vertex figure of brinoh
- more general:
- n,oct-dip (n,m-ap)-dip
- segmentotera:
- squasquippy
- general polytopal classes:
- Wythoffian polytera segmentotera lace simplices Hanner polytopes
links
| Acronym | squoct |
| Name |
square-octahedron duoprism, vertex figure of brinoh |
| Circumradius | 1 |
| Volume | sqrt(2)/3 = 0.471405 |
| Face vector | 24, 72, 86, 48, 12 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x4o x3o4o . . . . . | 24 | 2 4 | 1 8 4 | 4 8 1 | 4 2 ----------+----+-------+---------+---------+---- x . . . . | 2 | 24 * | 1 4 0 | 4 4 0 | 4 1 . . x . . | 2 | * 48 | 0 2 2 | 1 4 1 | 2 2 ----------+----+-------+---------+---------+---- x4o . . . | 4 | 4 0 | 6 * * | 4 0 0 | 4 0 x . x . . | 4 | 2 2 | * 48 * | 1 2 0 | 2 1 . . x3o . | 3 | 0 3 | * * 32 | 0 2 1 | 1 2 ----------+----+-------+---------+---------+---- x4o x . . ♦ 8 | 8 4 | 2 4 0 | 12 * * | 2 0 x . x3o . ♦ 6 | 3 6 | 0 3 2 | * 32 * | 1 1 . . x3o4o ♦ 6 | 0 12 | 0 0 8 | * * 4 | 0 2 ----------+----+-------+---------+---------+---- x4o x3o . ♦ 12 | 12 12 | 3 12 4 | 3 4 0 | 8 * x . x3o4o ♦ 12 | 6 24 | 0 12 16 | 0 8 2 | * 4
x4o o3x3o . . . . . | 24 | 2 4 | 1 8 2 2 | 4 4 4 1 | 2 2 2 ----------+----+-------+------------+------------+------ x . . . . | 2 | 24 * | 1 4 0 0 | 4 2 2 0 | 2 2 1 . . . x . | 2 | * 48 | 0 2 1 1 | 1 2 2 1 | 1 1 2 ----------+----+-------+------------+------------+------ x4o . . . | 4 | 4 0 | 6 * * * | 4 0 0 0 | 2 2 0 x . . x . | 4 | 2 2 | * 48 * * | 1 1 1 0 | 1 1 1 . . o3x . | 3 | 0 3 | * * 16 * | 0 2 0 1 | 1 0 2 . . . x3o | 3 | 0 3 | * * * 16 | 0 0 2 1 | 0 1 2 ----------+----+-------+------------+------------+------ x4o . x . ♦ 8 | 8 4 | 2 4 0 0 | 12 * * * | 1 1 0 x . o3x . ♦ 6 | 3 6 | 0 3 2 0 | * 16 * * | 1 0 1 x . . x3o ♦ 6 | 3 6 | 0 3 0 2 | * * 16 * | 0 1 1 . . o3x3o ♦ 6 | 0 12 | 0 0 4 4 | * * * 4 | 0 0 2 ----------+----+-------+------------+------------+------ x4o o3x . ♦ 12 | 12 12 | 3 12 4 0 | 3 4 0 0 | 4 * * x4o . x3o ♦ 12 | 12 12 | 3 12 0 4 | 3 0 4 0 | * 4 * x . o3x3o ♦ 12 | 6 24 | 0 12 8 8 | 0 4 4 2 | * * 4
x x x3o4o . . . . . | 24 | 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 ----------+----+----------+------------+------------+------ x . . . . | 2 | 12 * * | 1 4 0 0 | 4 4 0 0 | 4 1 0 . x . . . | 2 | * 12 * | 1 0 4 0 | 4 0 4 0 | 4 0 1 . . x . . | 2 | * * 48 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------+----+----------+------------+------------+------ x x . . . | 4 | 2 2 0 | 6 * * * | 4 0 0 0 | 4 0 0 x . x . . | 4 | 2 0 2 | * 24 * * | 1 2 0 0 | 2 1 0 . x x . . | 4 | 0 2 2 | * * 24 * | 1 0 2 0 | 2 0 1 . . x3o . | 3 | 0 0 3 | * * * 32 | 0 1 1 1 | 1 1 1 ----------+----+----------+------------+------------+------ x x x . . ♦ 8 | 4 4 4 | 2 2 2 0 | 12 * * * | 2 0 0 x . x3o . ♦ 6 | 3 0 6 | 0 3 0 2 | * 16 * * | 1 1 0 . x x3o . ♦ 6 | 0 3 6 | 0 0 3 2 | * * 16 * | 1 0 1 . . x3o4o ♦ 6 | 0 0 12 | 0 0 0 8 | * * * 4 | 0 1 1 ----------+----+----------+------------+------------+------ x x x3o . ♦ 12 | 6 6 12 | 3 6 6 4 | 3 2 2 0 | 8 * * x . x3o4o ♦ 12 | 6 0 24 | 0 12 0 16 | 0 8 0 2 | * 2 * . x x3o4o ♦ 12 | 0 6 24 | 0 0 12 16 | 0 0 8 2 | * * 2
x x o3x3o . . . . . | 24 | 1 1 4 | 1 4 4 2 2 | 4 2 2 2 2 1 | 2 2 1 1 ----------+----+----------+---------------+--------------+-------- x . . . . | 2 | 12 * * | 1 4 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0 . x . . . | 2 | * 12 * | 1 0 4 0 0 | 4 0 0 2 2 0 | 2 2 0 1 . . . x . | 2 | * * 48 | 0 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 ----------+----+----------+---------------+--------------+-------- x x . . . | 4 | 2 2 0 | 6 * * * * | 4 0 0 0 0 0 | 2 2 0 0 x . . x . | 4 | 2 0 2 | * 24 * * * | 1 1 1 0 0 0 | 1 1 1 0 . x . x . | 4 | 0 2 2 | * * 24 * * | 1 0 0 1 1 0 | 1 1 0 1 . . o3x . | 3 | 0 0 3 | * * * 16 * | 0 1 0 1 1 0 | 1 0 1 1 . . . x3o | 3 | 0 0 3 | * * * * 16 | 0 0 1 0 1 1 | 0 1 1 1 ----------+----+----------+---------------+--------------+-------- x x . x . ♦ 8 | 4 4 4 | 2 2 2 0 0 | 12 * * * * * | 1 1 0 0 x . o3x . ♦ 6 | 3 0 6 | 0 3 0 2 0 | * 8 * * * * | 1 0 1 0 x . . x3o ♦ 6 | 3 0 6 | 0 3 0 0 2 | * * 8 * * * | 0 1 0 1 . x o3x . ♦ 6 | 0 3 6 | 0 0 3 2 0 | * * * 8 * * | 1 0 1 0 . x . x3o ♦ 6 | 0 3 6 | 0 0 3 0 2 | * * * * 8 * | 0 1 0 1 . . o3x3o ♦ 6 | 0 0 12 | 0 0 0 4 4 | * * * * * 4 | 0 0 1 1 ----------+----+----------+---------------+--------------+-------- x x o3x . ♦ 12 | 6 6 12 | 3 6 6 4 0 | 3 2 0 2 0 0 | 4 * * * x x . x3o ♦ 12 | 6 6 12 | 3 6 6 0 4 | 3 0 2 0 2 0 | * 4 * * x . o3x3o ♦ 12 | 6 0 24 | 0 12 0 8 8 | 0 4 0 4 0 2 | * * 2 * . x o3x3o ♦ 12 | 0 6 24 | 0 0 12 8 8 | 0 0 4 0 4 2 | * * * 2
xx xx3oo4oo&#x → height = 1
(ope || ope)
o. o.3o.4o. | 12 * | 1 4 1 0 0 | 4 4 1 4 0 0 | 4 1 4 4 0 0 | 1 4 1 0
.o .o3.o4.o | * 12 | 0 0 1 1 4 | 0 0 1 4 4 4 | 0 0 4 4 4 1 | 0 4 1 1
---------------+-------+--------------+------------------+---------------+--------
x. .. .. .. | 2 0 | 6 * * * * | 4 0 1 0 0 0 | 4 0 4 0 0 0 | 1 4 0 0
.. x. .. .. | 2 0 | * 24 * * * | 1 2 0 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
oo oo3oo4oo&#x | 1 1 | * * 12 * * | 0 0 1 4 0 0 | 0 0 4 4 0 0 | 0 4 1 0
.x .. .. .. | 0 2 | * * * 6 * | 0 0 1 0 4 0 | 0 0 4 0 4 0 | 0 4 0 1
.. .x .. .. | 0 2 | * * * * 24 | 0 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1
---------------+-------+--------------+------------------+---------------+--------
x. x. .. .. | 4 0 | 2 2 0 0 0 | 12 * * * * * | 2 0 1 0 0 0 | 1 2 0 0
.. x.3o. .. | 3 0 | 0 3 0 0 0 | * 16 * * * * | 1 1 0 1 0 0 | 1 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * 6 * * * | 0 0 4 0 0 0 | 0 4 0 0
.. xx .. ..&#x | 2 2 | 0 1 2 0 1 | * * * 24 * * | 0 0 1 2 0 0 | 0 2 1 0
.x .x .. .. | 0 4 | 0 0 0 2 2 | * * * * 12 * | 0 0 1 0 2 0 | 0 2 0 1
.. .x3.o .. | 0 3 | 0 0 0 0 3 | * * * * * 16 | 0 0 0 1 1 1 | 0 1 1 1
---------------+-------+--------------+------------------+---------------+--------
x. x.3o. .. ♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 | 8 * * * * * | 1 1 0 0
.. x.3o.4o. ♦ 6 0 | 0 12 0 0 0 | 0 8 0 0 0 0 | * 2 * * * * | 1 0 1 0
xx xx .. ..&#x ♦ 4 4 | 2 2 4 2 2 | 1 0 2 2 1 0 | * * 12 * * * | 0 2 0 0
.. xx3oo ..&#x ♦ 3 3 | 0 3 3 0 3 | 0 1 0 3 0 1 | * * * 16 * * | 0 1 1 0
.x .x3.o .. ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 3 2 | * * * * 8 * | 0 1 0 1
.. .x3.o4.o ♦ 0 6 | 0 0 0 0 12 | 0 0 0 0 0 8 | * * * * * 2 | 0 0 1 1
---------------+-------+--------------+------------------+---------------+--------
x. x.3o.4o. ♦ 12 0 | 6 24 0 0 0 | 12 16 0 0 0 0 | 8 2 0 0 0 0 | 1 * * *
xx xx3oo ..&#x ♦ 6 6 | 3 6 6 3 6 | 3 2 3 6 3 2 | 1 0 3 2 1 0 | * 8 * *
.. xx3oo4oo&#x ♦ 6 6 | 0 12 6 0 12 | 0 8 0 12 0 8 | 0 1 0 8 0 1 | * * 2 *
.x .x3.o4.o ♦ 0 12 | 0 0 0 6 24 | 0 0 0 0 12 16 | 0 0 0 0 8 2 | * * * 1
xx oo3xx3oo&#x → height = 1
(ope || ope)
o. o.3o.3o. | 12 * | 1 4 1 0 0 | 4 2 2 1 4 0 0 0 | 2 2 1 4 2 2 0 0 0 | 1 2 2 1 0
.o .o3.o3.o | * 12 | 0 0 1 1 4 | 0 0 0 1 4 4 2 2 | 0 0 0 4 2 2 2 2 1 | 0 2 2 1 1
---------------+-------+--------------+--------------------+--------------------+----------
x. .. .. .. | 2 0 | 6 * * * * | 4 0 0 1 0 0 0 0 | 2 2 0 4 0 0 0 0 0 | 1 2 2 0 0
.. .. x. .. | 2 0 | * 24 * * * | 1 1 1 0 1 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
oo oo3oo3oo&#x | 1 1 | * * 12 * * | 0 0 0 1 4 0 0 0 | 0 0 0 4 2 2 0 0 0 | 0 2 2 1 0
.x .. .. .. | 0 2 | * * * 6 * | 0 0 0 1 0 4 0 0 | 0 0 0 4 0 0 2 2 0 | 0 2 2 0 1
.. .. .x .. | 0 2 | * * * * 24 | 0 0 0 0 1 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
---------------+-------+--------------+--------------------+--------------------+----------
x. .. x. .. | 4 0 | 2 2 0 0 0 | 12 * * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
.. o.3x. .. | 3 0 | 0 3 0 0 0 | * 8 * * * * * * | 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
.. .. x.3o. | 3 0 | 0 3 0 0 0 | * * 8 * * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 6 * * * * | 0 0 0 4 0 0 0 0 0 | 0 2 2 0 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * 24 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.x .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * 12 * * | 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1
.. .o3.x .. | 0 3 | 0 0 0 0 3 | * * * * * * 8 * | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
.. .. .x3.o | 0 3 | 0 0 0 0 3 | * * * * * * * 8 | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
---------------+-------+--------------+--------------------+--------------------+----------
x. o.3x. .. ♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 0 0 | 4 * * * * * * * * | 1 1 0 0 0
x. .. x.3o. ♦ 6 0 | 3 6 0 0 0 | 3 0 2 0 0 0 0 0 | * 4 * * * * * * * | 1 0 1 0 0
.. o.3x.3o. ♦ 6 0 | 0 12 0 0 0 | 0 4 4 0 0 0 0 0 | * * 2 * * * * * * | 1 0 0 1 0
xx .. xx ..&#x ♦ 4 4 | 2 2 4 2 2 | 1 0 0 2 2 1 0 0 | * * * 12 * * * * * | 0 1 1 0 0
.. oo3xx ..&#x ♦ 3 3 | 0 3 3 0 3 | 0 1 0 0 3 0 1 0 | * * * * 8 * * * * | 0 1 0 1 0
.. .. xx3oo&#x ♦ 3 3 | 0 3 3 0 3 | 0 0 1 0 3 0 0 1 | * * * * * 8 * * * | 0 0 1 1 0
.x .o3.x .. ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 3 2 0 | * * * * * * 4 * * | 0 1 0 0 1
.x .. .x3.o ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 3 0 2 | * * * * * * * 4 * | 0 0 1 0 1
.. .o3.x3.o ♦ 0 6 | 0 0 0 0 12 | 0 0 0 0 0 0 4 4 | * * * * * * * * 2 | 0 0 0 1 1
---------------+-------+--------------+--------------------+--------------------+----------
x. o.3x.3o. ♦ 12 0 | 6 24 0 0 0 | 12 8 8 0 0 0 0 0 | 4 4 2 0 0 0 0 0 0 | 1 * * * *
xx oo3xx ..&#x ♦ 6 6 | 3 6 6 3 6 | 3 2 0 3 6 3 2 0 | 1 0 0 3 2 0 1 0 0 | * 4 * * *
xx .. xx3oo&#x ♦ 6 6 | 3 6 6 3 6 | 3 0 2 3 6 3 0 2 | 0 1 0 3 0 2 0 1 0 | * * 4 * *
.. oo3xx3oo&#x ♦ 6 6 | 0 12 6 0 12 | 0 4 4 0 12 0 4 4 | 0 0 1 0 4 4 0 0 1 | * * * 2 *
.x .o3.x3.o ♦ 0 12 | 0 0 0 6 24 | 0 0 0 0 0 12 8 8 | 0 0 0 0 0 0 4 4 2 | * * * * 1
xo3ox xx4oo&#x → height = sqrt(2/3) = 0.816497
(tisdip || {3}-gyro tisdip)
o.3o. o.4o. | 12 * | 2 2 2 0 0 | 1 4 1 2 1 4 0 0 0 | 2 2 1 4 2 2 0 0 | 1 2 2 1 0
.o3.o .o4.o | * 12 | 0 0 2 2 2 | 0 0 0 1 2 4 1 4 1 | 0 0 1 2 4 2 2 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x. .. .. .. | 2 0 | 12 * * * * | 1 2 0 1 0 0 0 0 0 | 2 1 1 2 0 0 0 0 | 1 2 1 0 0
.. .. x. .. | 2 0 | * 12 * * * | 0 2 1 0 0 2 0 0 0 | 1 2 0 2 1 2 0 0 | 1 2 2 1 0
oo3oo oo4oo&#x | 1 1 | * * 24 * * | 0 0 0 1 1 2 0 0 0 | 0 0 1 2 2 1 0 0 | 0 1 1 1 0
.. .x .. .. | 0 2 | * * * 12 * | 0 0 0 0 1 0 1 2 0 | 0 0 1 0 2 0 2 1 | 0 2 0 1 1
.. .. .x .. | 0 2 | * * * * 12 | 0 0 0 0 0 2 0 2 1 | 0 0 0 1 2 2 1 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. .. .. | 3 0 | 3 0 0 0 0 | 4 * * * * * * * * | 2 0 1 0 0 0 0 0 | 1 2 0 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 | * 12 * * * * * * * | 1 1 0 1 0 0 0 0 | 1 1 1 0 0
.. .. x.4o. | 4 0 | 0 4 0 0 0 | * * 3 * * * * * * | 0 2 0 0 0 2 0 0 | 1 0 2 1 0
xo .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 12 * * * * * | 0 0 1 2 0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x | 1 2 | 0 0 2 1 0 | * * * * 12 * * * * | 0 0 1 0 2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * * 24 * * * | 0 0 0 1 1 1 0 0 | 0 1 1 1 0
.o3.x .. .. | 0 3 | 0 0 0 3 0 | * * * * * * 4 * * | 0 0 1 0 0 0 2 0 | 0 2 0 0 1
.. .x .x .. | 0 4 | 0 0 0 2 2 | * * * * * * * 12 * | 0 0 0 0 1 0 1 1 | 0 1 0 1 1
.. .. .x4.o | 0 4 | 0 0 0 0 4 | * * * * * * * * 3 | 0 0 0 0 0 2 0 2 | 0 0 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 0 | 4 * * * * * * * | 1 1 0 0 0
x. .. x.4o. ♦ 8 0 | 4 8 0 0 0 | 0 4 2 0 0 0 0 0 0 | * 3 * * * * * * | 1 0 1 0 0
xo3ox .. ..&#x ♦ 3 3 | 3 0 6 3 0 | 1 0 0 3 3 0 1 0 0 | * * 4 * * * * * | 0 2 0 0 0
xo .. xx ..&#x ♦ 4 2 | 2 2 4 0 1 | 0 1 0 2 0 2 0 0 0 | * * * 12 * * * * | 0 1 1 0 0
.. ox xx ..&#x ♦ 2 4 | 0 1 4 2 2 | 0 0 0 0 2 2 0 1 0 | * * * * 12 * * * | 0 1 0 1 0
.. .. xx4oo&#x ♦ 4 4 | 0 4 4 0 4 | 0 0 1 0 0 4 0 0 1 | * * * * * 6 * * | 0 0 1 1 0
.o3.x .x .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 2 3 0 | * * * * * * 4 * | 0 1 0 0 1
.. .x .x4.o ♦ 0 8 | 0 0 0 4 8 | 0 0 0 0 0 0 0 4 2 | * * * * * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.4o. ♦ 12 0 | 12 12 0 0 0 | 4 12 3 0 0 0 0 0 0 | 4 3 0 0 0 0 0 0 | 1 * * * *
xo3ox xx ..&#x ♦ 6 6 | 6 6 6 6 6 | 2 3 0 6 6 6 2 3 0 | 1 0 2 3 3 0 1 0 | * 4 * * *
xo .. xx4oo&#x ♦ 8 4 | 4 8 8 0 4 | 0 4 2 4 0 8 0 0 1 | 0 1 0 4 0 2 0 0 | * * 3 * *
.. ox xx4oo&#x ♦ 4 8 | 0 4 8 4 8 | 0 0 1 0 4 8 0 4 2 | 0 0 0 0 4 2 0 1 | * * * 3 *
.o3.x .x4.o ♦ 0 12 | 0 0 0 12 12 | 0 0 0 0 0 0 4 12 3 | 0 0 0 0 0 0 4 3 | * * * * 1
xx xx xo3ox&#x → height = sqrt(2/3) = 0.816497
(tisdip || {3}-gyro tisdip)
o. o. o.3o. | 12 * | 1 1 2 2 0 0 0 | 1 2 2 1 2 2 2 1 0 0 0 0 | 2 1 1 2 2 1 2 1 1 0 0 0 | 1 2 1 1 1 0
.o .o .o3.o | * 12 | 0 0 0 2 1 1 2 | 0 0 0 0 2 2 1 2 1 2 2 1 | 0 0 0 2 1 2 1 2 1 2 1 1 | 0 1 2 1 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. .. .. .. | 2 0 | 6 * * * * * * | 1 2 0 0 2 0 0 0 0 0 0 0 | 2 1 0 2 2 1 0 0 0 0 0 0 | 1 2 1 1 0 0
.. x. .. .. | 2 0 | * 6 * * * * * | 1 0 2 0 0 2 0 0 0 0 0 0 | 2 0 1 2 0 0 2 1 0 0 0 0 | 1 2 1 0 1 0
.. .. x. .. | 2 0 | * * 12 * * * * | 0 1 1 1 0 0 1 0 0 0 0 0 | 1 1 1 0 1 0 1 0 1 0 0 0 | 1 1 0 1 1 0
oo oo oo3oo&#x | 1 1 | * * * 24 * * * | 0 0 0 0 1 1 1 1 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 | 0 1 1 1 1 0
.x .. .. .. | 0 2 | * * * * 6 * * | 0 0 0 0 2 0 0 0 1 2 0 0 | 0 0 0 2 1 2 0 0 0 2 1 0 | 0 1 2 1 0 1
.. .x .. .. | 0 2 | * * * * * 6 * | 0 0 0 0 0 2 0 0 1 0 2 0 | 0 0 0 2 0 0 1 2 0 2 0 1 | 0 1 2 0 1 1
.. .. .. .x | 0 2 | * * * * * * 12 | 0 0 0 0 0 0 0 1 0 1 1 1 | 0 0 0 0 0 1 0 1 1 1 1 1 | 0 0 1 1 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. x. .. .. | 4 0 | 2 2 0 0 0 0 0 | 3 * * * * * * * * * * * | 2 0 0 2 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0
x. .. x. .. | 4 0 | 2 0 2 0 0 0 0 | * 6 * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
.. x. x. .. | 4 0 | 0 2 2 0 0 0 0 | * * 6 * * * * * * * * * | 1 0 1 0 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0
.. .. x.3o. | 3 0 | 0 0 3 0 0 0 0 | * * * 4 * * * * * * * * | 0 1 1 0 0 0 0 0 1 0 0 0 | 1 0 0 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 0 2 1 0 0 | * * * * 12 * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
.. xx .. ..&#x | 2 2 | 0 1 0 2 0 1 0 | * * * * * 12 * * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 | 0 1 1 0 1 0
.. .. xo ..&#x | 2 1 | 0 0 1 2 0 0 0 | * * * * * * 12 * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 | 0 1 0 1 1 0
.. .. .. ox&#x | 1 2 | 0 0 0 2 0 0 1 | * * * * * * * 12 * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 | 0 0 1 1 1 0
.x .x .. .. | 0 4 | 0 0 0 0 2 2 0 | * * * * * * * * 3 * * * | 0 0 0 2 0 0 0 0 0 2 0 0 | 0 1 2 0 0 1
.x .. .. .x | 0 4 | 0 0 0 0 2 0 2 | * * * * * * * * * 6 * * | 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 1 1 0 1
.. .x .. .x | 0 4 | 0 0 0 0 0 2 2 | * * * * * * * * * * 6 * | 0 0 0 0 0 0 0 1 0 1 0 1 | 0 0 1 0 1 1
.. .. .o3.x | 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. x. x. .. ♦ 8 0 | 4 4 4 0 0 0 0 | 2 2 2 0 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * | 1 1 0 0 0 0
x. .. x.3o. ♦ 6 0 | 3 0 6 0 0 0 0 | 0 3 0 2 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * | 1 0 0 1 0 0
.. x. x.3o. ♦ 6 0 | 0 3 6 0 0 0 0 | 0 0 3 2 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * | 1 0 0 0 1 0
xx xx .. ..&#x ♦ 4 4 | 2 2 0 4 2 2 0 | 1 0 0 0 2 2 0 0 1 0 0 0 | * * * 6 * * * * * * * * | 0 1 1 0 0 0
xx .. xo ..&#x ♦ 4 2 | 2 0 2 4 1 0 0 | 0 1 0 0 2 0 2 0 0 0 0 0 | * * * * 6 * * * * * * * | 0 1 0 1 0 0
xx .. .. ox&#x ♦ 2 4 | 1 0 0 4 2 0 2 | 0 0 0 0 2 0 0 2 0 1 0 0 | * * * * * 6 * * * * * * | 0 0 1 1 0 0
.. xx xo ..&#x ♦ 4 2 | 0 2 2 4 0 1 0 | 0 0 1 0 0 2 2 0 0 0 0 0 | * * * * * * 6 * * * * * | 0 1 0 0 1 0
.. xx .. ox&#x ♦ 2 4 | 0 1 0 4 0 2 2 | 0 0 0 0 0 2 0 2 0 0 1 0 | * * * * * * * 6 * * * * | 0 0 1 0 1 0
.. .. xo3ox&#x ♦ 3 3 | 0 0 3 6 0 0 3 | 0 0 0 1 0 0 3 3 0 0 0 1 | * * * * * * * * 4 * * * | 0 0 0 1 1 0
.x .x .. .x ♦ 0 8 | 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 0 2 2 2 0 | * * * * * * * * * 3 * * | 0 0 1 0 0 1
.x .. .o3.x ♦ 0 6 | 0 0 0 0 3 0 6 | 0 0 0 0 0 0 0 0 0 3 0 2 | * * * * * * * * * * 2 * | 0 0 0 1 0 1
.. .x .o3.x ♦ 0 6 | 0 0 0 0 0 3 6 | 0 0 0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * 2 | 0 0 0 0 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. x. x.3o. ♦ 12 0 | 6 6 12 0 0 0 0 | 3 6 6 4 0 0 0 0 0 0 0 0 | 3 2 2 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xx xx xo ..&#x ♦ 8 4 | 4 4 4 8 2 2 0 | 2 2 2 0 4 4 4 0 1 0 0 0 | 1 0 0 2 2 0 2 0 0 0 0 0 | * 3 * * * *
xx xx .. ox&#x ♦ 4 8 | 2 2 0 8 4 4 4 | 1 0 0 0 4 4 0 4 2 2 2 0 | 0 0 0 2 0 2 0 2 0 1 0 0 | * * 3 * * *
xx .. xo3ox&#x ♦ 6 6 | 3 0 6 6 3 0 6 | 0 3 0 2 6 0 6 6 0 3 0 2 | 0 1 0 0 3 3 0 0 2 0 1 0 | * * * 2 * *
.. xx xo3ox&#x ♦ 6 6 | 0 3 6 6 0 3 6 | 0 0 3 2 0 6 6 6 0 0 3 2 | 0 0 1 0 0 0 3 3 2 0 0 1 | * * * * 2 *
.x .x .o3.x ♦ 0 12 | 0 0 0 0 6 6 12 | 0 0 0 0 0 0 0 0 3 6 6 4 | 0 0 0 0 0 0 0 0 0 3 2 2 | * * * * * 1
oxo4ooo xxx4ooo&#xt → both heights = 1/sqrt(2) = 0.707107 o..4o.. o..4o.. | 4 * * | 2 4 0 0 0 0 | 1 4 8 0 0 0 0 0 | 1 8 4 0 0 0 | 2 4 0 .o.4.o. .o.4.o. | * 16 * | 0 1 2 2 1 0 | 0 2 2 4 1 2 2 0 | 1 4 1 2 4 1 | 2 2 2 ..o4..o ..o4..o | * * 4 | 0 0 0 0 4 2 | 0 0 0 0 0 4 8 1 | 1 0 0 0 8 4 | 2 0 4 --------------------+--------+-----------------+----------------------+---------------+------ ... ... x.. ... | 2 0 0 | 4 * * * * * | 1 0 4 0 0 0 0 0 | 0 4 4 0 0 0 | 1 4 0 oo.4oo. oo.4oo.&#x | 1 1 0 | * 16 * * * * | 0 2 2 0 0 0 0 0 | 1 4 1 0 0 0 | 2 2 0 .x. ... ... ... | 0 2 0 | * * 16 * * * | 0 1 0 2 0 1 0 0 | 1 2 0 1 2 0 | 2 1 1 ... ... .x. ... | 0 2 0 | * * * 16 * * | 0 0 1 2 1 0 1 0 | 0 2 1 2 2 1 | 1 2 2 .oo4.oo .oo4.oo&#x | 0 1 1 | * * * * 16 * | 0 0 0 0 0 2 2 0 | 1 0 0 0 4 1 | 2 0 2 ... ... ..x ... | 0 0 2 | * * * * * 4 | 0 0 0 0 0 0 4 1 | 0 0 0 0 4 4 | 1 0 4 --------------------+--------+-----------------+----------------------+---------------+------ ... ... x..4o.. | 4 0 0 | 4 0 0 0 0 0 | 1 * * * * * * * | 0 0 4 0 0 0 | 0 4 0 ox. ... ... ...&#x | 1 2 0 | 0 2 1 0 0 0 | * 16 * * * * * * | 1 2 0 0 0 0 | 2 1 0 ... ... xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 | * * 16 * * * * * | 0 2 1 0 0 0 | 1 2 0 .x. ... .x. ... | 0 4 0 | 0 0 2 2 0 0 | * * * 16 * * * * | 0 1 0 1 1 0 | 1 1 1 ... ... .x.4.o. | 0 4 0 | 0 0 0 4 0 0 | * * * * 4 * * * | 0 0 1 2 0 1 | 0 2 2 .xo ... ... ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * * * 16 * * | 1 0 0 0 2 0 | 2 0 1 ... ... .xx ...&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * 16 * | 0 0 0 0 2 1 | 1 0 2 ... ... ..x4..o | 0 0 4 | 0 0 0 0 0 4 | * * * * * * * 1 | 0 0 0 0 0 4 | 0 0 4 --------------------+--------+-----------------+----------------------+---------------+------ oxo4ooo ... ...&#xt ♦ 1 4 1 | 0 4 4 0 4 0 | 0 4 0 0 0 4 0 0 | 4 * * * * * | 2 0 0 ox. ... xx. ...&#x ♦ 2 4 0 | 1 4 2 2 0 0 | 0 2 2 1 0 0 0 0 | * 16 * * * * | 1 1 0 ... ... xx.4oo.&#x ♦ 4 4 0 | 4 4 0 4 0 0 | 1 0 4 0 1 0 0 0 | * * 4 * * * | 0 2 0 .x. ... .x.4.o. ♦ 0 8 0 | 0 0 4 8 0 0 | 0 0 0 4 2 0 0 0 | * * * 4 * * | 0 1 1 .xo ... .xx ...&#x ♦ 0 4 2 | 0 0 2 2 4 1 | 0 0 0 1 0 2 2 0 | * * * * 16 * | 1 0 1 ... ... .xx4.oo&#x ♦ 0 4 4 | 0 0 0 4 4 4 | 0 0 0 0 1 0 4 1 | * * * * * 4 | 0 0 2 --------------------+--------+-----------------+----------------------+---------------+------ oxo4ooo xxx ...&#xt ♦ 2 8 2 | 1 8 8 4 8 1 | 0 8 4 4 0 8 4 0 | 2 4 0 0 4 0 | 4 * * ox. ... xx.4oo.&#x ♦ 4 8 0 | 4 8 4 8 0 0 | 1 4 8 4 2 0 0 0 | 0 4 2 1 0 0 | * 4 * .xo ... .xx4.oo&#x ♦ 0 8 4 | 0 0 4 8 8 4 | 0 0 0 4 2 4 8 1 | 0 0 0 1 4 2 | * * 4
or o..4o.. o..4o.. & | 8 * | 2 4 0 0 | 1 4 8 0 0 | 1 8 4 0 | 2 4 .o.4.o. .o.4.o. | * 16 | 0 2 2 2 | 0 4 4 4 1 | 1 8 2 2 | 2 4 ----------------------+------+------------+--------------+----------+---- ... ... x.. ... & | 2 0 | 8 * * * | 1 0 4 0 0 | 0 4 4 0 | 1 4 oo.4oo. oo.4oo.&#x & | 1 1 | * 32 * * | 0 2 2 0 0 | 1 4 1 0 | 2 2 .x. ... ... ... | 0 2 | * * 16 * | 0 2 0 2 0 | 1 4 0 1 | 2 2 ... ... .x. ... | 0 2 | * * * 16 | 0 0 2 2 1 | 0 4 2 2 | 1 4 ----------------------+------+------------+--------------+----------+---- ... ... x..4o.. & | 4 0 | 4 0 0 0 | 2 * * * * | 0 0 4 0 | 0 4 ox. ... ... ...&#x & | 1 2 | 0 2 1 0 | * 32 * * * | 1 2 0 0 | 2 1 ... ... xx. ...&#x & | 2 2 | 1 2 0 1 | * * 32 * * | 0 2 1 0 | 1 2 .x. ... .x. ... | 0 4 | 0 0 2 2 | * * * 16 * | 0 2 0 1 | 1 2 ... ... .x.4.o. | 0 4 | 0 0 0 4 | * * * * 4 | 0 0 2 2 | 0 4 ----------------------+------+------------+--------------+----------+---- oxo4ooo ... ...&#xt ♦ 2 4 | 0 8 4 0 | 0 8 0 0 0 | 4 * * * | 2 0 ox. ... xx. ...&#x & ♦ 2 4 | 1 4 2 2 | 0 2 2 1 0 | * 32 * * | 1 1 ... ... xx.4oo.&#x & ♦ 4 4 | 4 4 0 4 | 1 0 4 0 1 | * * 8 * | 0 2 .x. ... .x.4.o. ♦ 0 8 | 0 0 4 8 | 0 0 0 4 2 | * * * 4 | 0 2 ----------------------+------+------------+--------------+----------+---- oxo4ooo xxx ...&#xt ♦ 4 8 | 2 16 8 4 | 0 16 8 4 0 | 2 8 0 0 | 4 * ox. ... xx.4oo.&#x & ♦ 4 8 | 4 8 4 8 | 1 4 8 4 2 | 0 4 2 1 | * 8
qo ox4oo xx4oo&#zx → height = 0 (tegum sum of q x4o and ortho base-para tes) o. o.4o. o.4o. | 8 * | 2 4 0 0 | 1 4 8 0 0 | 1 8 4 0 | 2 4 .o .o4.o .o4.o | * 16 | 0 2 2 2 | 0 4 4 4 1 | 1 8 2 2 | 2 4 -------------------+------+------------+--------------+----------+---- .. .. .. x. .. | 2 0 | 8 * * * | 1 0 4 0 0 | 0 4 4 0 | 1 4 oo oo4oo oo4oo&#x | 1 1 | * 32 * * | 0 2 2 0 0 | 1 4 1 0 | 2 2 .. .x .. .. .. | 0 2 | * * 16 * | 0 2 0 2 0 | 1 4 0 1 | 2 2 .. .. .. .x .. | 0 2 | * * * 16 | 0 0 2 2 1 | 0 4 2 2 | 1 4 -------------------+------+------------+--------------+----------+---- .. .. .. x.4o. | 4 0 | 4 0 0 0 | 2 * * * * | 0 0 4 0 | 0 4 .. ox .. .. ..&#x | 1 2 | 0 2 1 0 | * 32 * * * | 1 2 0 0 | 2 1 .. .. .. xx ..&#x | 2 2 | 1 2 0 1 | * * 32 * * | 0 2 1 0 | 1 2 .. .x .. .x .. | 0 4 | 0 0 2 2 | * * * 16 * | 0 2 0 1 | 1 2 .. .. .. .x4.o | 0 4 | 0 0 0 4 | * * * * 4 | 0 0 2 2 | 0 4 -------------------+------+------------+--------------+----------+---- qo ox4oo .. ..&#zx ♦ 2 4 | 0 8 4 0 | 0 8 0 0 0 | 4 * * * | 2 0 .. ox .. xx ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 1 0 | * 32 * * | 1 1 .. .. .. xx4oo&#x ♦ 4 4 | 4 4 0 4 | 1 0 4 0 1 | * * 8 * | 0 2 .. .x .. .x4.o ♦ 0 8 | 0 0 4 8 | 0 0 0 4 2 | * * * 4 | 0 2 -------------------+------+------------+--------------+----------+---- qo ox4oo xx ..&#zx ♦ 4 8 | 2 16 8 4 | 0 16 8 4 0 | 2 8 0 0 | 4 * .. ox .. xx4oo&#x ♦ 4 8 | 4 8 4 8 | 1 4 8 4 2 | 0 4 2 1 | * 8
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