Acronym | octepe |
Name | octahedral pennene |
Circumradius | 1/sqrt(2) = 0.707107 |
Face vector | 10, 42, 96, 130, 106, 50, 12 |
Confer |
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Incidence matrix according to Dynkin symbol
xo3oo3oo ox3oo4oo&#x → height = 1/sqrt(8) = 0.353553 (pyramid product of tet with oct) o.3o.3o. o.3o.4o. | 4 * ♦ 3 6 0 | 3 18 12 0 | 1 18 36 8 0 | 6 36 24 1 | 12 24 3 | 8 3 .o3.o3.o .o3.o4.o | * 6 ♦ 0 4 4 | 0 6 16 4 | 0 4 24 16 1 | 1 16 24 4 | 4 16 6 | 4 4 ---------------------+-----+---------+-----------+--------------+-----------+---------+---- x. .. .. .. .. .. | 2 0 | 6 * * ♦ 2 6 0 0 | 1 12 12 0 0 | 6 24 8 0 | 12 16 1 | 8 2 oo3oo3oo oo3oo4oo&#x | 1 1 | * 24 * | 0 3 4 0 | 0 3 12 4 0 | 1 12 12 1 | 4 12 3 | 4 3 .. .. .. .x .. .. | 0 2 | * * 12 | 0 0 4 2 | 0 0 6 8 1 | 0 4 12 4 | 1 8 6 | 2 4 ---------------------+-----+---------+-----------+--------------+-----------+---------+---- x.3o. .. .. .. .. | 3 0 | 3 0 0 | 4 * * * ♦ 1 6 0 0 0 | 6 12 0 0 | 12 8 0 | 8 1 xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 36 * * | 0 2 4 0 0 | 1 8 4 0 | 4 8 1 | 4 2 .. .. .. ox .. ..&#x | 1 2 | 0 2 1 | * * 48 * | 0 0 3 2 0 | 0 3 6 1 | 1 6 3 | 2 3 .. .. .. .x3.o .. | 0 3 | 0 0 3 | * * * 8 | 0 0 0 4 1 | 0 0 6 4 | 0 4 6 | 1 4 ---------------------+-----+---------+-----------+--------------+-----------+---------+---- x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 1 * * * * ♦ 6 0 0 0 | 12 0 0 | 8 0 xo3oo .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | * 24 * * * | 1 4 0 0 | 4 4 0 | 4 1 xo .. .. ox .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * * 72 * * | 0 2 2 0 | 1 4 1 | 2 2 .. .. .. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * * 32 * | 0 0 3 1 | 0 3 3 | 1 3 .. .. .. .x3.o4.o ♦ 0 6 | 0 0 12 | 0 0 0 8 | * * * * 1 ♦ 0 0 0 4 | 0 0 6 | 0 4 ---------------------+-----+---------+-----------+--------------+-----------+---------+---- xo3oo3oo .. .. ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 | 1 4 0 0 0 | 6 * * * | 4 0 0 | 4 0 xo3oo .. ox .. ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 0 2 3 0 0 | * 48 * * | 1 2 0 | 2 1 xo .. .. ox3oo ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 0 3 2 0 | * * 48 * | 0 2 1 | 1 2 .. .. .. ox3oo4oo&#x ♦ 1 6 | 0 6 12 | 0 0 12 8 | 0 0 0 8 1 | * * * 4 | 0 0 3 | 0 3 ---------------------+-----+---------+-----------+--------------+-----------+---------+---- xo3oo3oo ox .. ..&#x ♦ 4 2 | 6 8 1 | 4 12 4 0 | 1 8 6 0 0 | 2 4 0 0 | 12 * * | 2 0 xo3oo .. ox3oo ..&#x ♦ 3 3 | 3 9 3 | 1 9 9 1 | 0 3 9 3 0 | 0 3 3 0 | * 32 * | 1 1 xo .. .. ox3oo4oo&#x ♦ 2 6 | 1 12 12 | 0 6 24 8 | 0 0 12 16 1 | 0 0 8 2 | * * 6 | 0 2 ---------------------+-----+---------+-----------+--------------+-----------+---------+---- xo3oo3oo ox3oo ..&#x ♦ 4 3 | 6 12 3 | 4 18 12 1 | 1 12 18 4 0 | 3 12 6 0 | 3 4 0 | 8 * xo3oo .. ox3oo4oo&#x ♦ 3 6 | 3 18 12 | 1 18 36 8 | 0 6 36 24 1 | 0 12 24 3 | 0 8 3 | * 4
xo3oo3oo oo3ox3oo&#x → height = 1/sqrt(8) = 0.353553 (pyramid product of tet with oct) o.3o.3o. o.3o.3o. | 4 * ♦ 3 6 0 | 3 18 12 0 0 | 1 18 36 4 4 0 | 6 36 12 12 1 | 12 12 12 3 | 4 4 3 .o3.o3.o .o3.o3.o | * 6 ♦ 0 4 4 | 0 6 16 2 2 | 0 4 24 8 8 1 | 1 16 12 12 4 | 4 8 8 6 | 2 2 4 ---------------------+-----+---------+-------------+-----------------+--------------+------------+------ x. .. .. .. .. .. | 2 0 | 6 * * ♦ 2 6 0 0 0 | 1 12 12 0 0 0 | 6 24 4 4 0 | 12 8 8 1 | 4 4 2 oo3oo3oo oo3oo3oo&#x | 1 1 | * 24 * | 0 3 4 0 0 | 0 3 12 2 2 0 | 1 12 6 6 1 | 4 6 6 3 | 2 2 3 .. .. .. .. .x .. | 0 2 | * * 12 | 0 0 4 1 1 | 0 0 6 4 4 1 | 0 4 6 6 4 | 1 4 4 6 | 1 1 4 ---------------------+-----+---------+-------------+-----------------+--------------+------------+------ x.3o. .. .. .. .. | 3 0 | 3 0 0 | 4 * * * * ♦ 1 6 0 0 0 0 | 6 12 0 0 0 | 12 4 4 0 | 4 4 1 xo .. .. .. .. ..&#x | 2 1 | 1 2 0 | * 36 * * * | 0 2 4 0 0 0 | 1 8 4 0 0 | 4 4 4 1 | 2 2 2 .. .. .. .. ox ..&#x | 1 2 | 0 2 1 | * * 48 * * | 0 0 3 1 1 0 | 0 3 3 3 1 | 1 3 3 3 | 1 1 3 .. .. .. .o3.x .. | 0 3 | 0 0 3 | * * * 4 * | 0 0 0 4 0 1 | 0 0 6 0 4 | 0 4 0 6 | 1 0 4 .. .. .. .. .x3.o | 0 3 | 0 0 3 | * * * * 4 | 0 0 0 0 4 1 | 0 0 0 6 4 | 0 0 4 6 | 0 1 4 ---------------------+-----+---------+-------------+-----------------+--------------+------------+------ x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 0 | 1 * * * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 4 4 0 xo3oo .. .. .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 0 | * 24 * * * * | 1 4 0 0 0 | 4 2 2 0 | 2 2 1 xo .. .. .. ox ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 0 | * * 72 * * * | 0 2 1 1 0 | 1 2 2 1 | 1 1 2 .. .. .. oo3ox ..&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 0 | * * * 16 * * | 0 0 3 0 1 | 0 3 0 3 | 1 0 3 .. .. .. .. ox3oo&#x ♦ 1 3 | 0 3 3 | 0 0 3 0 1 | * * * * 16 * | 0 0 0 3 1 | 0 0 3 3 | 0 1 3 .. .. .. .o3.x3.o ♦ 0 6 | 0 0 12 | 0 0 0 4 4 | * * * * * 1 ♦ 0 0 0 0 4 | 0 0 0 6 | 0 0 4 ---------------------+-----+---------+-------------+-----------------+--------------+------------+------ xo3oo3oo .. .. ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 0 | 1 4 0 0 0 0 | 6 * * * * | 4 0 0 0 | 2 2 0 xo3oo .. .. ox ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 0 | 0 2 3 0 0 0 | * 48 * * * | 1 1 1 0 | 1 1 1 xo .. .. oo3ox ..&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 0 | 0 0 3 2 0 0 | * * 24 * * | 0 2 0 1 | 1 0 2 xo .. .. .. ox3oo&#x ♦ 2 3 | 1 6 3 | 0 3 6 0 1 | 0 0 3 0 2 0 | * * * 24 * | 0 0 2 1 | 0 1 2 .. .. .. oo3ox3oo&#x ♦ 1 6 | 0 6 12 | 0 0 12 4 4 | 0 0 0 4 4 1 | * * * * 4 | 0 0 0 3 | 0 0 3 ---------------------+-----+---------+-------------+-----------------+--------------+------------+------ xo3oo3oo .. ox ..&#x ♦ 4 2 | 6 8 1 | 4 12 4 0 0 | 1 8 6 0 0 0 | 2 4 0 0 0 | 12 * * * | 1 1 0 xo3oo .. oo3ox ..&#x ♦ 3 3 | 3 9 3 | 1 9 9 1 0 | 0 3 9 3 0 0 | 0 3 3 0 0 | * 16 * * | 1 0 1 xo3oo .. .. ox3oo&#x ♦ 3 3 | 3 9 3 | 1 9 9 0 1 | 0 3 9 0 3 0 | 0 3 0 3 0 | * * 16 * | 0 1 1 xo .. .. oo3ox3oo&#x ♦ 2 6 | 1 12 12 | 0 6 24 4 4 | 0 0 12 8 8 1 | 0 0 4 4 2 | * * * 6 | 0 0 2 ---------------------+-----+---------+-------------+-----------------+--------------+------------+------ xo3oo3oo oo3ox ..&#x ♦ 4 3 | 6 12 3 | 4 18 12 1 0 | 1 12 18 4 0 0 | 3 12 6 0 0 | 3 4 0 0 | 4 * * xo3oo3oo .. ox3oo&#x ♦ 4 3 | 6 12 3 | 4 18 12 0 1 | 1 12 18 0 4 0 | 3 12 0 6 0 | 3 0 4 0 | * 4 * xo3oo .. oo3ox3oo&#x ♦ 3 6 | 3 18 12 | 1 18 36 4 4 | 0 6 36 12 12 1 | 0 12 12 12 3 | 0 4 4 3 | * * 4
xoo3oox oxo3ooo3ooo&#x → height(1,2) = height(2,3) = sqrt(7/24) = 0.540062 height(1,3) = sqrt(2/3) = 0.816497 o..3o.. o..3o..3o.. & | 6 * ♦ 2 4 2 0 | 1 8 6 3 8 0 | 4 4 4 1 12 12 0 | 6 8 1 4 18 8 | 4 2 6 12 2 | 1 4 3 .o.3.o. .o.3.o.3.o. | * 4 ♦ 0 6 0 3 | 0 6 18 0 6 3 | 2 18 12 0 6 18 1 | 6 18 6 1 18 18 | 6 6 3 12 6 | 2 3 6 -------------------------+-----+----------+----------------+-------------------+-----------------+------------+------ x.. ... ... ... ... & | 2 0 | 6 * * * | 1 4 0 1 0 0 | 4 9 0 1 4 0 0 | 6 4 0 4 6 0 | 4 1 6 4 0 | 1 4 1 oo.3oo. oo.3oo.3oo.&#x & | 1 1 | * 24 * * | 0 2 3 0 2 0 | 1 6 3 0 3 6 0 | 3 6 1 1 9 6 | 3 2 3 9 2 | 1 3 3 o.o3o.o o.o3o.o3o.o&#x | 2 0 | * * 6 * | 0 0 0 2 4 0 | 0 0 0 1 8 6 0 | 0 0 0 4 12 4 | 0 0 6 8 1 | 0 4 2 ... ... .x. ... ... | 0 2 | * * * 6 ♦ 0 0 6 0 0 2 | 0 6 12 0 0 6 1 | 2 12 6 0 6 12 | 4 6 1 12 6 | 2 2 6 -------------------------+-----+----------+----------------+-------------------+-----------------+------------+------ x..3o.. ... ... ... & | 3 0 | 3 0 0 0 | 2 * * * * * | 4 0 0 1 0 0 0 | 6 0 0 4 0 0 | 4 0 6 0 0 | 1 4 0 xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | * 24 * * * * | 1 3 0 0 1 0 0 | 3 3 0 1 3 0 | 3 1 3 3 0 | 1 3 1 ... ... ox. ... ...&#x & | 1 2 | 0 2 0 1 | * * 36 * * * | 0 2 2 0 0 2 0 | 1 4 1 0 3 4 | 2 2 1 6 2 | 1 2 3 x.o ... ... ... ...&#x & | 3 0 | 1 0 2 0 | * * * 6 * * | 0 0 0 1 4 0 0 | 0 0 0 4 6 0 | 0 0 6 4 0 | 0 4 1 ooo3ooo ooo3ooo3ooo&#x | 2 1 | 0 2 1 0 | * * * * 24 * | 0 0 0 0 2 3 0 | 0 0 0 1 6 3 | 0 0 3 6 1 | 0 3 2 ... ... .x.3.o. ... | 0 3 | 0 0 0 3 | * * * * * 4 ♦ 0 0 6 0 0 0 1 | 0 6 6 0 0 6 | 2 6 0 6 6 | 2 1 6 -------------------------+-----+----------+----------------+-------------------+-----------------+------------+------ xo.3oo. ... ... ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 0 | 8 * * * * * * | 3 0 0 1 0 0 | 3 0 3 0 0 | 1 3 0 xo. ... ox. ... ...&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 0 | * 36 * * * * * | 1 2 0 0 1 0 | 2 1 1 2 0 | 1 2 1 ... ... ox.3oo. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 | * * 24 * * * * | 0 2 1 0 0 2 | 1 2 0 3 2 | 1 1 3 x.o3o.x ... ... ...&#x ♦ 6 0 | 6 0 6 0 | 2 0 0 6 0 0 | * * * 1 * * * ♦ 0 0 0 4 0 0 | 0 0 6 0 0 | 0 4 0 xoo ... ... ... ...&#x & ♦ 3 1 | 1 3 2 0 | 0 1 0 1 2 0 | * * * * 24 * * | 0 0 0 1 3 0 | 0 0 3 3 0 | 0 3 1 ... ... oxo ... ...&#x ♦ 2 2 | 0 4 1 1 | 0 0 2 0 2 0 | * * * * * 36 * | 0 0 0 0 2 2 | 0 0 1 4 1 | 0 2 2 ... ... .x.3.o.3.o. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 4 | * * * * * * 1 ♦ 0 0 6 0 0 0 | 0 6 0 0 6 | 2 0 6 -------------------------+-----+----------+----------------+-------------------+-----------------+------------+------ xo.3oo. ox. ... ...&#x & ♦ 3 2 | 3 6 0 1 | 1 6 3 0 0 0 | 2 3 0 0 0 0 0 | 12 * * * * * | 2 0 1 0 0 | 1 2 0 xo. ... ox.3oo. ...&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 0 1 | 0 3 2 0 0 0 0 | * 24 * * * * | 1 1 0 1 0 | 1 1 1 ... ... ox.3oo.3oo.&#x & ♦ 1 4 | 0 4 0 6 | 0 0 6 0 0 4 | 0 0 4 0 0 0 1 | * * 6 * * * | 0 2 0 0 2 | 1 0 3 xoo3oox ... ... ...&#x ♦ 6 1 | 6 6 6 0 | 2 6 0 6 6 0 | 2 0 0 1 6 0 0 | * * * 4 * * | 0 0 3 0 0 | 0 3 0 xoo ... oxo ... ...&#x & ♦ 3 2 | 1 6 2 1 | 0 2 3 1 4 0 | 0 1 0 0 2 2 0 | * * * * 36 * | 0 0 1 2 0 | 0 2 1 ... ... oxo3ooo ...&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 0 3 1 | 0 0 2 0 0 3 0 | * * * * * 24 | 0 0 0 2 1 | 0 1 2 -------------------------+-----+----------+----------------+-------------------+-----------------+------------+------ xo.3oo. ox.3oo. ...&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 0 1 | 3 9 3 0 0 0 0 | 3 3 0 0 0 0 | 8 * * * * | 1 1 0 xo. ... ox.3oo.3oo.&#x & ♦ 2 4 | 1 8 0 6 | 0 4 12 0 0 4 | 0 6 8 0 0 0 1 | 0 4 2 0 0 0 | * 6 * * * | 1 0 1 xoo3oox oxo ... ...&#x ♦ 6 2 | 6 12 6 1 | 2 12 6 6 12 0 | 4 6 0 1 12 6 0 | 2 0 0 2 6 0 | * * 6 * * | 0 2 0 xoo ... oxo3ooo ...&#x & ♦ 3 3 | 1 9 2 3 | 0 3 9 1 6 1 | 0 3 3 0 3 6 0 | 0 1 0 0 3 2 | * * * 24 * | 0 1 1 ... ... oxo3ooo3ooo&#x ♦ 2 4 | 0 8 1 6 | 0 0 12 0 4 4 | 0 0 8 0 0 6 1 | 0 0 2 0 0 4 | * * * * 6 | 0 0 2 -------------------------+-----+----------+----------------+-------------------+-----------------+------------+------ xo.3oo. ox.3oo.3oo.&#x & ♦ 3 4 | 3 12 0 6 | 1 12 18 0 0 4 | 4 18 12 0 0 0 1 | 6 12 3 0 0 0 | 4 3 0 0 0 | 2 * * xoo3oox oxo3ooo ...&#x ♦ 6 3 | 6 18 6 3 | 2 18 18 6 18 1 | 6 18 6 1 18 18 0 | 6 6 0 3 18 6 | 2 0 3 6 0 | * 4 * xoo ... oxo3ooo3ooo&#x & ♦ 3 4 | 1 12 2 6 | 0 4 18 1 8 4 | 0 6 12 0 4 12 1 | 0 4 3 0 6 8 | 0 1 0 4 2 | * * 6
xoo3ooo oxo3ooo4ooo&#x → height(1,2) = 1/sqrt(6) = 0.408248 height(1,3) = sqrt(2/3) = 0.816497 height(2,3) = 1/sqrt(2) = 0.707107 o..3o.. o..3o..4o.. | 3 * * ♦ 2 6 1 0 0 | 1 12 12 2 6 0 0 | 6 24 8 1 12 12 0 0 | 12 16 1 6 24 8 0 | 8 2 12 16 1 | 1 8 2 .o.3.o. .o.3.o.4.o. | * 6 * ♦ 0 3 0 4 1 | 0 3 12 0 3 4 4 | 1 12 12 0 3 12 1 4 | 4 12 3 1 12 12 1 | 4 3 4 12 3 | 1 4 3 ..o3..o ..o3..o4..o | * * 1 ♦ 0 0 3 0 6 | 0 0 0 3 18 0 12 | 0 0 0 1 18 36 0 8 | 0 0 0 6 36 24 1 | 0 0 12 24 3 | 0 8 3 -----------------------+-------+-------------+-------------------+---------------------+-------------------+-------------+------ x.. ... ... ... ... | 2 0 0 | 3 * * * * ♦ 1 6 0 1 0 0 0 | 6 12 0 1 6 0 0 0 | 12 8 0 6 12 0 0 | 8 1 12 8 0 | 1 8 1 oo.3oo. oo.3oo.4oo.&#x | 1 1 0 | * 18 * * * | 0 2 4 0 1 0 0 | 1 8 4 0 2 4 0 0 | 4 8 1 1 8 4 0 | 4 2 2 8 1 | 1 4 2 o.o3o.o o.o3o.o4o.o&#x | 1 0 1 | * * 3 * * ♦ 0 0 0 2 6 0 0 | 0 0 0 1 12 12 0 0 | 0 0 0 6 24 8 0 | 0 0 12 16 1 | 0 8 2 ... ... .x. ... ... | 0 2 0 | * * * 12 * | 0 0 3 0 0 2 1 | 0 3 6 0 0 3 1 2 | 1 6 3 0 3 6 1 | 2 3 1 6 3 | 1 2 3 .oo3.oo .oo3.oo4.oo&#x | 0 1 1 | * * * * 6 | 0 0 0 0 3 0 4 | 0 0 0 0 3 12 0 4 | 0 0 0 1 12 12 1 | 0 0 4 12 3 | 0 4 3 -----------------------+-------+-------------+-------------------+---------------------+-------------------+-------------+------ x..3o.. ... ... ... | 3 0 0 | 3 0 0 0 0 | 1 * * * * * * ♦ 6 0 0 1 0 0 0 0 | 12 0 0 6 0 0 0 | 8 0 12 0 0 | 1 8 0 xo. ... ... ... ...&#x | 2 1 0 | 1 2 0 0 0 | * 18 * * * * * | 1 4 0 0 1 0 0 0 | 4 4 0 1 4 0 0 | 4 1 4 4 0 | 1 4 1 ... ... ox. ... ...&#x | 1 2 0 | 0 2 0 1 0 | * * 36 * * * * | 0 2 2 0 0 1 0 0 | 1 4 1 0 2 2 0 | 2 2 1 4 1 | 1 2 2 x.o ... ... ... ...&#x | 2 0 1 | 1 0 2 0 0 | * * * 3 * * * ♦ 0 0 0 1 6 0 0 0 | 0 0 0 6 12 0 0 | 0 0 12 8 0 | 0 8 1 ooo3ooo ooo3ooo4ooo&#x | 1 1 1 | 0 1 1 0 1 | * * * * 18 * * | 0 0 0 0 2 4 0 0 | 0 0 0 1 8 4 0 | 0 0 4 8 1 | 0 4 2 ... ... .x.3.o. ... | 0 3 0 | 0 0 0 3 0 | * * * * * 8 * | 0 0 3 0 0 0 0 1 | 0 3 3 0 0 3 1 | 1 3 0 3 3 | 1 1 3 ... ... .xo ... ...&#x | 0 2 1 | 0 0 0 1 2 | * * * * * * 12 | 0 0 0 0 0 3 0 2 | 0 0 0 0 3 6 1 | 0 0 1 6 3 | 0 2 3 -----------------------+-------+-------------+-------------------+---------------------+-------------------+-------------+------ xo.3oo. ... ... ...&#x ♦ 3 1 0 | 3 3 0 0 0 | 1 3 0 0 0 0 0 | 6 * * * * * * * | 4 0 0 1 0 0 0 | 4 0 4 0 0 | 1 4 0 xo. ... ox. ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 | 0 2 2 0 0 0 0 | * 36 * * * * * * | 1 2 0 0 1 0 0 | 2 1 1 2 0 | 1 2 1 ... ... ox.3oo. ...&#x ♦ 1 3 0 | 0 3 0 3 0 | 0 0 3 0 0 1 0 | * * 24 * * * * * | 0 2 1 0 0 1 0 | 1 2 0 2 1 | 1 1 2 x.o3o.o ... ... ...&#x ♦ 3 0 1 | 3 0 3 0 0 | 1 0 0 3 0 0 0 | * * * 1 * * * * ♦ 0 0 0 6 0 0 0 | 0 0 12 0 0 | 0 8 0 xoo ... ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 | 0 1 0 1 2 0 0 | * * * * 18 * * * | 0 0 0 1 4 0 0 | 0 0 4 4 0 | 0 4 1 ... ... oxo ... ...&#x ♦ 1 2 1 | 0 2 1 1 2 | 0 0 1 0 2 0 1 | * * * * * 36 * * | 0 0 0 0 2 2 0 | 0 0 1 4 1 | 0 2 2 ... ... .x.3.o.4.o. ♦ 0 6 0 | 0 0 0 12 0 | 0 0 0 0 0 8 0 | * * * * * * 1 * ♦ 0 0 3 0 0 0 1 | 0 3 0 0 3 | 1 0 3 ... ... .xo3.oo ...&#x ♦ 0 3 1 | 0 0 0 3 3 | 0 0 0 0 0 1 3 | * * * * * * * 8 | 0 0 0 0 0 3 1 | 0 0 0 3 1 | 0 1 3 -----------------------+-------+-------------+-------------------+---------------------+-------------------+-------------+------ xo.3oo. ox. ... ...&#x ♦ 3 2 0 | 3 6 0 1 0 | 1 6 3 0 0 0 0 | 2 3 0 0 0 0 0 0 | 12 * * * * * * | 2 0 1 0 0 | 1 2 0 xo. ... ox.3oo. ...&#x ♦ 2 3 0 | 1 6 0 3 0 | 0 3 6 0 0 1 0 | 0 3 2 0 0 0 0 0 | * 24 * * * * * | 1 1 0 1 0 | 1 1 1 ... ... ox.3oo.4oo.&#x ♦ 1 6 0 | 0 6 0 12 0 | 0 0 12 0 0 8 0 | 0 0 8 0 0 0 1 0 | * * 3 * * * * | 0 2 0 0 1 | 1 0 2 xoo3ooo ... ... ...&#x ♦ 3 1 1 | 3 3 3 0 1 | 1 3 0 3 3 0 0 | 1 0 0 1 3 0 0 0 | * * * 6 * * * | 0 0 4 0 0 | 0 4 0 xoo ... oxo ... ...&#x ♦ 2 2 1 | 1 4 2 1 2 | 0 2 2 1 4 0 1 | 0 1 0 0 2 2 0 0 | * * * * 36 * * | 0 0 1 2 0 | 0 2 1 ... ... oxo3ooo ...&#x ♦ 1 3 1 | 0 3 1 3 3 | 0 0 3 0 3 1 3 | 0 0 1 0 0 3 0 1 | * * * * * 24 * | 0 0 0 2 1 | 0 1 2 ... ... .xo3.oo4.oo&#x ♦ 0 6 1 | 0 0 0 12 6 | 0 0 0 0 0 8 12 | 0 0 0 0 0 0 1 8 | * * * * * * 1 | 0 0 0 0 3 | 0 0 3 -----------------------+-------+-------------+-------------------+---------------------+-------------------+-------------+------ xo.3oo. ox.3oo. ...&#x ♦ 3 3 0 | 3 9 0 3 0 | 1 9 9 0 0 1 0 | 3 9 3 0 0 0 0 0 | 3 3 0 0 0 0 0 | 8 * * * * | 1 1 0 xo. ... ox.3oo.4oo.&#x ♦ 2 6 0 | 1 12 0 12 0 | 0 6 24 0 0 8 0 | 0 12 16 0 0 0 1 0 | 0 8 2 0 0 0 0 | * 3 * * * | 1 0 1 xoo3ooo oxo ... ...&#x ♦ 3 2 1 | 3 6 3 1 2 | 1 6 3 3 6 0 1 | 2 3 0 1 6 3 0 0 | 1 0 0 2 3 0 0 | * * 12 * * | 0 2 0 xoo ... oxo3ooo ...&#x ♦ 2 3 1 | 1 6 2 3 3 | 0 3 6 1 6 1 3 | 0 3 2 0 3 6 0 1 | 0 1 0 0 3 2 0 | * * * 24 * | 0 1 1 ... ... oxo3ooo4ooo&#x ♦ 1 6 1 | 0 6 1 12 6 | 0 0 12 0 6 8 12 | 0 0 8 0 0 12 1 8 | 0 0 1 0 0 8 1 | * * * * 3 | 0 0 2 -----------------------+-------+-------------+-------------------+---------------------+-------------------+-------------+------ xo.3oo. ox.3oo.4oo.&#x ♦ 3 6 0 | 3 18 0 12 0 | 1 18 36 0 0 8 0 | 6 36 24 0 0 0 1 0 | 12 24 3 0 0 0 0 | 8 3 0 0 0 | 1 * * xoo3ooo oxo3ooo ...&#x ♦ 3 3 1 | 3 9 3 3 3 | 1 9 9 3 9 1 3 | 3 9 3 1 9 9 0 1 | 3 3 0 3 9 3 0 | 1 0 3 3 0 | * 8 * xoo ... oxo3ooo4ooo&#x ♦ 2 6 1 | 1 12 2 12 6 | 0 6 24 1 12 8 12 | 0 12 16 0 6 24 1 8 | 0 8 2 0 12 16 1 | 0 1 0 8 2 | * * 3
xoo oox oxo3ooo4ooo&#x → height(1,2) = height(2,3) = 1/2 height(1,3) = 1/sqrt(2) = 0.707107 o.. o.. o..3o..3o.. & | 4 * ♦ 1 6 2 0 | 6 12 3 12 0 | 12 8 1 18 24 0 | 8 1 6 36 16 | 1 12 24 2 | 8 3 .o. .o. .o.3.o.3.o. | * 6 ♦ 0 4 0 4 | 2 16 0 4 4 | 8 16 0 4 16 1 | 8 4 1 16 16 | 2 4 16 4 | 4 4 -------------------------+-----+-----------+--------------+-----------------+--------------+-----------+---- x.. ... ... ... ... & | 2 0 | 2 * * * ♦ 6 0 2 0 0 | 12 0 1 12 0 0 | 8 0 6 24 0 | 1 12 16 0 | 8 2 oo. oo. oo.3oo.3oo.&#x & | 1 1 | * 24 * * | 1 4 0 2 0 | 4 4 0 3 8 0 | 4 1 1 12 8 | 1 4 12 2 | 4 3 o.o o.o o.o3o.o3o.o&#x | 2 0 | * * 4 * ♦ 0 0 2 6 0 | 0 0 1 12 12 0 | 0 0 6 24 8 | 0 12 16 1 | 8 2 ... ... .x. ... ... | 0 2 | * * * 12 | 0 4 0 0 2 | 2 8 0 0 4 1 | 4 4 0 4 8 | 2 1 8 4 | 2 4 -------------------------+-----+-----------+--------------+-----------------+--------------+-----------+---- xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | 12 * * * * | 4 0 0 2 0 0 | 4 0 1 8 0 | 1 4 8 0 | 4 2 ... ... ox. ... ...&#x & | 1 2 | 0 2 0 1 | * 48 * * * | 1 2 0 0 2 0 | 2 1 0 3 4 | 1 1 6 2 | 2 3 x.o ... ... ... ...&#x & | 3 0 | 1 0 2 0 | * * 4 * * ♦ 0 0 1 6 0 0 | 0 0 6 12 0 | 0 12 8 0 | 8 1 ooo ooo ooo3ooo3ooo&#x | 2 1 | 0 2 1 0 | * * * 24 * | 0 0 0 2 4 0 | 0 0 1 8 4 | 0 4 8 1 | 4 2 ... ... .x.3.o. ... | 0 3 | 0 0 0 3 | * * * * 8 | 0 4 0 0 0 1 | 2 4 0 0 4 | 2 0 4 4 | 1 4 -------------------------+-----+-----------+--------------+-----------------+--------------+-----------+---- xo. ... ox. ... ...&#x & ♦ 2 2 | 1 4 0 1 | 2 2 0 0 0 | 24 * * * * * | 2 0 0 2 0 | 1 1 4 0 | 2 2 ... ... ox.3oo. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 3 0 0 1 | * 32 * * * * | 1 1 0 0 2 | 1 0 3 2 | 1 3 x.o o.x ... ... ...&#x ♦ 4 0 | 2 0 4 0 | 0 0 4 0 0 | * * 1 * * * ♦ 0 0 6 0 0 | 0 12 0 0 | 8 0 xoo ... ... ... ...&#x & ♦ 3 1 | 1 3 2 0 | 1 0 1 2 0 | * * * 24 * * | 0 0 1 4 0 | 0 4 4 0 | 4 1 ... ... oxo ... ...&#x ♦ 2 2 | 0 4 1 1 | 0 2 0 2 0 | * * * * 48 * | 0 0 0 2 2 | 0 1 4 1 | 2 2 ... ... .x.3.o.4.o. ♦ 0 6 | 0 0 0 12 | 0 0 0 0 8 | * * * * * 1 | 0 4 0 0 0 | 2 0 0 4 | 0 4 -------------------------+-----+-----------+--------------+-----------------+--------------+-----------+---- xo. ... ox.3oo. ...&#x & ♦ 2 3 | 1 6 0 3 | 3 6 0 0 1 | 3 2 0 0 0 0 | 16 * * * * | 1 0 2 0 | 1 2 ... ... ox.3oo.4oo.&#x & ♦ 1 6 | 0 6 0 12 | 0 12 0 0 8 | 0 8 0 0 0 1 | * 4 * * * | 1 0 0 2 | 0 3 xoo oox ... ... ...&#x ♦ 4 1 | 2 4 4 0 | 2 0 4 4 0 | 0 0 1 4 0 0 | * * 6 * * | 0 4 0 0 | 4 0 xoo ... oxo ... ...&#x & ♦ 3 2 | 1 6 2 1 | 2 3 1 4 0 | 1 0 0 2 2 0 | * * * 48 * | 0 1 2 0 | 2 1 ... ... oxo3ooo ...&#x ♦ 2 3 | 0 6 1 3 | 0 6 0 3 1 | 0 2 0 0 3 0 | * * * * 32 | 0 0 2 1 | 1 2 -------------------------+-----+-----------+--------------+-----------------+--------------+-----------+---- xo. ... ox.3oo.4oo.&#x & ♦ 2 6 | 1 12 0 12 | 6 24 0 0 8 | 12 16 0 0 0 1 | 8 2 0 0 0 | 2 * * * | 0 2 xoo oox oxo ... ...&#x ♦ 4 2 | 2 8 4 1 | 4 4 4 8 0 | 2 0 1 8 4 0 | 0 0 2 4 0 | * 12 * * | 2 0 xoo ... oxo3ooo ...&#x & ♦ 3 3 | 1 9 2 3 | 3 9 1 6 1 | 3 3 0 3 6 0 | 1 0 0 3 2 | * * 32 * | 1 1 ... ... oxo3ooo4ooo&#x ♦ 2 6 | 0 12 1 12 | 0 24 0 6 8 | 0 16 0 0 12 1 | 0 2 0 0 8 | * * * 4 | 0 2 -------------------------+-----+-----------+--------------+-----------------+--------------+-----------+---- xoo oox oxo3ooo ...&#x ♦ 4 3 | 2 12 4 3 | 6 12 4 12 1 | 6 4 1 12 12 0 | 2 0 3 12 4 | 0 3 4 0 | 8 * xoo ... oxo3ooo4ooo&#x & ♦ 3 6 | 1 18 2 12 | 6 36 1 12 8 | 12 24 0 6 24 1 | 8 3 0 12 16 | 1 0 8 2 | * 4
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