vertex figure of tark
- general polytopal classes:
- Wythoffian polyexa segmentoexa
links
| Acronym | tethex |
| Name |
tetrahedron - hexadecachoron duoprism, vertex figure of tark |
| Circumradius | sqrt(7/8) = 0.935414 |
| Volume | sqrt(2)/72 = 0.019642 |
| Face vector | 32, 144, 304, 360, 252, 102, 20 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o3o x3o3o4o . . . . . . . | 32 | 3 6 | 3 18 12 | 1 18 36 8 | 6 36 24 1 | 12 24 3 | 8 3 --------------+----+-------+------------+-------------+-------------+---------+----- x . . . . . . | 2 | 48 * | 2 6 0 | 1 12 12 0 | 6 24 8 0 | 12 16 1 | 8 2 . . . x . . . | 2 | * 96 | 0 3 4 | 0 3 12 4 | 1 12 12 1 | 4 12 3 | 4 3 --------------+----+-------+------------+-------------+-------------+---------+----- x3o . . . . . | 3 | 3 0 | 32 * * | 1 6 0 0 | 6 12 0 0 | 12 8 0 | 8 1 x . . x . . . | 4 | 2 2 | * 144 * | 0 2 4 0 | 1 8 4 0 | 4 8 1 | 4 2 . . . x3o . . | 3 | 0 3 | * * 128 | 0 0 3 2 | 0 3 6 1 | 1 6 3 | 2 3 --------------+----+-------+------------+-------------+-------------+---------+----- x3o3o . . . . ♦ 4 | 6 0 | 4 0 0 | 8 * * * ♦ 6 0 0 0 | 12 0 0 | 8 0 x3o . x . . . ♦ 6 | 6 3 | 2 3 0 | * 96 * * | 1 4 0 0 | 4 4 0 | 4 1 x . . x3o . . ♦ 6 | 3 6 | 0 3 2 | * * 192 * | 0 2 2 0 | 1 4 1 | 2 2 . . . x3o3o . ♦ 4 | 0 6 | 0 0 4 | * * * 64 | 0 0 3 1 | 0 3 3 | 1 3 --------------+----+-------+------------+-------------+-------------+---------+----- x3o3o x . . . ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 | 24 * * * | 4 0 0 | 4 0 x3o . x3o . . ♦ 9 | 9 9 | 3 9 3 | 0 3 3 0 | * 128 * * | 1 2 0 | 2 1 x . . x3o3o . ♦ 8 | 4 12 | 0 6 8 | 0 0 4 2 | * * 96 * | 0 2 1 | 1 2 . . . x3o3o4o ♦ 8 | 0 24 | 0 0 32 | 0 0 0 16 | * * * 4 | 0 0 3 | 0 3 --------------+----+-------+------------+-------------+-------------+---------+----- x3o3o x3o . . ♦ 12 | 18 12 | 12 18 4 | 3 12 6 0 | 3 4 0 0 | 32 * * | 2 0 x3o . x3o3o . ♦ 12 | 12 18 | 4 18 12 | 0 6 12 3 | 0 4 3 0 | * 64 * | 1 1 x . . x3o3o4o ♦ 16 | 8 48 | 0 24 64 | 0 0 32 32 | 0 0 16 2 | * * 6 | 0 2 --------------+----+-------+------------+-------------+-------------+---------+----- x3o3o x3o3o . ♦ 16 | 24 24 | 16 36 16 | 4 24 24 4 | 6 16 6 0 | 4 4 0 | 16 * x3o . x3o3o4o ♦ 24 | 24 72 | 8 72 96 | 0 24 96 48 | 0 32 48 3 | 0 16 3 | * 4
x3o3o x3o3o *e3o . . . . . . . | 32 | 3 6 | 3 18 12 | 1 18 36 4 4 | 6 36 12 12 1 | 12 12 12 3 | 4 4 3 -----------------+----+-------+------------+----------------+----------------+------------+------ x . . . . . . | 2 | 48 * | 2 6 0 | 1 12 12 0 0 | 6 24 4 4 0 | 12 8 8 1 | 4 4 2 . . . x . . . | 2 | * 96 | 0 3 4 | 0 3 12 2 2 | 1 12 6 6 1 | 4 6 6 3 | 2 2 3 -----------------+----+-------+------------+----------------+----------------+------------+------ x3o . . . . . | 3 | 3 0 | 32 * * | 1 6 0 0 0 | 6 12 0 0 0 | 12 4 4 0 | 4 4 1 x . . x . . . | 4 | 2 2 | * 144 * | 0 2 4 0 0 | 1 8 2 2 0 | 4 4 4 1 | 2 2 2 . . . x3o . . | 3 | 0 3 | * * 128 | 0 0 3 1 1 | 0 3 3 3 1 | 1 3 3 3 | 1 1 3 -----------------+----+-------+------------+----------------+----------------+------------+------ x3o3o . . . . ♦ 4 | 6 0 | 4 0 0 | 8 * * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 4 4 0 x3o . x . . . ♦ 6 | 6 3 | 2 3 0 | * 96 * * * | 1 4 0 0 0 | 4 2 2 0 | 2 2 1 x . . x3o . . ♦ 6 | 3 6 | 0 3 2 | * * 192 * * | 0 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x3o3o . ♦ 4 | 0 6 | 0 0 4 | * * * 32 * | 0 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . x3o . *e3o ♦ 4 | 0 6 | 0 0 4 | * * * * 32 | 0 0 0 3 1 | 0 0 3 3 | 0 1 3 -----------------+----+-------+------------+----------------+----------------+------------+------ x3o3o x . . . ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 0 | 24 * * * * | 4 0 0 0 | 2 2 0 x3o . x3o . . ♦ 9 | 9 9 | 3 9 3 | 0 3 3 0 0 | * 128 * * * | 1 1 1 0 | 1 1 1 x . . x3o3o . ♦ 8 | 4 12 | 0 6 8 | 0 0 4 2 0 | * * 48 * * | 0 2 0 1 | 1 0 2 x . . x3o . *e3o ♦ 8 | 4 12 | 0 6 8 | 0 0 4 0 2 | * * * 48 * | 0 0 2 1 | 0 1 2 . . . x3o3o *e3o ♦ 8 | 0 24 | 0 0 32 | 0 0 0 8 8 | * * * * 4 | 0 0 0 3 | 0 0 3 -----------------+----+-------+------------+----------------+----------------+------------+------ x3o3o x3o . . ♦ 12 | 18 12 | 12 18 4 | 3 12 6 0 0 | 3 4 0 0 0 | 32 * * * | 1 1 0 x3o . x3o3o . ♦ 12 | 12 18 | 4 18 12 | 0 6 12 3 0 | 0 4 3 0 0 | * 32 * * | 1 0 1 x3o . x3o . *e3o ♦ 12 | 12 18 | 4 18 12 | 0 6 12 0 3 | 0 4 0 3 0 | * * 32 * | 0 1 1 x . . x3o3o *e3o ♦ 16 | 8 48 | 0 24 64 | 0 0 32 16 16 | 0 0 8 8 2 | * * * 6 | 0 0 2 -----------------+----+-------+------------+----------------+----------------+------------+------ x3o3o x3o3o . ♦ 16 | 24 24 | 16 36 16 | 4 24 24 4 0 | 6 16 6 0 0 | 4 4 0 0 | 8 * * x3o3o x3o . *e3o ♦ 16 | 24 24 | 16 36 16 | 4 24 24 0 4 | 6 16 0 6 0 | 4 0 4 0 | * 8 * x3o . x3o3o *e3o ♦ 24 | 24 72 | 8 72 96 | 0 24 96 24 24 | 0 32 24 24 3 | 0 8 8 3 | * * 4
xo3oo3ox xx3oo3oo&#x → height = 1/sqrt(2) = 0.707107
(tetdip || para-dual tetdip)
o.3o.3o. o.3o.3o. | 16 * | 3 3 3 0 0 | 3 9 3 6 3 9 0 0 0 | 1 9 9 1 3 3 18 1 9 9 0 0 0 0 | 3 9 3 1 9 9 18 3 9 3 0 0 0 | 3 3 3 9 9 6 3 3 0 0 | 1 3 3 3 1 0
.o3.o3.o .o3.o3.o | * 16 | 0 0 3 3 3 | 0 0 0 3 6 9 3 9 3 | 0 0 0 0 1 3 9 3 18 9 1 9 9 1 | 0 0 0 1 3 9 9 9 18 3 3 9 3 | 0 0 3 3 9 3 9 6 3 3 | 0 3 1 3 3 1
---------------------+-------+----------------+----------------------------+---------------------------------------+-----------------------------------+--------------------------+------------
x. .. .. .. .. .. | 2 0 | 24 * * * * | 2 3 0 2 0 0 0 0 0 | 1 6 3 0 2 1 6 0 0 0 0 0 0 0 | 3 6 1 1 6 3 6 0 0 0 0 0 0 | 3 2 3 6 3 2 0 0 0 0 | 1 3 2 1 0 0
.. .. .. x. .. .. | 2 0 | * 24 * * * | 0 3 2 0 0 3 0 0 0 | 0 3 6 1 0 0 6 0 3 6 0 0 0 0 | 1 6 3 0 3 3 12 1 6 3 0 0 0 | 2 3 1 6 6 6 2 3 0 0 | 1 2 3 3 1 0
oo3oo3oo oo3oo3oo&#x | 1 1 | * * 48 * * | 0 0 0 2 2 3 0 0 0 | 0 0 0 0 1 2 6 1 6 3 0 0 0 0 | 0 0 0 1 3 6 6 3 6 1 0 0 0 | 0 0 3 3 6 2 3 2 0 0 | 0 3 1 2 1 0
.. .. .x .. .. .. | 0 2 | * * * 24 * | 0 0 0 0 2 0 2 3 0 | 0 0 0 0 0 1 0 2 6 0 1 6 3 0 | 0 0 0 1 0 3 0 6 6 0 3 6 1 | 0 0 3 0 3 0 6 2 3 2 | 0 3 0 1 2 1
.. .. .. .x .. .. | 0 2 | * * * * 24 | 0 0 0 0 0 3 0 3 2 | 0 0 0 0 0 0 3 0 6 6 0 3 6 1 | 0 0 0 0 1 3 6 3 12 3 1 6 3 | 0 0 1 2 6 3 6 6 2 3 | 0 2 1 3 3 1
---------------------+-------+----------------+----------------------------+---------------------------------------+-----------------------------------+--------------------------+------------
x.3o. .. .. .. .. | 3 0 | 3 0 0 0 0 | 16 * * * * * * * * | 1 3 0 0 1 0 0 0 0 0 0 0 0 0 | 3 3 0 1 3 0 0 0 0 0 0 0 0 | 3 1 3 3 0 0 0 0 0 0 | 1 3 1 0 0 0
x. .. .. x. .. .. | 4 0 | 2 2 0 0 0 | * 36 * * * * * * * | 0 2 2 0 0 0 2 0 0 0 0 0 0 0 | 1 4 1 0 2 1 4 0 0 0 0 0 0 | 2 2 1 4 2 2 0 0 0 0 | 1 2 2 1 0 0
.. .. .. x.3o. .. | 3 0 | 0 3 0 0 0 | * * 16 * * * * * * | 0 0 3 1 0 0 0 0 0 3 0 0 0 0 | 0 3 3 0 0 0 6 0 3 3 0 0 0 | 1 3 0 3 3 6 1 3 0 0 | 1 1 3 3 1 0
xo .. .. .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 48 * * * * * | 0 0 0 0 1 1 3 0 0 0 0 0 0 0 | 0 0 0 1 3 3 3 0 0 0 0 0 0 | 0 0 3 3 3 1 0 0 0 0 | 0 3 1 1 0 0
.. .. ox .. .. ..&#x | 1 2 | 0 0 2 1 0 | * * * * 48 * * * * | 0 0 0 0 0 1 0 1 3 0 0 0 0 0 | 0 0 0 1 0 3 0 3 3 0 0 0 0 | 0 0 3 0 3 0 3 1 0 0 | 0 3 0 1 1 0
.. .. .. xx .. ..&#x | 2 2 | 0 1 2 0 1 | * * * * * 72 * * * | 0 0 0 0 0 0 2 0 2 2 0 0 0 0 | 0 0 0 0 1 2 4 1 4 1 0 0 0 | 0 0 1 2 4 2 2 2 0 0 | 0 2 1 2 1 0
.. .o3.x .. .. .. | 0 3 | 0 0 0 3 0 | * * * * * * 16 * * | 0 0 0 0 0 0 0 1 0 0 1 3 0 0 | 0 0 0 1 0 0 0 3 0 0 3 3 0 | 0 0 3 0 0 0 3 0 3 1 | 0 3 0 0 1 1
.. .. .x .x .. .. | 0 4 | 0 0 0 2 2 | * * * * * * * 36 * | 0 0 0 0 0 0 0 0 2 0 0 2 2 0 | 0 0 0 0 0 1 0 2 4 0 1 4 1 | 0 0 1 0 2 0 4 2 2 2 | 0 2 0 1 2 1
.. .. .. .x3.o .. | 0 3 | 0 0 0 0 3 | * * * * * * * * 16 | 0 0 0 0 0 0 0 0 0 3 0 0 3 1 | 0 0 0 0 0 0 3 0 6 3 0 3 3 | 0 0 0 1 3 3 3 6 1 3 | 0 1 1 3 3 1
---------------------+-------+----------------+----------------------------+---------------------------------------+-----------------------------------+--------------------------+------------
x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 0 0 | 4 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * | 3 0 0 1 0 0 0 0 0 0 0 0 0 | 3 0 3 0 0 0 0 0 0 0 | 1 3 0 0 0 0
x.3o. .. x. .. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 0 | * 24 * * * * * * * * * * * * | 1 2 0 0 1 0 0 0 0 0 0 0 0 | 2 1 1 2 0 0 0 0 0 0 | 1 2 1 0 0 0
x. .. .. x.3o. .. ♦ 6 0 | 3 6 0 0 0 | 0 3 2 0 0 0 0 0 0 | * * 24 * * * * * * * * * * * | 0 2 1 0 0 0 2 0 0 0 0 0 0 | 1 2 0 2 1 2 0 0 0 0 | 1 1 2 1 0 0
.. .. .. x.3o.3o. ♦ 4 0 | 0 6 0 0 0 | 0 0 4 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * ♦ 0 0 3 0 0 0 0 0 0 3 0 0 0 | 0 3 0 0 0 6 0 3 0 0 | 1 0 3 3 1 0
xo3oo .. .. .. ..&#x ♦ 3 1 | 3 0 3 0 0 | 1 0 0 3 0 0 0 0 0 | * * * * 16 * * * * * * * * * | 0 0 0 1 3 0 0 0 0 0 0 0 0 | 0 0 3 3 0 0 0 0 0 0 | 0 3 1 0 0 0
xo .. ox .. .. ..&#x ♦ 2 2 | 1 0 4 1 0 | 0 0 0 2 2 0 0 0 0 | * * * * * 24 * * * * * * * * | 0 0 0 1 0 3 0 0 0 0 0 0 0 | 0 0 3 0 3 0 0 0 0 0 | 0 3 0 1 0 0
xo .. .. xx .. ..&#x ♦ 4 2 | 2 2 4 0 1 | 0 1 0 2 0 2 0 0 0 | * * * * * * 72 * * * * * * * | 0 0 0 0 1 1 2 0 0 0 0 0 0 | 0 0 1 2 2 1 0 0 0 0 | 0 2 1 1 0 0
.. oo3ox .. .. ..&#x ♦ 1 3 | 0 0 3 3 0 | 0 0 0 0 3 0 1 0 0 | * * * * * * * 16 * * * * * * | 0 0 0 1 0 0 0 3 0 0 0 0 0 | 0 0 3 0 0 0 3 0 0 0 | 0 3 0 0 1 0
.. .. ox xx .. ..&#x ♦ 2 4 | 0 1 4 2 2 | 0 0 0 0 2 2 0 1 0 | * * * * * * * * 72 * * * * * | 0 0 0 0 0 1 0 1 2 0 0 0 0 | 0 0 1 0 2 0 2 1 0 0 | 0 2 0 1 1 0
.. .. .. xx3oo ..&#x ♦ 3 3 | 0 3 3 0 3 | 0 0 1 0 0 3 0 0 1 | * * * * * * * * * 48 * * * * | 0 0 0 0 0 0 2 0 2 1 0 0 0 | 0 0 0 1 2 2 1 2 0 0 | 0 1 1 2 1 0
.o3.o3.x .. .. .. ♦ 0 4 | 0 0 0 6 0 | 0 0 0 0 0 0 4 0 0 | * * * * * * * * * * 4 * * * | 0 0 0 1 0 0 0 0 0 0 3 0 0 | 0 0 3 0 0 0 0 0 3 0 | 0 3 0 0 0 1
.. .o3.x .x .. .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 2 3 0 | * * * * * * * * * * * 24 * * | 0 0 0 0 0 0 0 1 0 0 1 2 0 | 0 0 1 0 0 0 2 0 2 1 | 0 2 0 0 1 1
.. .. .x .x3.o .. ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * * 24 * | 0 0 0 0 0 0 0 0 2 0 0 2 1 | 0 0 0 0 1 0 2 2 1 2 | 0 1 0 1 2 1
.. .. .. .x3.o3.o ♦ 0 4 | 0 0 0 0 6 | 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * 4 ♦ 0 0 0 0 0 0 0 0 0 3 0 0 3 | 0 0 0 0 0 3 0 6 0 3 | 0 0 1 3 3 1
---------------------+-------+----------------+----------------------------+---------------------------------------+-----------------------------------+--------------------------+------------
x.3o.3o. x. .. .. ♦ 8 0 | 12 4 0 0 0 | 8 6 0 0 0 0 0 0 0 | 2 4 0 0 0 0 0 0 0 0 0 0 0 0 | 6 * * * * * * * * * * * * | 2 0 1 0 0 0 0 0 0 0 | 1 2 0 0 0 0
x.3o. .. x.3o. .. ♦ 9 0 | 9 9 0 0 0 | 3 9 3 0 0 0 0 0 0 | 0 3 3 0 0 0 0 0 0 0 0 0 0 0 | * 16 * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0 0
x. .. .. x.3o.3o. ♦ 8 0 | 4 12 0 0 0 | 0 6 8 0 0 0 0 0 0 | 0 0 4 2 0 0 0 0 0 0 0 0 0 0 | * * 6 * * * * * * * * * * | 0 2 0 0 0 2 0 0 0 0 | 1 0 2 1 0 0
xo3oo3ox .. .. ..&#x ♦ 4 4 | 6 0 12 6 0 | 4 0 0 12 12 0 4 0 0 | 1 0 0 0 4 6 0 4 0 0 1 0 0 0 | * * * 4 * * * * * * * * * | 0 0 3 0 0 0 0 0 0 0 | 0 3 0 0 0 0
xo3oo .. xx .. ..&#x ♦ 6 2 | 6 3 6 0 1 | 2 3 0 6 0 3 0 0 0 | 0 1 0 0 2 0 3 0 0 0 0 0 0 0 | * * * * 24 * * * * * * * * | 0 0 1 2 0 0 0 0 0 0 | 0 2 1 0 0 0
xo .. ox xx .. ..&#x ♦ 4 4 | 2 2 8 2 2 | 0 1 0 4 4 4 0 1 0 | 0 0 0 0 0 2 2 0 2 0 0 0 0 0 | * * * * * 36 * * * * * * * | 0 0 1 0 2 0 0 0 0 0 | 0 2 0 1 0 0
xo .. .. xx3oo ..&#x ♦ 6 3 | 3 6 6 0 3 | 0 3 2 3 0 6 0 0 1 | 0 0 1 0 0 0 3 0 0 2 0 0 0 0 | * * * * * * 48 * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 0
.. oo3ox xx .. ..&#x ♦ 2 6 | 0 1 6 6 3 | 0 0 0 0 6 3 2 3 0 | 0 0 0 0 0 0 0 2 3 0 0 1 0 0 | * * * * * * * 24 * * * * * | 0 0 1 0 0 0 2 0 0 0 | 0 2 0 0 1 0
.. .. ox xx3oo ..&#x ♦ 3 6 | 0 3 6 3 6 | 0 0 1 0 3 6 0 3 2 | 0 0 0 0 0 0 0 0 3 2 0 0 1 0 | * * * * * * * * 48 * * * * | 0 0 0 0 1 0 1 1 0 0 | 0 1 0 1 1 0
.. .. .. xx3oo3oo&#x ♦ 4 4 | 0 6 4 0 6 | 0 0 4 0 0 6 0 0 4 | 0 0 0 1 0 0 0 0 0 4 0 0 0 1 | * * * * * * * * * 12 * * * | 0 0 0 0 0 2 0 2 0 0 | 0 0 1 2 1 0
.o3.o3.x .x .. .. ♦ 0 8 | 0 0 0 12 4 | 0 0 0 0 0 0 8 6 0 | 0 0 0 0 0 0 0 0 0 0 2 4 0 0 | * * * * * * * * * * 6 * * | 0 0 1 0 0 0 0 0 2 0 | 0 2 0 0 0 1
.. .o3.x .x3.o .. ♦ 0 9 | 0 0 0 9 9 | 0 0 0 0 0 0 3 9 3 | 0 0 0 0 0 0 0 0 0 0 0 3 3 0 | * * * * * * * * * * * 16 * | 0 0 0 0 0 0 1 0 1 1 | 0 1 0 0 1 1
.. .. .x .x3.o3.o ♦ 0 8 | 0 0 0 4 12 | 0 0 0 0 0 0 0 6 8 | 0 0 0 0 0 0 0 0 0 0 0 0 4 2 | * * * * * * * * * * * * 6 | 0 0 0 0 0 0 0 2 0 2 | 0 0 0 1 2 1
---------------------+-------+----------------+----------------------------+---------------------------------------+-----------------------------------+--------------------------+------------
x.3o.3o. x.3o. .. ♦ 12 0 | 18 12 0 0 0 | 12 18 4 0 0 0 0 0 0 | 3 12 6 0 0 0 0 0 0 0 0 0 0 0 | 3 4 0 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * | 1 1 0 0 0 0
x.3o. .. x.3o.3o. ♦ 12 0 | 12 18 0 0 0 | 4 18 12 0 0 0 0 0 0 | 0 6 12 3 0 0 0 0 0 0 0 0 0 0 | 0 4 3 0 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * | 1 0 1 0 0 0
xo3oo3ox xx .. ..&#x ♦ 8 8 | 12 4 24 12 4 | 8 6 0 24 24 12 8 6 0 | 2 4 0 0 8 12 12 8 12 0 2 4 0 0 | 1 0 0 2 4 6 0 4 0 0 1 0 0 | * * 6 * * * * * * * | 0 2 0 0 0 0
xo3oo .. xx3oo ..&#x ♦ 9 3 | 9 9 9 0 3 | 3 9 3 9 0 9 0 0 1 | 0 3 3 0 3 0 9 0 0 3 0 0 0 0 | 0 1 0 0 3 0 3 0 0 0 0 0 0 | * * * 16 * * * * * * | 0 1 1 0 0 0
xo .. ox xx3oo ..&#x ♦ 6 6 | 3 6 12 3 6 | 0 3 2 6 6 12 0 3 2 | 0 0 1 0 0 3 6 0 6 4 0 0 1 0 | 0 0 0 0 0 3 2 0 2 0 0 0 0 | * * * * 24 * * * * * | 0 1 0 1 0 0
xo .. .. xx3oo3oo&#x ♦ 8 4 | 4 12 8 0 6 | 0 6 8 4 0 12 0 0 4 | 0 0 4 2 0 0 6 0 0 8 0 0 0 1 | 0 0 1 0 0 0 4 0 0 2 0 0 0 | * * * * * 12 * * * * | 0 0 1 1 0 0
.. oo3ox xx3oo ..&#x ♦ 3 9 | 0 3 9 9 9 | 0 0 1 0 9 9 3 9 3 | 0 0 0 0 0 0 0 3 9 3 0 3 3 0 | 0 0 0 0 0 0 0 3 3 0 0 1 0 | * * * * * * 16 * * * | 0 1 0 0 1 0
.. .. ox xx3oo3oo&#x ♦ 4 8 | 0 6 8 4 12 | 0 0 4 0 4 12 0 6 8 | 0 0 0 1 0 0 0 0 6 8 0 0 4 2 | 0 0 0 0 0 0 0 0 4 2 0 0 1 | * * * * * * * 12 * * | 0 0 0 1 1 0
.o3.o3.x .x3.o .. ♦ 0 12 | 0 0 0 18 12 | 0 0 0 0 0 0 12 18 4 | 0 0 0 0 0 0 0 0 0 0 3 12 6 0 | 0 0 0 0 0 0 0 0 0 0 3 4 0 | * * * * * * * * 4 * | 0 1 0 0 0 1
.. .o3.x .x3.o3.o ♦ 0 12 | 0 0 0 12 18 | 0 0 0 0 0 0 4 18 12 | 0 0 0 0 0 0 0 0 0 0 0 6 12 3 | 0 0 0 0 0 0 0 0 0 0 0 4 3 | * * * * * * * * * 4 | 0 0 0 0 1 1
---------------------+-------+----------------+----------------------------+---------------------------------------+-----------------------------------+--------------------------+------------
x.3o.3o. x.3o.3o. ♦ 16 0 | 24 24 0 0 0 | 16 36 16 0 0 0 0 0 0 | 4 24 24 4 0 0 0 0 0 0 0 0 0 0 | 6 16 6 0 0 0 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 | 1 * * * * *
xo3oo3ox xx3oo ..&#x ♦ 12 12 | 18 12 36 18 12 | 12 18 4 36 36 36 12 18 4 | 3 12 6 0 12 18 36 12 36 12 3 12 6 0 | 3 4 0 3 12 18 12 12 12 0 3 4 0 | 1 0 3 4 6 0 4 0 1 0 | * 4 * * * *
xo3oo .. xx3oo3oo&#x ♦ 12 4 | 12 18 12 0 6 | 4 18 12 12 0 18 0 0 4 | 0 6 12 3 4 0 18 0 0 12 0 0 0 1 | 0 4 3 0 6 0 12 0 0 3 0 0 0 | 0 1 0 4 0 3 0 0 0 0 | * * 4 * * *
xo .. ox xx3oo3oo&#x ♦ 8 8 | 4 12 16 4 12 | 0 6 8 8 8 24 0 6 8 | 0 0 4 2 0 4 12 0 12 16 0 0 4 2 | 0 0 1 0 0 6 8 0 8 4 0 0 1 | 0 0 0 0 4 2 0 2 0 0 | * * * 6 * *
.. oo3ox xx3oo3oo&#x ♦ 4 12 | 0 6 12 12 18 | 0 0 4 0 12 18 4 18 12 | 0 0 0 1 0 0 0 4 18 12 0 6 12 3 | 0 0 0 0 0 0 0 6 12 3 0 4 3 | 0 0 0 0 0 0 4 3 0 1 | * * * * 4 *
.o3.o3.x .x3.o3.o ♦ 0 16 | 0 0 0 24 24 | 0 0 0 0 0 0 16 36 16 | 0 0 0 0 0 0 0 0 0 0 4 24 24 4 | 0 0 0 0 0 0 0 0 0 0 6 16 6 | 0 0 0 0 0 0 0 0 4 4 | * * * * * 1
xo3oo xx3oo3oo4oo&#x → height = sqrt(2/3) = 0.816497
(trahex || hex)
o.3o. o.3o.3o.4o. | 24 * | 2 6 1 0 | 1 12 12 2 6 0 | 6 24 8 1 12 12 0 | 12 16 1 6 24 8 0 | 8 2 12 16 1 | 1 8 2
.o3.o .o3.o3.o4.o | * 8 | 0 0 3 6 | 0 0 0 3 18 12 | 0 0 0 1 18 36 8 | 0 0 0 6 36 24 1 | 0 0 12 24 3 | 0 8 3
---------------------+------+-------------+------------------+---------------------+--------------------+--------------+-------
x. .. .. .. .. .. | 2 0 | 24 * * * | 1 6 0 1 0 0 | 6 12 0 1 6 0 0 | 12 8 0 6 12 0 0 | 8 1 12 8 0 | 1 8 1
.. .. x. .. .. .. | 2 0 | * 72 * * | 0 2 4 0 1 0 | 1 8 4 0 2 4 0 | 4 8 1 1 8 4 0 | 4 2 4 8 1 | 1 4 2
oo3oo oo3oo3oo4oo&#x | 1 1 | * * 24 * | 0 0 0 2 6 0 | 0 0 0 1 12 12 0 | 0 0 0 6 24 8 0 | 0 0 12 16 1 | 0 8 2
.. .. .x .. .. .. | 0 2 | * * * 24 | 0 0 0 0 3 4 | 0 0 0 0 3 12 4 | 0 0 0 1 12 12 1 | 0 0 4 12 3 | 0 4 3
---------------------+------+-------------+------------------+---------------------+--------------------+--------------+-------
x.3o. .. .. .. .. | 3 0 | 3 0 0 0 | 8 * * * * * | 6 0 0 1 0 0 0 | 12 0 0 6 0 0 0 | 8 0 12 0 0 | 1 8 0
x. .. x. .. .. .. | 4 0 | 2 2 0 0 | * 72 * * * * | 1 4 0 0 1 0 0 | 4 4 0 1 4 0 0 | 4 1 4 4 0 | 1 4 1
.. .. x.3o. .. .. | 3 0 | 0 3 0 0 | * * 96 * * * | 0 2 2 0 0 1 0 | 1 4 1 0 2 2 0 | 2 2 1 4 1 | 1 2 2
xo .. .. .. .. ..&#x | 2 1 | 1 0 2 0 | * * * 24 * * | 0 0 0 1 6 0 0 | 0 0 0 6 12 0 0 | 0 0 12 8 0 | 0 8 1
.. .. xx .. .. ..&#x | 2 2 | 0 1 2 1 | * * * * 72 * | 0 0 0 0 2 4 0 | 0 0 0 1 8 4 0 | 0 0 4 8 1 | 0 4 2
.. .. .x3.o .. .. | 0 3 | 0 0 0 3 | * * * * * 32 | 0 0 0 0 0 3 2 | 0 0 0 0 3 6 1 | 0 0 1 6 3 | 0 2 3
---------------------+------+-------------+------------------+---------------------+--------------------+--------------+-------
x.3o. x. .. .. .. ♦ 6 0 | 6 3 0 0 | 2 3 0 0 0 0 | 24 * * * * * * | 4 0 0 1 0 0 0 | 4 0 4 0 0 | 1 4 0
x. .. x.3o. .. .. ♦ 6 0 | 3 6 0 0 | 0 3 2 0 0 0 | * 96 * * * * * | 1 2 0 0 1 0 0 | 2 1 1 2 0 | 1 2 1
.. .. x.3o.3o. .. ♦ 4 0 | 0 6 0 0 | 0 0 4 0 0 0 | * * 48 * * * * | 0 2 1 0 0 1 0 | 1 2 0 2 1 | 1 1 2
xo3oo .. .. .. ..&#x ♦ 3 1 | 3 0 3 0 | 1 0 0 3 0 0 | * * * 8 * * * ♦ 0 0 0 6 0 0 0 | 0 0 12 0 0 | 0 8 0
xo .. xx .. .. ..&#x ♦ 4 2 | 2 2 4 1 | 0 1 0 2 2 0 | * * * * 72 * * | 0 0 0 1 4 0 0 | 0 0 4 4 0 | 0 4 1
.. .. xx3oo .. ..&#x ♦ 3 3 | 0 3 3 3 | 0 0 1 0 3 1 | * * * * * 96 * | 0 0 0 0 2 2 0 | 0 0 1 4 1 | 0 2 2
.. .. .x3.o3.o .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 4 | * * * * * * 16 | 0 0 0 0 0 3 1 | 0 0 0 3 3 | 0 1 3
---------------------+------+-------------+------------------+---------------------+--------------------+--------------+-------
x.3o. x.3o. .. .. ♦ 9 0 | 9 9 0 0 | 3 9 3 0 0 0 | 3 3 0 0 0 0 0 | 32 * * * * * * | 2 0 1 0 0 | 1 2 0
x. .. x.3o.3o. .. ♦ 8 0 | 4 12 0 0 | 0 6 8 0 0 0 | 0 4 2 0 0 0 0 | * 48 * * * * * | 1 1 0 1 0 | 1 1 1
.. .. x.3o.3o.4o. ♦ 8 0 | 0 24 0 0 | 0 0 32 0 0 0 | 0 0 16 0 0 0 0 | * * 3 * * * * | 0 2 0 0 1 | 1 0 2
xo3oo xx .. .. ..&#x ♦ 6 2 | 6 3 6 1 | 2 3 0 6 3 0 | 1 0 0 2 3 0 0 | * * * 24 * * * | 0 0 4 0 0 | 0 4 0
xo .. xx3oo .. ..&#x ♦ 6 3 | 3 6 6 3 | 0 3 2 3 6 1 | 0 1 0 0 3 2 0 | * * * * 96 * * | 0 0 1 2 0 | 0 2 1
.. .. xx3oo3oo ..&#x ♦ 4 4 | 0 6 4 6 | 0 0 4 0 6 4 | 0 0 1 0 0 4 1 | * * * * * 48 * | 0 0 0 2 1 | 0 1 2
.. .. .x3.o3.o4.o ♦ 0 8 | 0 0 0 24 | 0 0 0 0 0 32 | 0 0 0 0 0 0 16 | * * * * * * 1 | 0 0 0 0 3 | 0 0 3
---------------------+------+-------------+------------------+---------------------+--------------------+--------------+-------
x.3o. x.3o.3o. .. ♦ 12 0 | 12 18 0 0 | 4 18 12 0 0 0 | 6 12 3 0 0 0 0 | 4 3 0 0 0 0 0 | 16 * * * * | 1 1 0
x. .. x.3o.3o.4o. ♦ 16 0 | 8 48 0 0 | 0 24 64 0 0 0 | 0 32 32 0 0 0 0 | 0 16 2 0 0 0 0 | * 3 * * * | 1 0 1
xo3oo xx3oo .. ..&#x ♦ 9 3 | 9 9 9 3 | 3 9 3 9 9 1 | 3 3 0 3 9 3 0 | 1 0 0 3 3 0 0 | * * 32 * * | 0 2 0
xo .. xx3oo3oo ..&#x ♦ 8 4 | 4 12 8 6 | 0 6 8 4 12 4 | 0 4 2 0 6 8 1 | 0 1 0 0 4 2 0 | * * * 48 * | 0 1 1
.. .. xx3oo3oo4oo&#x ♦ 8 8 | 0 24 8 24 | 0 0 32 0 24 32 | 0 0 16 0 0 32 16 | 0 0 1 0 0 16 1 | * * * * 3 | 0 0 2
---------------------+------+-------------+------------------+---------------------+--------------------+--------------+-------
x.3o. x.3o.3o.4o. ♦ 24 0 | 24 72 0 0 | 8 72 96 0 0 0 | 24 96 48 0 0 0 0 | 32 48 3 0 0 0 0 | 16 3 0 0 0 | 1 * *
xo3oo xx3oo3oo ..&#x ♦ 12 4 | 12 18 12 6 | 4 18 12 12 18 4 | 6 12 3 4 18 12 1 | 4 3 0 6 12 3 0 | 1 0 4 3 0 | * 16 *
xo .. xx3oo3oo4oo&#x ♦ 16 8 | 8 48 16 24 | 0 24 64 8 48 32 | 0 32 32 0 24 64 16 | 0 16 2 0 32 32 1 | 0 1 0 16 2 | * * 3
xo ox xx3oo3oo4oo&#x → 1/sqrt(2) = 0.707107
(hexip || lacing-ortho hexip)
o. o. o.3o.3o.4o. & | 32 | 1 6 2 | 6 12 3 12 | 12 8 1 18 24 | 8 1 6 36 16 | 1 12 24 2 | 8 3
-----------------------+----+----------+--------------+----------------+----------------+-----------+-----
x. .. .. .. .. .. & | 2 | 16 * * | 6 0 2 0 | 12 0 1 12 0 | 8 0 6 24 0 | 1 12 16 0 | 8 2
.. .. x. .. .. .. & | 2 | * 96 * | 1 4 0 2 | 4 4 0 3 8 | 4 1 1 12 8 | 1 4 12 2 | 4 3
oo oo oo3oo3oo4oo&#x | 2 | * * 32 | 0 0 2 6 | 0 0 1 12 12 | 0 0 6 24 8 | 0 12 16 1 | 8 2
-----------------------+----+----------+--------------+----------------+----------------+-----------+-----
x. .. x. .. .. .. & | 4 | 2 2 0 | 48 * * * | 4 0 0 2 0 | 4 0 1 8 0 | 1 4 8 0 | 4 2
.. .. x.3.o .. .. & | 3 | 0 3 0 | * 128 * * | 1 2 0 0 2 | 2 1 0 3 4 | 1 1 6 2 | 2 3
xo .. .. .. .. ..&#x & | 3 | 1 0 2 | * * 32 * | 0 0 1 6 0 | 0 0 6 12 0 | 0 12 8 0 | 8 1
.. .. xx .. .. ..&#x | 4 | 0 2 2 | * * * 96 | 0 0 0 2 4 | 0 0 1 8 4 | 0 4 8 1 | 4 2
-----------------------+----+----------+--------------+----------------+----------------+-----------+-----
x. .. x.3o. .. .. & ♦ 6 | 3 6 0 | 3 2 0 0 | 64 * * * * | 2 0 0 2 0 | 1 1 4 0 | 2 2
.. .. x.3o.3o. .. & ♦ 4 | 0 6 0 | 0 4 0 0 | * 64 * * * | 1 1 0 0 2 | 1 0 3 2 | 1 3
xo ox .. .. .. ..&#x ♦ 4 | 2 0 4 | 0 0 4 0 | * * 8 * * ♦ 0 0 6 0 0 | 0 12 0 0 | 8 0
xo .. xx .. .. ..&#x & ♦ 6 | 2 3 4 | 1 0 2 2 | * * * 96 * | 0 0 1 4 0 | 0 4 4 0 | 4 1
.. .. xx3oo .. ..&#x ♦ 6 | 0 6 3 | 0 2 0 3 | * * * * 128 | 0 0 0 2 2 | 0 1 4 1 | 2 2
-----------------------+----+----------+--------------+----------------+----------------+-----------+-----
x. .. x.3o.3o. .. & ♦ 8 | 4 12 0 | 6 8 0 0 | 4 2 0 0 0 | 32 * * * * | 1 0 2 0 | 1 2
.. .. x.3o.3o.4o. & ♦ 8 | 0 24 0 | 0 32 0 0 | 0 16 0 0 0 | * 4 * * * | 1 0 0 2 | 0 3
xo ox xx .. .. ..&#x ♦ 8 | 4 4 8 | 2 0 8 4 | 0 0 2 4 0 | * * 24 * * | 0 4 0 0 | 4 0
xo .. xx3oo .. ..&#x & ♦ 9 | 3 9 6 | 3 3 3 6 | 1 0 0 3 2 | * * * 128 * | 0 1 2 0 | 2 1
.. .. xx3oo3oo ..&#x ♦ 8 | 0 12 4 | 0 8 0 6 | 0 2 0 0 4 | * * * * 64 | 0 0 2 1 | 1 2
-----------------------+----+----------+--------------+----------------+----------------+-----------+-----
x. .. x.3o.3o.4o. & ♦ 16 | 8 48 0 | 24 64 0 0 | 32 32 0 0 0 | 16 2 0 0 0 | 2 * * * | 0 2
xo ox xx3oo .. ..&#x ♦ 12 | 6 12 12 | 6 4 12 12 | 2 0 3 12 4 | 0 0 3 4 0 | * 32 * * | 2 0
xo .. xx3oo3oo ..&#x & ♦ 12 | 4 18 8 | 6 12 4 12 | 4 3 0 6 8 | 1 0 0 4 2 | * * 64 * | 1 1
.. .. xx3oo3oo4oo&#x ♦ 16 | 0 48 8 | 0 64 0 24 | 0 32 0 0 32 | 0 2 0 0 16 | * * * 4 | 0 2
-----------------------+----+----------+--------------+----------------+----------------+-----------+-----
xo ox xx3oo3oo ..&#x ♦ 16 | 8 24 16 | 12 16 16 24 | 8 4 4 24 16 | 2 0 6 16 4 | 0 4 4 0 | 16 *
xo .. xx3oo3oo4oo&#x & ♦ 24 | 8 72 16 | 24 96 8 48 | 32 48 0 24 64 | 16 3 0 32 32 | 1 0 16 2 | * 4
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