4 8 | 0 4 2 0 | * 2N * | 2 0 x . . . x4o ♦ 8 | 4 8 | 0 4 0 2 | * * 2N | 0 2 ------------+----+-------+-----------+----------+---- x4o . o4x . ♦ 16 | 16 16 | 4 16 4 0 | 4 4 0 | N * x4o . . x4o ♦ 16 | 16 16 | 4 16 0 4 | 4 0 4 | * N
x4o4o x4o4x (N → ∞) . . . . . . | 4N ♦ 4 2 2 | 4 8 8 1 2 1 | 8 8 4 8 4 | 4 8 4 ------------+----+----------+-----------------+----------------+------- x . . . . . | 2 | 8N * * ♦ 2 2 2 0 0 0 | 4 4 1 2 1 | 2 4 2 . . . x . . | 2 | * 4N * ♦ 0 4 0 1 1 0 | 4 0 4 4 0 | 4 4 0 . . . . . x | 2 | * * 4N ♦ 0 0 4 0 1 1 | 0 4 0 4 4 | 0 4 4 ------------+----+----------+-----------------+----------------+------- x4o . . . . | 4 | 4 0 0 | 4N * * * * * | 2 2 0 0 0 | 1 2 1 x . . x . . | 4 | 2 2 0 | * 8N * * * * | 2 0 1 1 0 | 2 2 0 x . . . . x | 4 | 2 0 2 | * * 8N * * * | 0 2 0 1 1 | 0 2 2 . . . x4o . | 4 | 0 4 0 | * * * N * * | 0 0 4 0 0 | 4 0 0 . . . x . x | 4 | 0 2 2 | * * * * 2N * | 0 0 0 4 0 | 0 4 0 . . . . o4x | 4 | 0 0 4 | * * * * * N | 0 0 0 0 4 | 0 0 4 ------------+----+----------+-----------------+----------------+------- x4o . x . . ♦ 8 | 8 4 0 | 2 4 0 0 0 0 | 4N * * * * | 1 1 0 x4o . . . x ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * 4N * * * | 0 1 1 x . . x4o . ♦ 8 | 4 8 0 | 0 4 0 2 0 0 | * * 2N * * | 2 0 0 x . . x . x ♦ 8 | 4 4 4 | 0 2 2 0 2 0 | * * * 4N * | 0 2 0 x . . . o4x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 2N | 0 0 2 ------------+----+----------+-----------------+----------------+------- x4o . x4o . ♦ 16 | 16 16 0 | 4 16 0 4 0 0 | 4 0 4 0 0 | N * * x4o . x . x ♦ 16 | 16 8 8 | 4 8 8 0 4 0 | 2 2 0 4 0 | * 2N * x4o . . o4x ♦ 16 | 16 0 16 | 4 0 16 0 0 4 | 0 4 0 0 4 | * * N
o4x4o o4x4o (N → ∞) . . . . . . | 4N ♦ 4 4 | 2 2 16 2 2 | 8 8 8 8 | 4 4 4 4 ------------+----+-------+-----------------+-------------+-------- . x . . . . | 2 | 8N * ♦ 1 1 4 0 0 | 4 4 2 2 | 2 2 2 2 . . . . x . | 2 | * 8N ♦ 0 0 4 1 1 | 2 2 4 4 | 2 2 2 2 ------------+----+-------+-----------------+-------------+-------- o4x . . . . | 4 | 4 0 | 2N * * * * | 4 0 0 0 | 2 2 0 0 . x4o . . . | 4 | 4 0 | * 2N * * * | 0 4 0 0 | 0 0 2 2 . x . . x . | 4 | 2 2 | * * 16N * * | 1 1 1 1 | 1 1 1 1 . . . o4x . | 4 | 0 4 | * * * 2N * | 0 0 4 0 | 2 0 2 0 . . . . x4o | 4 | 0 4 | * * * * 2N | 0 0 0 4 | 0 2 0 2 ------------+----+-------+-----------------+-------------+-------- o4x . . x . ♦ 8 | 8 4 | 2 0 4 0 0 | 4N * * * | 1 1 0 0 . x4o . x . ♦ 8 | 8 4 | 0 2 4 0 0 | * 4N * * | 0 0 1 1 . x . o4x . ♦ 8 | 4 8 | 0 0 4 2 0 | * * 4N * | 1 0 1 0 . x . . x4o ♦ 8 | 4 8 | 0 0 4 0 2 | * * * 4N | 0 1 0 1 ------------+----+-------+-----------------+-------------+-------- o4x . o4x . ♦ 16 | 16 16 | 4 0 16 4 0 | 4 0 4 0 | N * * * o4x . . x4o ♦ 16 | 16 16 | 4 0 16 0 4 | 4 0 0 4 | * N * * . x4o o4x . ♦ 16 | 16 16 | 0 4 16 4 0 | 0 4 4 0 | * * N * . x4o . x4o ♦ 16 | 16 16 | 0 4 16 0 4 | 0 4 0 4 | * * * N
o4x4o x4o4x (N → ∞) . . . . . . | 8N ♦ 4 2 2 | 2 2 8 8 1 2 1 | 4 4 4 4 4 8 4 | 2 4 2 2 4 2 ------------+----+-----------+------------------------+----------------------+-------------- . x . . . . | 2 | 16N * * ♦ 1 1 2 2 0 0 0 | 2 2 2 2 1 2 1 | 1 2 1 1 2 1 . . . x . . | 2 | * 8N * ♦ 0 0 4 0 1 1 0 | 2 0 2 0 4 4 0 | 2 2 0 2 2 0 . . . . . x | 2 | * * 8N ♦ 0 0 0 4 0 1 1 | 0 2 0 2 0 4 4 | 0 2 2 0 2 2 ------------+----+-----------+------------------------+----------------------+-------------- o4x . . . . | 4 | 4 0 0 | 4N * * * * * * | 2 2 0 0 0 0 0 | 1 2 1 0 0 0 . x4o . . . | 4 | 4 0 0 | * 4N * * * * * | 0 0 2 2 0 0 0 | 0 0 0 1 2 1 . x . x . . | 4 | 2 2 0 | * * 16N * * * * | 1 0 1 0 1 1 0 | 1 1 0 1 1 0 . x . . . x | 4 | 2 0 2 | * * * 16N * * * | 0 1 0 1 0 1 1 | 0 1 1 0 1 1 . . . x4o . | 4 | 0 4 0 | * * * * 2N * * | 0 0 0 0 4 0 0 | 2 0 0 2 0 0 . . . x . x | 4 | 0 2 2 | * * * * * 4N * | 0 0 0 0 0 4 0 | 0 2 0 0 2 0 . . . . o4x | 4 | 0 0 4 | * * * * * * 2N | 0 0 0 0 0 0 4 | 0 0 2 0 0 2 ------------+----+-----------+------------------------+----------------------+-------------- o4x . x . . ♦ 8 | 8 4 0 | 2 0 4 0 0 0 0 | 4N * * * * * * | 1 1 0 0 0 0 o4x . . . x ♦ 8 | 8 0 4 | 2 0 0 4 0 0 0 | * 4N * * * * * | 0 1 1 0 0 0 . x4o x . . ♦ 8 | 8 4 0 | 0 2 4 0 0 0 0 | * * 4N * * * * | 0 0 0 1 1 0 . x4o . . x ♦ 8 | 8 0 4 | 0 2 0 4 0 0 0 | * * * 4N * * * | 0 0 0 0 1 1 . x . x4o . ♦ 8 | 4 8 0 | 0 0 4 0 2 0 0 | * * * * 4N * * | 1 0 0 1 0 0 . x . x . x ♦ 8 | 4 4 4 | 0 0 2 2 0 2 0 | * * * * * 8N * | 0 1 0 0 1 0 . x . . o4x ♦ 8 | 4 0 8 | 0 0 0 4 0 0 2 | * * * * * * 4N | 0 0 1 0 0 1 ------------+----+-----------+------------------------+----------------------+-------------- o4x . x4o . ♦ 16 | 16 16 0 | 4 0 16 0 4 0 0 | 4 0 0 0 4 0 0 | N * * * * * o4x . x . x ♦ 16 | 16 8 8 | 4 0 8 8 0 4 0 | 2 2 0 0 0 4 0 | * 2N * * * * o4x . . o4x ♦ 16 | 16 0 16 | 4 0 0 16 0 0 4 | 0 4 0 0 0 0 4 | * * N * * * . x4o x4o . ♦ 16 | 16 16 0 | 0 4 16 0 4 0 0 | 0 0 4 0 4 0 0 | * * * N * * . x4o x . x ♦ 16 | 16 8 8 | 0 4 8 8 0 4 0 | 0 0 2 2 0 4 0 | * * * * 2N * . x4o . o4x ♦ 16 | 16 0 16 | 0 4 0 16 0 0 4 | 0 0 0 4 0 0 4 | * * * * * N
x4o4x x4o4x (N → ∞) . . . . . . | 16N ♦ 2 2 2 2 | 1 2 4 4 1 4 4 1 2 1 | 2 2 4 4 2 4 2 2 2 2 4 2 | 1 2 1 2 4 2 1 2 1 ------------+-----+-----------------+-----------------------------------+-------------------------------------+----------------------- x . . . . . | 2 | 16N * * * ♦ 1 1 2 2 0 0 0 0 0 0 | 2 2 2 2 1 2 1 0 0 0 0 0 | 1 2 1 1 2 1 0 0 0 . . x . . . | 2 | * 16N * * ♦ 0 1 0 0 1 2 2 0 0 0 | 0 0 2 2 0 0 0 2 2 1 2 1 | 0 0 0 1 2 1 1 2 1 . . . x . . | 2 | * * 16N * ♦ 0 0 2 0 0 2 0 1 1 0 | 1 0 2 0 2 2 0 1 0 2 2 0 | 1 1 0 2 2 0 1 1 0 . . . . . x | 2 | * * * 16N ♦ 0 0 0 2 0 0 2 0 1 1 | 0 1 0 2 0 2 2 0 1 0 2 2 | 0 1 1 0 2 2 0 1 1 ------------+-----+-----------------+-----------------------------------+-------------------------------------+----------------------- x4o . . . . | 4 | 4 0 0 0 | 4N * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 x . x . . . | 4 | 2 2 0 0 | * 8N * * * * * * * * | 0 0 2 2 0 0 0 0 0 0 0 0 | 0 0 0 1 2 1 0 0 0 x . . x . . | 4 | 2 0 2 0 | * * 16N * * * * * * * | 1 0 1 0 1 1 0 0 0 0 0 0 | 1 1 0 1 1 0 0 0 0 x . . . . x | 4 | 2 0 0 2 | * * * 16N * * * * * * | 0 1 0 1 0 1 1 0 0 0 0 0 | 0 1 1 0 1 1 0 0 0 . o4x . . . | 4 | 0 4 0 0 | * * * * 4N * * * * * | 0 0 0 0 0 0 0 2 2 0 0 0 | 0 0 0 0 0 0 1 2 1 . . x x . . | 4 | 0 2 2 0 | * * * * * 16N * * * * | 0 0 1 0 0 0 0 1 0 1 1 0 | 0 0 0 1 1 0 1 1 0 . . x . . x | 4 | 0 2 0 2 | * * * * * * 16N * * * | 0 0 0 1 0 0 0 0 1 0 1 1 | 0 0 0 0 1 1 0 1 1 . . . x4o . | 4 | 0 0 4 0 | * * * * * * * 4N * * | 0 0 0 0 2 0 0 0 0 2 0 0 | 1 0 0 2 0 0 1 0 0 . . . x . x | 4 | 0 0 2 2 | * * * * * * * * 8N * | 0 0 0 0 0 2 0 0 0 0 2 0 | 0 1 0 0 2 0 0 1 0 . . . . o4x | 4 | 0 0 0 4 | * * * * * * * * * 4N | 0 0 0 0 0 0 2 0 0 0 0 2 | 0 0 1 0 0 2 0 0 1 ------------+-----+-----------------+-----------------------------------+-------------------------------------+----------------------- x4o . x . . ♦ 8 | 8 0 4 0 | 2 0 4 0 0 0 0 0 0 0 | 4N * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 x4o . . . x ♦ 8 | 8 0 0 4 | 2 0 0 4 0 0 0 0 0 0 | * 4N * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 x . x x . . ♦ 8 | 4 4 4 0 | 0 2 2 0 0 2 0 0 0 0 | * * 8N * * * * * * * * * | 0 0 0 1 1 0 0 0 0 x . x . . x ♦ 8 | 4 4 0 4 | 0 2 0 2 0 0 2 0 0 0 | * * * 8N * * * * * * * * | 0 0 0 0 1 1 0 0 0 x . . x4o . ♦ 8 | 4 0 8 0 | 0 0 4 0 0 0 0 2 0 0 | * * * * 4N * * * * * * * | 1 0 0 1 0 0 0 0 0 x . . x . x ♦ 8 | 4 0 4 4 | 0 0 2 2 0 0 0 0 2 0 | * * * * * 8N * * * * * * | 0 1 0 0 1 0 0 0 0 x . . . o4x ♦ 8 | 4 0 0 8 | 0 0 0 4 0 0 0 0 0 2 | * * * * * * 4N * * * * * | 0 0 1 0 0 1 0 0 0 . o4x x . . ♦ 8 | 0 8 4 0 | 0 0 0 0 2 4 0 0 0 0 | * * * * * * * 4N * * * * | 0 0 0 0 0 0 1 1 0 . o4x . . x ♦ 8 | 0 8 0 4 | 0 0 0 0 2 0 4 0 0 0 | * * * * * * * * 4N * * * | 0 0 0 0 0 0 0 1 1 . . x x4o . ♦ 8 | 0 4 8 0 | 0 0 0 0 0 4 0 2 0 0 | * * * * * * * * * 4N * * | 0 0 0 1 0 0 1 0 0 . . x x . x ♦ 8 | 0 4 4 4 | 0 0 0 0 0 2 2 0 2 0 | * * * * * * * * * * 8N * | 0 0 0 0 1 0 0 1 0 . . x . o4x ♦ 8 | 0 4 0 8 | 0 0 0 0 0 0 4 0 0 2 | * * * * * * * * * * * 4N | 0 0 0 0 0 1 0 0 1 ------------+-----+-----------------+-----------------------------------+-------------------------------------+----------------------- x4o . x4o . ♦ 16 | 16 0 16 0 | 4 0 16 0 0 0 0 4 0 0 | 4 0 0 0 4 0 0 0 0 0 0 0 | N * * * * * * * * x4o . x . x ♦ 16 | 16 0 8 8 | 4 0 8 8 0 0 0 0 4 0 | 2 2 0 0 0 4 0 0 0 0 0 0 | * 2N * * * * * * * x4o . . o4x ♦ 16 | 16 0 0 16 | 4 0 0 16 0 0 0 0 0 4 | 0 4 0 0 0 0 4 0 0 0 0 0 | * * N * * * * * * x . x x4o . ♦ 16 | 8 8 16 0 | 0 4 8 0 0 8 0 4 0 0 | 0 0 4 0 2 0 0 0 0 2 0 0 | * * * 2N * * * * * x . x x . x ♦ 16 | 8 8 8 8 | 0 4 4 4 0 4 4 0 4 0 | 0 0 2 2 0 2 0 0 0 0 2 0 | * * * * 4N * * * * x . x . o4x ♦ 16 | 8 8 0 16 | 0 4 0 8 0 0 8 0 0 4 | 0 0 0 4 0 0 2 0 0 0 0 2 | * * * * * 2N * * * . o4x x4o . ♦ 16 | 0 16 16 0 | 0 0 0 0 4 16 0 4 0 0 | 0 0 0 0 0 0 0 4 0 4 0 0 | * * * * * * N * * . o4x x . x ♦ 16 | 0 16 8 8 | 0 0 0 0 4 8 8 0 4 0 | 0 0 0 0 0 0 0 2 2 0 4 0 | * * * * * * * 2N * . o4x . o4x ♦ 16 | 0 16 0 16 | 0 0 0 0 4 0 16 0 0 4 | 0 0 0 0 0 0 0 0 4 0 0 4 | * * * * * * * * N
x∞o x∞o x4o4o (N → ∞) . . . . . . . | N ♦ 2 2 4 | 4 8 8 4 | 16 8 8 | 16 --------------+----+--------+-----------+--------+--- x . . . . . . | 2 | N * * ♦ 2 4 0 0 | 8 4 0 | 8 . . x . . . . | 2 | * N * ♦ 2 0 4 0 | 8 0 4 | 8 . . . . x . . | 2 | * * 2N ♦ 0 2 2 2 | 4 4 4 | 8 --------------+----+--------+-----------+--------+--- x . x . . . . | 4 | 2 2 0 | N * * * | 4 0 0 | 4 x . . . x . . | 4 | 2 0 2 | * 2N * * | 2 2 0 | 4 . . x . x . . | 4 | 0 2 2 | * * 2N * | 2 0 2 | 4 . . . . x4o . | 4 | 0 0 4 | * * * N | 0 2 2 | 4 --------------+----+--------+-----------+--------+--- x . x . x . . ♦ 8 | 4 4 4 | 2 2 2 0 | 2N * * | 2 x . . . x4o . ♦ 8 | 4 0 8 | 0 4 0 2 | * N * | 2 . . x . x4o . ♦ 8 | 0 4 8 | 0 0 4 2 | * * N | 2 --------------+----+--------+-----------+--------+--- x . x . x4o . ♦ 16 | 8 8 16 | 4 8 8 4 | 4 2 2 | N
x∞o x∞o o4x4o (N → ∞) . . . . . . . | 2N ♦ 2 2 4 | 4 8 8 2 2 | 16 4 4 4 4 | 8 8 --------------+----+----------+--------------+------------+---- x . . . . . . | 2 | 2N * * ♦ 2 4 0 0 0 | 8 2 2 0 0 | 4 4 . . x . . . . | 2 | * 2N * ♦ 2 0 4 0 0 | 8 0 0 2 2 | 4 4 . . . . . x . | 2 | * * 4N ♦ 0 2 2 1 1 | 4 2 2 2 2 | 4 4 --------------+----+----------+--------------+------------+---- x . x . . . . | 4 | 2 2 0 | 2N * * * * | 4 0 0 0 0 | 2 2 x . . . . x . | 4 | 2 0 2 | * 4N * * * | 2 1 1 0 0 | 2 2 . . x . . x . | 4 | 0 2 2 | * * 4N * * | 2 0 0 1 1 | 2 2 . . . . o4x . | 4 | 0 0 4 | * * * N * | 0 2 0 2 0 | 4 0 . . . . . x4o | 4 | 0 0 4 | * * * * N | 0 0 2 0 2 | 0 4 --------------+----+----------+--------------+------------+---- x . x . . x . ♦ 8 | 4 4 4 | 2 2 2 0 0 | 4N * * * * | 1 1 x . . . o4x . ♦ 8 | 4 0 8 | 0 4 0 2 0 | * N * * * | 2 0 x . . . . x4o ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * N * * | 0 2 . . x . o4x . ♦ 8 | 0 4 8 | 0 0 4 2 0 | * * * N * | 2 0 . . x . . x4o ♦ 8 | 0 4 8 | 0 0 4 0 2 | * * * * N | 0 2 --------------+----+----------+--------------+------------+---- x . x . o4x . ♦ 16 | 8 8 16 | 4 8 8 4 0 | 4 2 0 2 0 | N * x . x . . x4o ♦ 16 | 8 8 16 | 4 8 8 0 4 | 4 0 2 0 2 | * N
x∞o x∞o x4o4x (N → ∞) . . . . . . . | 4N ♦ 2 2 2 2 | 4 4 4 4 4 1 2 1 | 8 8 2 4 2 2 4 2 | 4 8 4 --------------+----+-------------+-----------------------+---------------------+------- x . . . . . . | 2 | 4N * * * ♦ 2 2 2 0 0 0 0 0 | 4 4 1 2 1 0 0 0 | 2 4 2 . . x . . . . | 2 | * 4N * * ♦ 2 0 0 2 2 0 0 0 | 4 4 0 0 0 1 2 1 | 2 4 2 . . . . x . . | 2 | * * 4N * ♦ 0 2 0 2 0 1 1 0 | 4 0 2 2 0 2 2 0 | 4 4 0 . . . . . . x | 2 | * * * 4N ♦ 0 0 2 0 2 0 1 1 | 0 4 0 2 2 0 2 2 | 0 4 4 --------------+----+-------------+-----------------------+---------------------+------- x . x . . . . | 4 | 2 2 0 0 | 4N * * * * * * * | 2 2 0 0 0 0 0 0 | 1 2 1 x . . . x . . | 4 | 2 0 2 0 | * 4N * * * * * * | 2 0 1 1 0 0 0 0 | 2 2 0 x . . . . . x | 4 | 2 0 0 2 | * * 4N * * * * * | 0 2 0 1 1 0 0 0 | 0 2 2 . . x . x . . | 4 | 0 2 2 0 | * * * 4N * * * * | 2 0 0 0 0 1 1 0 | 2 2 0 . . x . . . x | 4 | 0 2 0 2 | * * * * 4N * * * | 0 2 0 0 0 0 1 1 | 0 2 2 . . . . x4o . | 4 | 0 0 4 0 | * * * * * N * * | 0 0 2 0 0 2 0 0 | 4 0 0 . . . . x . x | 4 | 0 0 2 2 | * * * * * * 2N * | 0 0 0 2 0 0 2 0 | 0 4 0 . . . . . o4x | 4 | 0 0 0 4 | * * * * * * * N | 0 0 0 0 2 0 0 2 | 0 0 4 --------------+----+-------------+-----------------------+---------------------+------- x . x . x . . ♦ 8 | 4 4 4 0 | 2 2 0 2 0 0 0 0 | 4N * * * * * * * | 1 1 0 x . x . . . x ♦ 8 | 4 4 0 4 | 2 0 2 0 2 0 0 0 | * 4N * * * * * * | 0 1 1 x . . . x4o . ♦ 8 | 4 0 8 0 | 0 4 0 0 0 2 0 0 | * * N * * * * * | 2 0 0 x . . . x . x ♦ 8 | 4 0 4 4 | 0 2 2 0 0 0 2 0 | * * * 2N * * * * | 0 2 0 x . . . . o4x ♦ 8 | 4 0 0 8 | 0 0 4 0 0 0 0 2 | * * * * N * * * | 0 0 2 . . x . x4o . ♦ 8 | 0 4 8 0 | 0 0 0 4 0 2 0 0 | * * * * * N * * | 2 0 0 . . x . x . x ♦ 8 | 0 4 4 4 | 0 0 0 2 2 0 2 0 | * * * * * * 2N * | 0 2 0 . . x . . o4x ♦ 8 | 0 4 0 8 | 0 0 0 0 4 0 0 2 | * * * * * * * N | 0 0 2 --------------+----+-------------+-----------------------+---------------------+------- x . x . x4o . ♦ 16 | 8 8 16 0 | 4 8 0 8 0 4 0 0 | 4 0 2 0 0 2 0 0 | N * * 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 | * 2N * x . x . . o4x ♦ 16 | 8 8 0 16 | 4 0 8 0 8 0 0 4 | 0 4 0 0 2 0 0 2 | * * N
x∞x x∞o x4o4o ...
x∞x x∞o o4x4o ...
x∞x x∞x x4o4o ...
x∞x x∞x o4x4o ...
x∞x x∞o x4o4x ...
x∞x x∞x x4o4x ...
x∞o x∞o x∞o x∞o ...
x∞x x∞o x∞o x∞o ...
x∞x x∞x x∞o x∞o ...
x∞x x∞x x∞x x∞o ...
x∞x x∞x x∞x x∞x ...
:qooo:3:oqoo:3:ooqo:3:oooq:3*a&##x (N → ∞) → all heights = 1/2 = 0.5 o... 3 o... 3 o... 3 o... 3*a | N * * * ♦ 4 0 0 4 | 6 12 6 0 | 4 12 12 4 | 2 4 6 4 .o.. 3 .o.. 3 .o.. 3 .o.. 3*a | * N * * ♦ 4 4 0 0 | 12 6 0 6 | 12 12 4 4 | 4 2 4 6 ..o. 3 ..o. 3 ..o. 3 ..o. 3*a | * * N * ♦ 0 4 4 0 | 6 0 6 12 | 12 4 4 12 | 6 4 2 4 ...o 3 ...o 3 ...o 3 ...o 3*a | * * * N ♦ 0 0 4 4 | 0 6 12 6 | 4 4 12 12 | 4 6 4 2 -----------------------------------+---------+-------------+-------------+-------------+-------- oo.. 3 oo.. 3 oo.. 3 oo.. 3*a&#x | 1 1 0 0 | 4N * * * ♦ 3 3 0 0 | 3 6 3 0 | 1 1 3 3 .oo. 3 .oo. 3 .oo. 3 .oo. 3*a&#x | 0 1 1 0 | * 4N * * ♦ 3 0 0 3 | 6 3 0 3 | 3 1 1 3 ..oo 3 ..oo 3 ..oo 3 ..oo 3*a&#x | 0 0 1 1 | * * 4N * ♦ 0 0 3 3 | 3 0 3 6 | 3 3 1 1 :o..o:3:o..o:3:o..o:3:o..o:3*a&#x | 1 0 0 1 | * * * 4N ♦ 0 3 3 0 | 0 3 6 3 | 1 3 3 1 -----------------------------------+---------+-------------+-------------+-------------+-------- .... oqo. .... .... &#xt | 1 2 1 0 | 2 2 0 0 | 6N * * * | 2 2 0 0 | 1 0 1 2 :qo.o: .... .... .... &#xt | 2 1 0 1 | 2 0 0 2 | * 6N * * | 0 2 2 0 | 0 1 2 1 .... .... .... :o.oq: &#xt | 1 0 1 2 | 0 0 2 2 | * * 6N * | 0 0 2 2 | 1 2 1 0 .... .... .oqo .... &#xt | 0 1 2 1 | 0 2 2 0 | * * * 6N | 2 0 0 2 | 2 1 0 1 -----------------------------------+---------+-------------+-------------+-------------+-------- .... oqoo 3 ooqo .... &#xt ♦ 1 3 3 1 | 3 6 3 0 | 3 0 0 3 | 4N * * * | 1 0 0 1 :qooo:3:oqoo: .... .... &#xt ♦ 3 3 1 1 | 6 3 0 3 | 3 3 0 0 | * 4N * * | 0 0 1 1 :qooo: .... .... :oooq:3*a&#xt ♦ 3 1 1 3 | 3 0 3 6 | 0 3 3 0 | * * 4N * | 0 1 1 0 .... .... :ooqo:3:oooq: &#xt ♦ 1 1 3 3 | 0 3 6 3 | 0 0 3 3 | * * * 4N | 1 1 0 0 -----------------------------------+---------+-------------+-------------+-------------+-------- .... :oqoo:3:ooqo:3:oooq: &#xt ♦ 2 4 6 4 | 4 12 12 4 | 6 0 6 12 | 4 0 0 4 | N * * * :qooo: .... :ooqo:3:oooq:3*a&#xt ♦ 4 2 4 6 | 4 4 12 12 | 0 6 12 6 | 0 0 4 4 | * N * * :qooo:3:oqoo: .... :oooq:3*a&#xt ♦ 6 4 2 4 | 12 4 4 12 | 6 12 6 0 | 0 4 4 0 | * * N * :qooo:3:oqoo:3:ooqo: .... &#xt ♦ 4 6 4 2 | 12 12 4 4 | 12 6 0 6 | 4 4 0 0 | * * * N
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