hexacross (β6),
aeropeton,
hexateral antiprism
- general polytopal classes:
- orthoplex
links
| Acronym | gee (old: xic) |
| Name |
hexacontitetrapeton, hexacross (β6), aeropeton, hexateral antiprism |
| Circumradius | 1/sqrt(2) = 0.707107 |
| Inradius | 1/sqrt(12) = 0.288675 |
| Coordinates | (1/sqrt(2), 0, 0, 0, 0, 0) & all permutations, all changes of sign |
| Dual | ax |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o3o3o3o4o . . . . . . | 12 ♦ 10 | 40 | 80 | 80 | 32 ------------+----+----+-----+-----+-----+--- x . . . . . | 2 | 60 ♦ 8 | 24 | 32 | 16 ------------+----+----+-----+-----+-----+--- x3o . . . . | 3 | 3 | 160 ♦ 6 | 12 | 8 ------------+----+----+-----+-----+-----+--- x3o3o . . . ♦ 4 | 6 | 4 | 240 | 4 | 4 ------------+----+----+-----+-----+-----+--- x3o3o3o . . ♦ 5 | 10 | 10 | 5 | 192 | 2 ------------+----+----+-----+-----+-----+--- x3o3o3o3o . ♦ 6 | 15 | 20 | 15 | 6 | 64
o3o3o *b3o3o3x . . . . . . | 12 ♦ 10 | 40 | 80 | 80 | 16 16 ---------------+----+----+-----+-----+-----+------ . . . . . x | 2 | 60 ♦ 8 | 24 | 32 | 8 8 ---------------+----+----+-----+-----+-----+------ . . . . o3x | 3 | 3 | 160 ♦ 6 | 12 | 4 4 ---------------+----+----+-----+-----+-----+------ . . . o3o3x ♦ 4 | 6 | 4 | 240 | 4 | 2 2 ---------------+----+----+-----+-----+-----+------ . o . *b3o3o3x ♦ 5 | 10 | 10 | 5 | 192 | 1 1 ---------------+----+----+-----+-----+-----+------ o3o . *b3o3o3x ♦ 6 | 15 | 20 | 15 | 6 | 32 * . o3o *b3o3o3x ♦ 6 | 15 | 20 | 15 | 6 | * 32
xo3oo3oo3oo3ox&#x → height = 1/sqrt(3) = 0.577350
(hix || inv hix)
o.3o.3o.3o.3o. & | 12 ♦ 5 5 | 10 30 | 10 40 30 | 5 25 50 | 1 6 15 10
---------------------+----+-------+--------+-----------+-----------+-----------
x. .. .. .. .. & | 2 | 30 * ♦ 4 4 | 6 12 6 | 4 12 16 | 1 4 7 4
oo3oo3oo3oo3oo&#x | 2 | * 30 ♦ 0 8 | 0 12 12 | 0 8 24 | 0 2 8 6
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o. .. .. .. & | 3 | 3 0 | 40 * ♦ 3 3 0 | 3 6 3 | 1 3 3 1
xo .. .. .. ..&#x & | 3 | 1 2 | * 120 ♦ 0 3 3 | 0 3 9 | 0 1 4 3
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o. .. .. & ♦ 4 | 6 0 | 4 0 | 30 * * | 2 2 0 | 1 2 1 0
xo3oo .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * 120 * | 0 2 2 | 0 1 2 1
xo .. .. .. ox& ♦ 4 | 2 4 | 0 4 | * * 90 | 0 0 4 | 0 0 2 2
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o.3o. .. & ♦ 5 | 10 0 | 10 0 | 5 0 0 | 12 * * | 1 1 0 0
xo3oo3oo .. ..&#x & ♦ 5 | 6 4 | 4 6 | 1 4 0 | * 60 * | 0 1 1 0
xo3oo .. .. ox&#x & ♦ 5 | 4 6 | 1 9 | 0 2 3 | * * 120 | 0 0 1 1
---------------------+----+-------+--------+-----------+-----------+-----------
x.3o.3o.3o.3o. & ♦ 6 | 15 0 | 20 0 | 15 0 0 | 6 0 0 | 2 * * *
xo3oo3oo3oo ..&#x & ♦ 6 | 10 5 | 10 10 | 5 10 0 | 1 5 0 | * 12 * *
xo3oo3oo .. ox&#x & ♦ 6 | 7 8 | 4 16 | 1 8 6 | 0 2 4 | * * 30 *
xo3oo .. oo3ox&#x ♦ 6 | 6 9 | 2 18 | 0 6 9 | 0 0 6 | * * * 20
oxo3ooo3ooo3ooo4ooo&#xt → both heights = 1/sqrt(2) = 0.707107 (pt || pseudo tac || pt) o..3o..3o..3o..4o.. & | 2 * ♦ 10 0 | 40 0 | 80 0 | 80 0 | 32 .o.3.o.3.o.3.o.4.o. | * 10 ♦ 2 8 | 16 24 | 48 32 | 64 16 | 32 --------------------------+------+-------+-------+--------+--------+--- oo.3oo.3oo.3oo.4oo.&#x & | 1 1 | 20 * ♦ 8 0 | 24 0 | 32 0 | 16 .x. ... ... ... ... | 0 2 | * 40 ♦ 2 6 | 12 12 | 24 8 | 16 --------------------------+------+-------+-------+--------+--------+--- ox. ... ... ... ...&#x & | 1 2 | 2 1 | 80 * ♦ 6 0 | 12 0 | 8 .x.3.o. ... ... ... | 0 3 | 0 3 | * 80 ♦ 2 4 | 8 4 | 8 --------------------------+------+-------+-------+--------+--------+--- ox.3oo. ... ... ...&#x & ♦ 1 3 | 3 3 | 3 1 | 160 * | 4 0 | 4 .x.3.o.3.o. ... ... ♦ 0 4 | 0 6 | 0 4 | * 80 | 2 2 | 4 --------------------------+------+-------+-------+--------+--------+--- ox.3oo.3oo. ... ...&#x & ♦ 1 4 | 4 6 | 6 4 | 4 1 | 160 * | 2 .x.3.o.3.o.3.o. ... ♦ 0 5 | 0 10 | 0 10 | 0 5 | * 32 | 2 --------------------------+------+-------+-------+--------+--------+--- ox.3oo.3oo.3oo. ...&#x & ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 | 64
ooo3ooo3ooo *b3ooo3oxo&#xt → both heights = 1/sqrt(2) = 0.707107 (pt || pseudo tac || pt) o..3o..3o.. *b3o..3o.. & | 2 * ♦ 10 0 | 40 0 | 80 0 | 80 0 0 | 16 16 .o.3.o.3.o. *b3.o.3.o. | * 10 ♦ 2 8 | 16 24 | 48 32 | 64 8 8 | 16 16 -----------------------------+------+-------+-------+--------+-----------+------ oo.3oo.3oo. *b3oo.3oo.&#x & | 1 1 | 20 * ♦ 8 0 | 24 0 | 32 0 0 | 8 8 ... ... ... ... .x. | 0 2 | * 40 ♦ 2 6 | 12 12 | 24 4 4 | 8 8 -----------------------------+------+-------+-------+--------+-----------+------ ... ... ... ... ox.&#x & | 1 2 | 2 1 | 80 * ♦ 6 0 | 12 0 0 | 4 4 ... ... ... .o.3.x. | 0 3 | 0 3 | * 80 ♦ 2 4 | 8 2 2 | 4 4 -----------------------------+------+-------+-------+--------+-----------+------ ... ... ... oo.3ox.&#x & ♦ 1 3 | 3 3 | 3 1 | 160 * | 4 0 0 | 2 2 ... .o. ... *b3.o.3.x. ♦ 0 4 | 0 6 | 0 4 | * 80 | 2 1 1 | 2 2 -----------------------------+------+-------+-------+--------+-----------+------ ... oo. ... *b3oo.3ox.&#x & ♦ 1 4 | 4 6 | 6 4 | 4 1 | 160 * * | 1 1 .o.3.o. ... *b3.o.3.x. ♦ 0 5 | 0 10 | 0 10 | 0 5 | * 16 * | 2 0 ... .o.3.o. *b3.o.3.x. ♦ 0 5 | 0 10 | 0 10 | 0 5 | * * 16 | 0 2 -----------------------------+------+-------+-------+--------+-----------+------ oo.3oo. ... *b3oo.3ox.&#x & ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 0 | 32 * ... oo.3oo. *b3oo.3ox.&#x & ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 0 1 | * 32
xox oxo3ooo3ooo4ooo&#xt → both heights = 1/2 (line || pseudo ortho hex || line) o.. o..3o..3o..4o.. & | 4 * ♦ 1 8 1 0 | 8 24 8 0 | 24 32 24 0 | 32 16 32 | 16 16 .o. .o.3.o.3.o.4.o. | * 8 ♦ 0 4 0 6 | 2 24 2 12 | 12 48 12 8 | 24 32 24 | 16 16 --------------------------+-----+-----------+-------------+--------------+----------+------ x.. ... ... ... ... & | 2 0 | 2 * * * ♦ 8 0 0 0 | 24 0 0 0 | 32 0 0 | 16 0 oo. oo.3oo.3oo.4oo.&#x & | 1 1 | * 32 * * ♦ 1 6 1 0 | 6 12 6 0 | 12 8 12 | 8 8 o.o o.o3o.o3o.o4o.o&#x | 2 0 | * * 2 * ♦ 0 0 8 0 | 0 0 24 0 | 0 0 32 | 0 16 ... .x. ... ... ... | 0 2 | * * * 24 ♦ 0 4 0 4 | 2 16 2 4 | 8 16 8 | 8 8 --------------------------+-----+-----------+-------------+--------------+----------+------ xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | 16 * * * ♦ 8 0 0 0 | 12 0 0 | 8 0 ... ox. ... ... ...&#x & | 1 2 | 0 2 0 1 | * 96 * * ♦ 1 4 1 0 | 4 4 4 | 4 4 ooo ooo3ooo3ooo4ooo&#x | 2 1 | 0 2 1 0 | * * 16 * ♦ 0 0 6 0 | 0 0 12 | 0 8 ... .x.3.o. ... ... | 0 3 | 0 0 0 3 | * * * 32 ♦ 0 4 0 2 | 2 8 2 | 4 4 --------------------------+-----+-----------+-------------+--------------+----------+------ xo. ox. ... ... ...&#x & ♦ 2 2 | 1 4 0 1 | 2 2 0 0 | 48 * * * | 4 0 0 | 4 0 ... ox.3oo. ... ...&#x & ♦ 1 3 | 0 3 0 3 | 0 3 0 1 | * 128 * * | 1 2 1 | 2 2 ... oxo ... ... ...&#x ♦ 2 2 | 0 4 1 1 | 0 2 2 0 | * * 48 * | 0 0 4 | 0 4 ... .x.3.o.3.o. ... ♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * 16 | 0 4 0 | 2 2 --------------------------+-----+-----------+-------------+--------------+----------+------ xo. ox.3oo. ... ...&#x & ♦ 2 3 | 1 6 0 3 | 3 6 0 1 | 3 2 0 0 | 64 * * | 2 0 ... ox.3oo.3oo. ...&#x & ♦ 1 4 | 0 4 0 6 | 0 6 0 4 | 0 4 0 1 | * 64 * | 1 1 ... oxo3ooo ... ...&#x ♦ 2 3 | 0 6 1 3 | 0 6 3 1 | 0 2 3 0 | * * 64 | 0 2 --------------------------+-----+-----------+-------------+--------------+----------+------ xo. ox.3oo.3oo. ...&#x & ♦ 2 4 | 1 8 0 6 | 4 12 0 4 | 6 8 0 1 | 4 2 0 | 32 * ... oxo3ooo3ooo ...&#x ♦ 2 4 | 0 8 1 6 | 0 12 4 4 | 0 8 6 1 | 0 2 4 | * 32
ooo3ooo3ooo *b3oxo xox&#xt → both heights = 1/2 (line || pseudo ortho hex || line) o..3o..3o.. *b3o.. o.. & | 4 * ♦ 1 8 1 0 | 24 8 8 0 | 32 24 24 0 0 | 8 8 32 32 | 8 8 8 8 .o.3.o.3.o. *b3.o. .o. | * 8 ♦ 0 4 0 6 | 24 2 2 12 | 48 12 12 4 4 | 16 16 24 24 | 8 8 8 8 -----------------------------+-----+-----------+-------------+---------------+-------------+------------ ... ... ... ... x.. & | 2 0 | 2 * * * ♦ 0 8 0 0 | 0 24 0 0 0 | 0 0 32 0 | 8 8 0 0 oo.3oo.3oo. *b3oo. oo.&#x & | 1 1 | * 32 * * ♦ 6 1 1 0 | 12 6 6 0 0 | 4 4 12 12 | 4 4 4 4 o.o3o.o3o.o *b3o.o o.o&#x | 2 0 | * * 2 * ♦ 0 0 8 0 | 0 0 24 0 0 | 0 0 0 32 | 0 0 8 8 ... ... ... .x. ... | 0 2 | * * * 24 ♦ 4 0 0 4 | 16 2 2 2 2 | 8 8 8 8 | 4 4 4 4 -----------------------------+-----+-----------+-------------+---------------+-------------+------------ ... ... ... ox. ...&#x & | 1 2 | 0 2 0 1 | 96 * * * ♦ 4 1 1 0 0 | 2 2 4 4 | 2 2 2 2 ... ... ... ... xo.&#x & | 2 1 | 1 2 0 0 | * 16 * * ♦ 0 6 0 0 0 | 0 0 12 0 | 4 4 0 0 ooo3ooo3ooo *b3ooo ooo&#x | 2 1 | 0 2 1 0 | * * 16 * ♦ 0 0 6 0 0 | 0 0 0 12 | 0 0 4 4 ... .o. ... *b3.x. ... | 0 3 | 0 0 0 3 | * * * 32 ♦ 4 0 0 1 1 | 4 4 2 2 | 2 2 2 2 -----------------------------+-----+-----------+-------------+---------------+-------------+------------ ... oo. ... *b3ox. ...&#x & ♦ 1 3 | 0 3 0 3 | 3 0 0 1 | 128 * * * * | 1 1 1 1 | 1 1 1 1 ... ... ... ox. xo.&#x & ♦ 2 2 | 1 4 0 1 | 2 2 0 0 | * 48 * * * | 0 0 4 0 | 2 2 0 0 ... ... ... oxo ...&#x & ♦ 2 2 | 0 4 1 1 | 2 0 2 0 | * * 48 * * | 0 0 0 4 | 0 0 2 2 .o.3.o. ... *b3.x. ... ♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * 8 * | 4 0 0 0 | 2 0 2 0 ... .o.3.o. *b3.x. ... ♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * * 8 | 0 4 0 0 | 0 2 0 2 -----------------------------+-----+-----------+-------------+---------------+-------------+------------ oo.3oo. ... *b3ox. ...&#x & ♦ 1 4 | 0 4 0 6 | 6 0 0 4 | 4 0 0 1 0 | 32 * * * | 1 0 1 0 ... oo.3oo. *b3ox. ...&#x & ♦ 1 4 | 0 4 0 6 | 6 0 0 4 | 4 0 0 0 1 | * 32 * * | 0 1 0 1 ... oo. ... *b3ox. xo.&#x & ♦ 2 3 | 1 6 0 3 | 6 3 0 1 | 2 3 0 0 0 | * * 64 * | 1 1 0 0 ... ooo ... *b3oxo ...&#x & ♦ 2 3 | 0 6 1 3 | 6 0 3 1 | 2 0 3 0 0 | * * * 64 | 0 0 1 1 -----------------------------+-----+-----------+-------------+---------------+-------------+------------ oo.3oo. ... *b3ox. xo.&#x & ♦ 2 4 | 1 8 0 6 | 12 4 0 4 | 8 6 0 1 0 | 2 0 4 0 | 16 * * * ... oo.3oo. *b3ox. xo.&#x & ♦ 2 4 | 1 8 0 6 | 12 4 0 4 | 8 6 0 0 1 | 0 2 4 0 | * 16 * * ooo3ooo ... *b3oxo ...&#x & ♦ 2 4 | 0 8 1 6 | 12 0 4 4 | 8 0 6 1 0 | 2 0 0 4 | * * 16 * ... ooo3ooo *b3oxo ...&#x & ♦ 2 4 | 0 8 1 6 | 12 0 4 4 | 8 0 6 0 1 | 0 2 0 4 | * * * 16
xoo3oox oxo3ooo4ooo&#xt → both heights = 1/sqrt(6) = 0.408248
({3} || pseudo ortho oct || dual {3})
o..3o.. o..3o..4o.. & | 6 * ♦ 2 6 2 0 | 1 12 12 3 12 0 | 6 24 8 18 24 | 12 16 36 16 | 8 24
.o.3.o. .o.3.o.4.o. | * 6 ♦ 0 6 0 4 | 0 6 24 0 6 4 | 2 24 24 6 24 | 8 24 24 24 | 8 24
--------------------------+-----+-----------+----------------+----------------+-------------+------
x.. ... ... ... ... & | 2 0 | 6 * * * ♦ 1 6 0 1 0 0 | 6 12 0 6 0 | 12 8 12 0 | 8 8
oo.3oo. oo.3oo.4oo.&#x & | 1 1 | * 36 * * ♦ 0 2 4 0 2 0 | 1 8 4 3 8 | 4 8 12 8 | 4 12
o.o3o.o o.o3o.o4o.o&#x | 2 0 | * * 6 * ♦ 0 0 0 2 6 0 | 0 0 0 12 12 | 0 0 24 8 | 0 16
... ... .x. ... ... | 0 2 | * * * 12 ♦ 0 0 6 0 0 2 | 0 6 12 0 6 | 2 12 6 12 | 4 12
--------------------------+-----+-----------+----------------+----------------+-------------+------
x..3o.. ... ... ... & | 3 0 | 3 0 0 0 | 2 * * * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 8 0
xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | * 36 * * * * ♦ 1 4 0 1 0 | 4 4 4 0 | 4 4
... ... ox. ... ...&#x & | 1 2 | 0 2 0 1 | * * 72 * * * ♦ 0 2 2 0 2 | 1 4 3 4 | 2 6
x.o ... ... ... ...&#x & | 3 0 | 1 0 2 0 | * * * 6 * * ♦ 0 0 0 6 0 | 0 0 12 0 | 0 8
ooo3ooo ooo3ooo4ooo&#x | 2 1 | 0 2 1 0 | * * * * 36 * ♦ 0 0 0 2 4 | 0 0 8 4 | 0 8
... ... .x.3.o. ... | 0 3 | 0 0 0 3 | * * * * * 8 ♦ 0 0 6 0 0 | 0 6 0 6 | 2 6
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ... ... ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 0 | 12 * * * * | 4 0 0 0 | 4 0
xo. ... ox. ... ...&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 0 | * 72 * * * | 1 2 1 0 | 2 2
... ... ox.3oo. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 | * * 48 * * | 0 2 0 2 | 1 3
xoo ... ... ... ...&#x & ♦ 3 1 | 1 3 2 0 | 0 1 0 1 2 0 | * * * 36 * | 0 0 4 0 | 0 4
... ... oxo ... ...&#x ♦ 2 2 | 0 4 1 1 | 0 0 2 0 2 0 | * * * * 72 | 0 0 2 2 | 0 4
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ox. ... ...&#x & ♦ 3 2 | 3 6 0 1 | 1 6 3 0 0 0 | 2 3 0 0 0 | 24 * * * | 2 0
xo. ... ox.3oo. ...&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 0 1 | 0 3 2 0 0 | * 48 * * | 1 1
xoo ... oxo ... ...&#x & ♦ 3 2 | 1 6 2 1 | 0 2 3 1 4 0 | 0 1 0 2 2 | * * 72 * | 0 2
... ... oxo3ooo ...&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 0 3 1 | 0 0 2 0 3 | * * * 48 | 0 2
--------------------------+-----+-----------+----------------+----------------+-------------+------
xo.3oo. ox.3oo. ...&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 0 1 | 3 9 3 0 0 | 3 3 0 0 | 16 *
xoo ... oxo3ooo ...&#x ♦ 3 3 | 1 9 2 3 | 0 3 9 1 6 1 | 0 3 3 3 6 | 0 1 3 2 | * 48
xoo3oox ooo3oxo3ooo&#xt → both heights = 1/sqrt(6) = 0.408248
({3} || pseudo ortho oct || dual {3})
o..3o.. o..3o..3o.. & | 6 * ♦ 2 6 2 0 | 1 12 12 3 12 0 0 | 6 24 4 4 18 24 | 12 8 8 36 8 8 | 4 4 12 12
.o.3.o. .o.3.o.3.o. | * 6 ♦ 0 6 0 4 | 0 6 24 0 6 2 2 | 2 24 12 12 6 24 | 8 12 12 24 12 12 | 4 4 12 12
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
x.. ... ... ... ... & | 2 0 | 6 * * * ♦ 1 6 0 1 0 0 0 | 6 12 0 0 6 0 | 12 4 4 12 0 0 | 4 4 4 4
oo.3oo. oo.3oo.3oo.&#x & | 1 1 | * 36 * * ♦ 0 2 4 0 2 0 0 | 1 8 2 2 3 8 | 4 4 4 12 4 4 | 2 2 6 6
o.o3o.o o.o3o.o3o.o&#x | 2 0 | * * 6 * ♦ 0 0 0 2 6 0 0 | 0 0 0 0 12 12 | 0 0 0 24 4 4 | 0 0 8 8
... ... ... .x. ... | 0 2 | * * * 12 ♦ 0 0 6 0 0 1 1 | 0 6 6 6 0 6 | 2 6 6 6 6 6 | 2 2 6 6
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
x..3o.. ... ... ... & | 3 0 | 3 0 0 0 | 2 * * * * * * ♦ 6 0 0 0 0 0 | 12 0 0 0 0 0 | 4 4 0 0
xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | * 36 * * * * * ♦ 1 4 0 0 1 0 | 4 2 2 4 0 0 | 2 2 2 2
... ... ... ox. ...&#x & | 1 2 | 0 2 0 1 | * * 72 * * * * ♦ 0 2 1 1 0 2 | 1 2 2 3 2 2 | 1 1 3 3
x.o ... ... ... ...&#x & | 3 0 | 1 0 2 0 | * * * 6 * * * ♦ 0 0 0 0 6 0 | 0 0 0 12 0 0 | 0 0 4 4
ooo3ooo ooo3ooo3ooo&#x | 2 1 | 0 2 1 0 | * * * * 36 * * ♦ 0 0 0 0 2 4 | 0 0 0 8 2 2 | 0 0 4 4
... ... .o.3.x. ... | 0 3 | 0 0 0 3 | * * * * * 4 * ♦ 0 0 6 0 0 0 | 0 6 0 0 6 0 | 2 0 6 0
... ... ... .x.3.o. | 0 3 | 0 0 0 3 | * * * * * * 4 ♦ 0 0 0 6 0 0 | 0 0 6 0 0 6 | 0 2 0 6
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. ... ... ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 0 0 | 12 * * * * * | 4 0 0 0 0 0 | 2 2 0 0
xo. ... ... ox. ...&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 0 0 | * 72 * * * * | 1 1 1 1 0 0 | 1 1 1 1
... ... oo.3ox. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 0 | * * 24 * * * | 0 2 0 0 2 0 | 1 0 3 0
... ... ... ox.3oo.&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 0 1 | * * * 24 * * | 0 0 2 0 0 2 | 0 1 0 3
xoo ... ... ... ...&#x & ♦ 3 1 | 1 3 2 0 | 0 1 0 1 2 0 0 | * * * * 36 * | 0 0 0 4 0 0 | 0 0 2 2
... ... ... oxo ...&#x ♦ 2 2 | 0 4 1 1 | 0 0 2 0 2 0 0 | * * * * * 72 | 0 0 0 2 1 1 | 0 0 2 2
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. ... ox. ...&#x & ♦ 3 2 | 3 6 0 1 | 1 6 3 0 0 0 0 | 2 3 0 0 0 0 | 24 * * * * * | 1 1 0 0
xo. ... oo.3ox. ...&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 0 1 0 | 0 3 2 0 0 0 | * 24 * * * * | 1 0 1 0
xo. ... ... ox.3oo.&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 0 0 1 | 0 3 0 2 0 0 | * * 24 * * * | 0 1 0 1
xoo ... ... oxo ...&#x & ♦ 3 2 | 1 6 2 1 | 0 2 3 1 4 0 0 | 0 1 0 0 2 2 | * * * 72 * * | 0 0 1 1
... ... ooo3oxo ...&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 0 3 1 0 | 0 0 2 0 0 3 | * * * * 24 * | 0 0 2 0
... ... ... oxo3ooo&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 0 3 0 1 | 0 0 0 2 0 3 | * * * * * 24 | 0 0 0 2
--------------------------+-----+-----------+------------------+-------------------+-------------------+----------
xo.3oo. oo.3ox. ...&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 0 1 0 | 3 9 3 0 0 0 | 3 3 0 0 0 0 | 8 * * *
xo.3oo. ... ox.3oo.&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 0 0 1 | 3 9 0 3 0 0 | 3 0 3 0 0 0 | * 8 * *
xoo ... ooo3oxo ...&#x & ♦ 3 3 | 1 9 2 3 | 0 3 9 1 6 1 0 | 0 3 3 0 3 6 | 0 1 0 3 2 0 | * * 24 *
xoo ... ... oxo3ooo&#x & ♦ 3 3 | 1 9 2 3 | 0 3 9 1 6 0 1 | 0 3 0 3 3 6 | 0 0 1 3 0 2 | * * * 24
oxoo3oooo3oooo3ooox&#xr → all heights = sqrt(3/5) = 0.774597 (pt || (pseudo pen || pseudo inv pen) || pt) o...3o...3o...3o... & | 2 * ♦ 5 5 0 0 | 10 10 20 0 0 | 10 10 30 30 0 0 0 | 5 5 20 30 20 0 0 0 | 1 1 5 10 10 5 .o..3.o..3.o..3.o.. & | * 10 ♦ 1 1 4 4 | 4 4 8 6 18 | 6 6 18 18 4 16 12 | 4 4 16 24 16 1 5 10 | 1 1 5 10 10 5 --------------------------+------+-------------+----------------+----------------------+------------------------+---------------- oo..3oo..3oo..3oo..&#x & | 1 1 | 10 * * * ♦ 4 0 4 0 0 | 6 0 12 6 0 0 0 | 4 0 12 12 4 0 0 0 | 1 0 4 6 4 1 o.o.3o.o.3o.o.3o.o.&#x & | 1 1 | * 10 * * ♦ 0 4 4 0 0 | 0 6 6 12 0 0 0 | 0 4 4 12 12 0 0 0 | 0 1 1 4 6 4 .x.. .... .... .... & | 0 2 | * * 20 * ♦ 1 1 0 3 3 | 3 3 3 3 3 6 3 | 3 3 6 6 6 1 3 4 | 1 1 3 4 4 3 .oo.3.oo.3.oo.3.oo.&#x | 0 2 | * * * 20 ♦ 0 0 2 0 6 | 0 0 6 6 0 6 6 | 0 0 6 12 6 0 2 6 | 0 0 2 6 6 2 --------------------------+------+-------------+----------------+----------------------+------------------------+---------------- ox.. .... .... ....&#x & | 1 2 | 2 0 1 0 | 20 * * * * ♦ 3 0 3 0 0 0 0 | 3 0 6 3 0 0 0 0 | 1 0 3 3 1 0 .... .... .... o.x.&#x & | 1 2 | 0 2 1 0 | * 20 * * * ♦ 0 3 0 3 0 0 0 | 0 3 0 3 6 0 0 0 | 0 1 0 1 3 3 ooo.3ooo.3ooo.3ooo.&#x & | 1 2 | 1 1 0 1 | * * 40 * * ♦ 0 0 3 3 0 0 0 | 0 0 3 6 3 0 0 0 | 0 0 1 3 3 1 .x..3.o.. .... .... & | 0 3 | 0 0 3 0 | * * * 20 * ♦ 1 1 0 0 2 2 0 | 2 2 2 0 2 1 2 1 | 1 1 2 1 1 2 .xo. .... .... ....&#x & | 0 3 | 0 0 1 2 | * * * * 60 ♦ 0 0 1 1 0 2 2 | 0 0 2 4 2 0 1 3 | 0 0 1 3 3 1 --------------------------+------+-------------+----------------+----------------------+------------------------+---------------- ox..3oo.. .... ....&#x & ♦ 1 3 | 3 0 3 0 | 3 0 0 1 0 | 20 * * * * * * | 2 0 2 0 0 0 0 0 | 1 0 2 1 0 0 .... .... o.o.3o.x.&#x & ♦ 1 3 | 0 3 3 0 | 0 3 0 1 0 | * 20 * * * * * | 0 2 0 0 2 0 0 0 | 0 1 0 0 1 2 oxo. .... .... ....&#x & ♦ 1 3 | 2 1 1 2 | 1 0 2 0 1 | * * 60 * * * * | 0 0 2 2 0 0 0 0 | 0 0 1 2 1 0 .... .... .... oox.&#x & ♦ 1 3 | 1 2 1 2 | 0 1 2 0 1 | * * * 60 * * * | 0 0 0 2 2 0 0 0 | 0 0 0 1 2 1 .x..3.o..3.o.. .... & ♦ 0 4 | 0 0 6 0 | 0 0 0 4 0 | * * * * 10 * * | 1 1 0 0 0 1 1 0 | 1 1 1 0 0 1 .xo.3.oo. .... ....&#x & ♦ 0 4 | 0 0 3 3 | 0 0 0 1 3 | * * * * * 40 * | 0 0 1 0 1 0 1 1 | 0 0 1 1 1 1 .xo. .... .... .ox.&#x ♦ 0 4 | 0 0 2 4 | 0 0 0 0 4 | * * * * * * 30 | 0 0 0 2 0 0 0 2 | 0 0 0 2 2 0 --------------------------+------+-------------+----------------+----------------------+------------------------+---------------- ox..3oo..3oo.. ....&#x & ♦ 1 4 | 4 0 6 0 | 6 0 0 4 0 | 4 0 0 0 1 0 0 | 10 * * * * * * * | 1 0 1 0 0 0 .... o.o.3o.o.3o.x.&#x & ♦ 1 4 | 0 4 6 0 | 0 6 0 4 0 | 0 4 0 0 1 0 0 | * 10 * * * * * * | 0 1 0 0 0 1 oxo.3ooo. .... ....&#x & ♦ 1 4 | 3 1 3 3 | 3 0 3 1 3 | 1 0 3 0 0 1 0 | * * 40 * * * * * | 0 0 1 1 0 0 oxo. .... .... oox.&#x & ♦ 1 4 | 2 2 2 4 | 1 1 4 0 4 | 0 0 2 2 0 0 1 | * * * 60 * * * * | 0 0 0 1 1 0 .... .... ooo.3oox.&#x & ♦ 1 4 | 1 3 3 3 | 0 3 3 1 3 | 0 1 0 3 0 1 0 | * * * * 40 * * * | 0 0 0 0 1 1 .x..3.o..3.o..3.o.. & ♦ 0 5 | 0 0 10 0 | 0 0 0 10 0 | 0 0 0 0 5 0 0 | * * * * * 2 * * | 1 1 0 0 0 0 .xo.3.oo.3.oo. ....&#x & ♦ 0 5 | 0 0 6 4 | 0 0 0 4 6 | 0 0 0 0 1 4 0 | * * * * * * 10 * | 0 0 1 0 0 1 .xo.3.oo. .... .ox.&#x & ♦ 0 5 | 0 0 4 6 | 0 0 0 1 9 | 0 0 0 0 0 2 3 | * * * * * * * 20 | 0 0 0 1 1 0 --------------------------+------+-------------+----------------+----------------------+------------------------+---------------- ox..3oo..3oo..3oo..&#x & ♦ 1 5 | 5 0 10 0 | 10 0 0 10 0 | 10 0 0 0 5 0 0 | 5 0 0 0 0 1 0 0 | 2 * * * * * o.o.3o.o.3o.o.3o.x.&#x & ♦ 1 5 | 0 5 10 0 | 0 10 0 10 0 | 0 10 0 0 5 0 0 | 0 5 0 0 0 1 0 0 | * 2 * * * * oxo.3ooo.3ooo. ....&#x & ♦ 1 5 | 4 1 6 4 | 6 0 4 4 6 | 4 0 6 0 1 4 0 | 1 0 4 0 0 0 1 0 | * * 10 * * * oxo.3ooo. .... oox.&#x & ♦ 1 5 | 3 2 4 6 | 3 1 6 1 9 | 1 0 6 3 0 2 3 | 0 0 2 3 0 0 0 1 | * * * 20 * * oxo. .... ooo.3oox.&#x & ♦ 1 5 | 2 3 4 6 | 1 3 6 1 9 | 0 1 3 6 0 2 3 | 0 0 0 3 2 0 0 1 | * * * * 20 * .... ooo.3ooo.3oox.&#x & ♦ 1 5 | 1 4 6 4 | 0 6 4 4 6 | 0 4 0 6 1 4 0 | 0 1 0 0 4 0 1 0 | * * * * * 10
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