vertex figure ofroc
- general polytopal classes:
- Wythoffian polypeta segmentopeta lace simplices
links
| Acronym | hixip |
| Name | hexateron prism, vertex figure ofroc |
| |,>,O device | line pyramid pyramid pyramid pyramid prism =|>>>>| |
| Circumradius | sqrt(2/3) = 0.816497 |
| Volume | sqrt(3)/480 = 0.0036084 |
| Face vector | 12, 36, 55, 50, 27, 8 |
| Confer |
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| External links | |
Incidence matrix according toDynkin symbol
x x3o3o3o3o. . . . . . | 12 | 1 5 | 5 10 | 10 10 | 10 5 | 5 1------------+----+------+-------+-------+-------+----x . . . . . | 2 | 6 *♦ 5 0 | 10 0 | 10 0 | 5 0. x . . . . | 2 | * 30 | 1 4 | 4 6 | 6 4 | 4 1------------+----+------+-------+-------+-------+----x x . . . . | 4 | 2 2 | 15 *♦ 4 0 | 6 0 | 4 0. x3o . . . | 3 | 0 3 | * 40 | 1 3 | 3 3 | 3 1------------+----+------+-------+-------+-------+----x x3o . . .♦ 6 | 3 6 | 3 2 | 20 * | 3 0 | 3 0. x3o3o . .♦ 4 | 0 6 | 0 4 | * 30 | 1 2 | 2 1------------+----+------+-------+-------+-------+----x x3o3o . .♦ 8 | 4 12 | 6 8 | 4 2 | 15 * | 2 0. x3o3o3o .♦ 5 | 0 10 | 0 10 | 0 5 | * 12 | 1 1------------+----+------+-------+-------+-------+----x x3o3o3o .♦ 10 | 5 20 | 10 20 | 10 10 | 5 2 | 6 *. x3o3o3o3o♦ 6 | 0 15 | 0 20 | 0 15 | 0 6 | * 2
xx3oo3oo3oo3oo&#x → height = 1(hix||hix)o.3o.3o.3o.3o. | 6 * | 5 1 0 | 10 5 0 | 10 10 0 | 5 10 0 | 1 5 0.o3.o3.o3.o3.o | * 6 | 0 1 5 | 0 5 10 | 0 10 10 | 0 10 5 | 0 5 1------------------+-----+---------+----------+----------+--------+------x. .. .. .. .. | 2 0 | 15 * * | 4 1 0 | 6 4 0 | 4 6 0 | 1 4 0oo3oo3oo3oo3oo&#x | 1 1 | * 6 *♦ 0 5 0 | 0 10 0 | 0 10 0 | 0 5 0.x .. .. .. .. | 0 2 | * * 15 | 0 1 4 | 0 4 6 | 0 6 4 | 0 4 1------------------+-----+---------+----------+----------+--------+------x.3o. .. .. .. | 3 0 | 3 0 0 | 20 * * | 3 1 0 | 3 3 0 | 1 3 0xx .. .. .. ..&#x | 2 2 | 1 2 1 | * 15 *♦ 0 4 0 | 0 6 0 | 0 4 0.x3.o .. .. .. | 0 3 | 0 0 3 | * * 20 | 0 1 3 | 0 3 3 | 0 3 1------------------+-----+---------+----------+----------+--------+------x.3o.3o. .. ..♦ 4 0 | 6 0 0 | 4 0 0 | 15 * * | 2 1 0 | 1 2 0xx3oo .. .. ..&#x♦ 3 3 | 3 3 3 | 1 3 1 | * 20 * | 0 3 0 | 0 3 0.x3.o3.o .. ..♦ 0 4 | 0 0 6 | 0 0 4 | * * 15 | 0 1 2 | 0 2 1------------------+-----+---------+----------+----------+--------+------x.3o.3o.3o. ..♦ 5 0 | 10 0 0 | 10 0 0 | 5 0 0 | 6 * * | 1 1 0xx3oo3oo .. ..&#x♦ 4 4 | 6 4 6 | 4 6 4 | 1 4 1 | * 15 * | 0 2 0.x3.o3.o3.o ..♦ 0 5 | 0 0 10 | 0 0 10 | 0 0 5 | * * 6 | 0 1 1------------------+-----+---------+----------+----------+--------+------x.3o.3o.3o.3o.♦ 6 0 | 15 0 0 | 20 0 0 | 15 0 0 | 6 0 0 |1 * *xx3oo3oo3oo ..&#x♦ 5 5 | 10 5 10 | 10 10 10 | 5 10 5 | 1 5 1 | * 6 *.x3.o3.o3.o3.o♦ 0 6 | 0 0 15 | 0 0 20 | 0 0 15 | 0 0 6 | * *1xx ox3oo3oo3oo&#x → height = sqrt(3/5) = 0.774597(line||penp)o. o.3o.3o.3o. | 2 * | 1 5 0 0 | 5 10 0 0 | 10 10 0 0 | 10 5 0 0 | 5 1 0.o .o3.o3.o3.o | * 10 | 0 1 1 4 | 1 4 4 6 | 4 6 6 4 | 6 4 4 1 | 4 1 1------------------+------+-----------+------------+-------------+-----------+------x. .. .. .. .. | 2 0 |1 * * *♦ 5 0 0 0 | 10 0 0 0 | 10 0 0 0 | 5 0 0oo oo3oo3oo3oo&#x | 1 1 | * 10 * * | 1 4 0 0 | 4 6 0 0 | 6 4 0 0 | 4 1 0.x .. .. .. .. | 0 2 | * * 5 *♦ 1 0 4 0 | 4 0 6 0 | 6 0 4 0 | 4 0 1.. .x .. .. .. | 0 2 | * * * 20 | 0 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1------------------+------+-----------+------------+-------------+-----------+------xx .. .. .. ..&#x | 2 2 | 1 2 1 0 | 5 * * *♦ 4 0 0 0 | 6 0 0 0 | 4 0 0.. ox .. .. ..&#x | 1 2 | 0 2 0 1 | * 20 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0.x .x .. .. .. | 0 4 | 0 0 2 2 | * * 10 *♦ 1 0 3 0 | 3 0 3 0 | 3 0 1.. .x3.o .. .. | 0 3 | 0 0 0 3 | * * * 20 | 0 1 1 2 | 1 2 2 1 | 2 1 1------------------+------+-----------+------------+-------------+-----------+------xx ox .. .. ..&#x♦ 2 4 | 1 4 2 2 | 2 2 1 0 | 10 * * * | 3 0 0 0 | 3 0 0.. ox3oo .. ..&#x♦ 1 3 | 0 3 0 3 | 0 3 0 1 | * 20 * * | 1 2 0 0 | 2 1 0.x .x3.o .. ..♦ 0 6 | 0 0 3 6 | 0 0 3 2 | * * 10 * | 1 0 2 0 | 2 0 1.. .x3.o3.o ..♦ 0 4 | 0 0 0 6 | 0 0 0 4 | * * * 10 | 0 1 1 1 | 1 1 1------------------+------+-----------+------------+-------------+-----------+------xx ox3oo .. ..&#x♦ 2 6 | 1 6 3 6 | 3 6 3 2 | 3 2 1 0 | 10 * * * | 2 0 0.. ox3oo3oo ..&#x♦ 1 4 | 0 4 0 6 | 0 6 0 4 | 0 4 0 1 | * 10 * * | 1 1 0.x .x3.o3.o ..♦ 0 8 | 0 0 4 12 | 0 0 6 8 | 0 0 4 2 | * * 5 * | 1 0 1.. .x3.o3.o3.o♦ 0 5 | 0 0 0 10 | 0 0 0 10 | 0 0 0 5 | * * * 2 | 0 1 1------------------+------+-----------+------------+-------------+-----------+------xx ox3oo3oo ..&#x♦ 2 8 | 1 8 4 12 | 4 12 6 8 | 6 8 4 2 | 4 2 1 0 | 5 * *.. ox3oo3oo3oo&#x♦ 1 5 | 0 5 0 10 | 0 10 0 10 | 0 10 0 5 | 0 5 0 1 | * 2 *.x .x3.o3.o3.o♦ 0 10 | 0 0 5 20 | 0 0 10 20 | 0 0 10 10 | 0 0 5 2 | * *1xx xo3oo ox3oo&#x → height = 1/sqrt(3) = 0.577350(trip|| (not fully) orthotrip)o. o.3o. o.3o. | 6 * | 1 2 3 0 0 | 2 1 3 6 3 0 0 | 1 6 3 3 6 1 0 | 3 6 1 3 2 | 3 2 1.o .o3.o .o3.o | * 6 | 0 0 3 1 2 | 0 0 3 3 6 2 1 | 0 3 6 1 6 3 1 | 1 6 3 2 3 | 2 3 1------------------+-----+------------+-----------------+----------------+-----------+------x. .. .. .. .. | 2 0 | 3 * * * *♦ 2 0 3 0 0 0 0 | 1 6 3 0 0 0 0 | 3 6 1 0 0 | 3 2 0.. x. .. .. .. | 2 0 | * 6 * * * | 1 1 0 3 0 0 0 | 1 3 0 3 3 0 0 | 3 3 0 3 1 | 3 1 1oo oo3oo oo3oo&#x | 1 1 | * * 18 * * | 0 0 1 2 2 0 0 | 0 2 2 1 4 1 0 | 1 4 1 2 2 | 2 2 1.x .. .. .. .. | 0 2 | * * * 3 *♦ 0 0 3 0 0 2 0 | 0 3 6 0 0 0 1 | 1 6 3 0 0 | 2 3 0.. .. .. .x .. | 0 2 | * * * * 6 | 0 0 0 0 3 1 1 | 0 0 3 0 3 3 1 | 0 3 3 1 3 | 1 3 1------------------+-----+------------+-----------------+----------------+-----------+------x. x. .. .. .. | 4 0 | 2 2 0 0 0 | 3 * * * * * *♦ 1 3 0 0 0 0 0 | 3 3 0 0 0 | 3 1 0.. x.3o. .. .. | 3 0 | 0 3 0 0 0 | * 2 * * * * * | 1 0 0 3 0 0 0 | 3 0 0 3 0 | 3 0 1xx .. .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * 9 * * * *♦ 0 2 2 0 0 0 0 | 1 4 1 0 0 | 2 2 0.. xo .. .. ..&#x | 2 1 | 0 1 2 0 0 | * * * 18 * * * | 0 1 0 1 2 0 0 | 1 2 0 2 1 | 2 1 1.. .. .. ox ..&#x | 1 2 | 0 0 2 0 1 | * * * * 18 * * | 0 0 1 0 2 1 0 | 0 2 1 1 2 | 1 2 1.x .. .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * 3 *♦ 0 0 3 0 0 0 1 | 0 3 3 0 0 | 1 3 0.. .. .. .x3.o | 0 3 | 0 0 0 0 3 | * * * * * * 2 | 0 0 0 0 0 3 1 | 0 0 3 0 3 | 0 3 1------------------+-----+------------+-----------------+----------------+-----------+------x. x.3o. .. ..♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 0 | 1 * * * * * * | 3 0 0 0 0 | 3 0 0xx xo .. .. ..&#x♦ 4 2 | 2 2 4 1 0 | 1 0 2 2 0 0 0 | * 9 * * * * * | 1 2 0 0 0 | 2 1 0xx .. .. ox ..&#x♦ 2 4 | 1 0 4 2 2 | 0 0 2 0 2 1 0 | * * 9 * * * * | 0 2 1 0 0 | 1 2 0.. xo3oo .. ..&#x♦ 3 1 | 0 3 3 0 0 | 0 1 0 3 0 0 0 | * * * 6 * * * | 1 0 0 2 0 | 2 0 1.. xo .. ox ..&#x♦ 2 2 | 0 1 4 0 1 | 0 0 0 2 2 0 0 | * * * * 18 * * | 0 1 0 1 1 | 1 1 1.. .. .. ox3oo&#x♦ 1 3 | 0 0 3 0 3 | 0 0 0 0 3 0 1 | * * * * * 6 * | 0 0 1 0 2 | 0 2 1.x .. .. .x3.o♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * 1 | 0 0 3 0 0 | 0 3 0------------------+-----+------------+-----------------+----------------+-----------+------xx xo3oo .. ..&#x♦ 6 2 | 3 6 6 1 0 | 3 2 3 6 0 0 0 | 1 3 0 2 0 0 0 | 3 * * * * | 2 0 0xx xo .. ox ..&#x♦ 4 4 | 2 2 8 2 2 | 1 0 4 4 4 1 0 | 0 2 2 0 2 0 0 | * 9 * * * | 1 1 0xx .. .. ox3oo&#x♦ 2 6 | 1 0 6 3 6 | 0 0 3 0 6 3 2 | 0 0 3 0 0 2 1 | * * 3 * * | 0 2 0.. xo3oo ox ..&#x♦ 3 2 | 0 3 6 0 1 | 0 1 0 6 3 0 0 | 0 0 0 2 3 0 0 | * * * 6 * | 1 0 1.. xo .. ox3oo&#x♦ 2 3 | 0 1 6 0 3 | 0 0 0 3 6 0 1 | 0 0 0 0 3 2 0 | * * * * 6 | 0 1 1------------------+-----+------------+-----------------+----------------+-----------+------xx xo3oo ox ..&#x♦ 6 4 | 3 6 12 2 2 | 3 2 6 12 6 1 0 | 1 6 3 4 6 0 0 | 2 3 0 2 0 | 3 * *xx xo .. ox3oo&#x♦ 4 6 | 2 2 12 3 6 | 1 0 6 6 12 3 2 | 0 3 6 0 6 4 1 | 0 3 2 0 2 | * 3 *.. xo3oo ox3oo&#x♦ 3 3 | 0 3 9 0 3 | 0 1 0 9 9 0 1 | 0 0 0 3 9 3 0 | 0 0 0 3 3 | * * 2xxoo3oooo3oooo3oooo&#xr → height(1,2) = height(3,4) = 1 height(1,4) = height(2,3) = sqrt(3/5) = 0.774597o...3o...3o...3o... | 5 * * * | 4 1 1 0 0 0 | 6 4 1 4 0 0 | 4 6 4 6 0 0 | 1 4 6 4 0 0 | 1 4 1 0.o..3.o..3.o..3.o.. | * 5 * * | 0 1 0 4 1 0 | 0 4 1 0 6 4 | 0 6 4 0 4 6 | 0 4 6 0 1 4 | 1 4 0 1..o.3..o.3..o.3..o. | * *1 * | 0 0 0 0 5 1 | 0 0 5 0 0 10 | 0 0 10 0 0 10 | 0 0 10 0 0 5 | 0 5 0 1...o3...o3...o3...o | * * *1 | 0 0 5 0 0 1 | 0 0 5 10 0 0 | 0 0 10 10 0 0 | 0 0 10 5 0 0 | 0 5 1 0------------------------+---------+---------------+------------------+-----------------+--------------+--------x... .... .... .... | 2 0 0 0 | 10 * * * * * | 3 1 0 1 0 0 | 3 3 1 3 0 0 | 1 3 3 3 0 0 | 1 3 1 0oo..3oo..3oo..3oo..&#x | 1 1 0 0 | * 5 * * * *♦ 0 4 1 0 0 0 | 0 6 4 0 0 0 | 0 4 6 0 0 0 | 1 4 0 0o..o3o..o3o..o3o..o&#x | 1 0 0 1 | * * 5 * * * | 0 0 1 4 0 0 | 0 0 4 6 0 0 | 0 0 6 4 0 0 | 0 4 1 0.x.. .... .... .... | 0 2 0 0 | * * * 10 * * | 0 1 0 0 3 1 | 0 3 1 0 3 3 | 0 3 3 0 1 3 | 1 3 0 1.oo.3.oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * * 5 * | 0 0 1 0 0 4 | 0 0 4 0 0 6 | 0 0 6 0 0 4 | 0 4 0 1..oo3..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * 1♦ 0 0 5 0 0 0 | 0 0 10 0 0 0 | 0 0 10 0 0 0 | 0 5 0 0------------------------+---------+---------------+------------------+-----------------+--------------+--------x...3o... .... .... | 3 0 0 0 | 3 0 0 0 0 0 | 10 * * * * * | 2 1 0 1 0 0 | 1 2 1 2 0 0 | 1 2 1 0xx.. .... .... ....&#x | 2 2 0 0 | 1 2 0 1 0 0 | * 10 * * * *♦ 0 3 1 0 0 0 | 0 3 3 0 0 0 | 1 3 0 0oooo3oooo3oooo3oooo&#xr | 1 1 1 1 | 0 1 1 0 1 1 | * * 5 * * *♦ 0 0 4 0 0 0 | 0 0 6 0 0 0 | 0 4 0 0x..o .... .... ....&#x | 2 0 0 1 | 1 0 2 0 0 0 | * * * 10 * * | 0 0 1 3 0 0 | 0 0 3 3 0 0 | 0 3 1 0.x..3.o.. .... .... | 0 3 0 0 | 0 0 0 3 0 0 | * * * * 10 * | 0 1 0 0 2 1 | 0 2 1 0 1 2 | 1 2 0 1.xo. .... .... ....&#x | 0 2 1 0 | 0 0 0 1 2 0 | * * * * * 10 | 0 0 1 0 0 3 | 0 0 3 0 0 3 | 0 3 0 1------------------------+---------+---------------+------------------+-----------------+--------------+--------x...3o...3o... ....♦ 4 0 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 | 5 * * * * * | 1 1 0 1 0 0 | 1 1 1 0xx..3oo.. .... ....&#x♦ 3 3 0 0 | 3 3 0 3 0 0 | 1 3 0 0 1 0 | * 10 * * * * | 0 2 1 0 0 0 | 1 2 0 0xxoo .... .... ....&#xr♦ 2 2 1 1 | 1 2 2 1 2 1 | 0 1 2 1 0 1 | * * 10 * * * | 0 0 3 0 0 0 | 0 3 0 0x..o3o..o .... ....&#x♦ 3 0 0 1 | 3 0 3 0 0 0 | 1 0 0 3 0 0 | * * * 10 * * | 0 0 1 2 0 0 | 0 2 1 0.x..3.o..3.o.. ....♦ 0 4 0 0 | 0 0 0 6 0 0 | 0 0 0 0 4 0 | * * * * 5 * | 0 1 0 0 1 1 | 1 1 0 1.xo.3.oo. .... ....&#x♦ 0 3 1 0 | 0 0 0 3 3 0 | 0 0 0 0 1 3 | * * * * * 10 | 0 0 1 0 0 2 | 0 2 0 1------------------------+---------+---------------+------------------+-----------------+--------------+--------x...3o...3o...3o...♦ 5 0 0 0 | 10 0 0 0 0 0 | 10 0 0 0 0 0 | 5 0 0 0 0 0 |1 * * * * * | 1 0 1 0xx..3oo..3oo.. ....&#x♦ 4 4 0 0 | 6 4 0 6 0 0 | 4 6 0 0 4 0 | 1 4 0 0 1 0 | * 5 * * * * | 1 1 0 0xxoo3oooo .... ....&#xr♦ 3 3 1 1 | 3 3 3 3 3 1 | 1 3 3 3 1 3 | 0 1 3 1 0 1 | * * 10 * * * | 0 2 0 0x..o3o..o3o..o ....&#x♦ 4 0 0 1 | 6 0 4 0 0 0 | 4 0 0 6 0 0 | 1 0 0 4 0 0 | * * * 5 * * | 0 1 1 0.x..3.o..3.o..3.o..♦ 0 5 0 0 | 0 0 0 10 0 0 | 0 0 0 0 10 0 | 0 0 0 0 5 0 | * * * *1 * | 1 0 0 1.xo.3.oo.3.oo. ....&#x♦ 0 4 1 0 | 0 0 0 6 4 0 | 0 0 0 0 4 6 | 0 0 0 0 1 4 | * * * * * 5 | 0 1 0 1------------------------+---------+---------------+------------------+-----------------+--------------+--------xx..3oo..3oo..3oo..&#x♦ 5 5 0 0 | 10 5 0 10 0 0 | 10 10 0 0 10 0 | 5 10 0 0 5 0 | 1 5 0 0 1 0 | 1 * * *xxoo3oooo3oooo ....&#xr♦ 4 4 1 1 | 6 4 4 6 4 1 | 4 6 4 6 4 6 | 1 4 6 4 1 4 | 0 1 4 1 0 1 | * 5 * *x..o3o..o3o..o3o..o&#x♦ 5 0 0 1 | 10 0 5 0 0 0 | 10 0 0 10 0 0 | 5 0 0 10 0 0 | 1 0 0 5 0 0 | * * 1 *.xo.3.oo.3.oo.3.oo.&#x♦ 0 5 1 0 | 0 0 0 10 5 0 | 0 0 0 0 10 10 | 0 0 0 0 5 10 | 0 0 0 0 1 5 | * * * 1
xxoo3oooo3oooo ooxx&#xr → height(1,2) = height(3,4) = 1 height(1,4) = height(2,3) = sqrt(3/8) = 0.612372o...3o...3o... o... | 4 * * * | 3 1 2 0 0 0 0 0 | 3 3 2 6 1 0 0 0 0 | 1 3 6 1 6 3 0 0 0 | 1 6 3 2 3 0 0 | 2 3 1 0.o..3.o..3.o.. .o.. | * 4 * * | 0 1 0 3 2 0 0 0 | 0 3 2 0 0 3 6 1 0 | 0 3 6 1 0 0 1 6 3 | 1 6 3 0 0 2 3 | 2 3 0 1..o.3..o.3..o. ..o. | * * 2 * | 0 0 0 0 4 1 1 0 | 0 0 4 0 0 0 6 4 1 | 0 0 6 4 0 0 0 4 6 | 0 4 6 0 0 1 4 | 1 4 0 1...o3...o3...o ...o | * * * 2 | 0 0 4 0 0 0 1 1 | 0 0 4 6 4 0 0 0 1 | 0 0 6 4 4 6 0 0 0 | 0 4 6 1 4 0 0 | 1 4 1 0------------------------+---------+-----------------+---------------------+--------------------+---------------+--------x... .... .... .... | 2 0 0 0 | 6 * * * * * * * | 2 1 0 2 0 0 0 0 0 | 1 2 2 0 4 1 0 0 0 | 1 4 1 2 2 0 0 | 2 2 1 0oo..3oo..3oo.. oo..&#x | 1 1 0 0 | * 4 * * * * * *♦ 0 3 2 0 0 0 0 0 0 | 0 3 6 1 0 0 0 0 0 | 1 6 3 0 0 0 0 | 2 3 0 0o..o3o..o3o..o o..o&#x | 1 0 0 1 | * * 8 * * * * * | 0 0 1 3 1 0 0 0 0 | 0 0 3 1 3 3 0 0 0 | 0 3 3 1 3 0 0 | 1 3 1 0.x.. .... .... .... | 0 2 0 0 | * * * 6 * * * * | 0 1 0 0 0 2 2 0 0 | 0 2 2 0 0 0 1 4 1 | 1 4 1 0 0 2 2 | 2 2 0 1.oo.3.oo.3.oo. .oo.&#x | 0 1 1 0 | * * * * 8 * * * | 0 0 1 0 0 0 3 1 0 | 0 0 3 1 0 0 0 3 3 | 0 3 3 0 0 1 3 | 1 3 0 1.... .... .... ..x. | 0 0 2 0 | * * * * *1 * * | 0 0 0 0 0 0 0 4 1 | 0 0 0 4 0 0 0 0 6 | 0 0 6 0 0 0 4 | 0 4 0 1..oo3..oo3..oo ..oo&#x | 0 0 1 1 | * * * * * * 2 *♦ 0 0 4 0 0 0 0 0 1 | 0 0 6 4 0 0 0 0 0 | 0 4 6 0 0 0 0 | 1 4 0 0.... .... .... ...x | 0 0 0 2 | * * * * * * *1 | 0 0 0 0 4 0 0 0 1 | 0 0 0 4 0 6 0 0 0 | 0 0 6 0 4 0 0 | 0 4 1 0------------------------+---------+-----------------+---------------------+--------------------+---------------+--------x...3o... .... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 | 4 * * * * * * * * | 1 1 0 0 2 0 0 0 0 | 1 2 0 2 1 0 0 | 2 1 1 0xx.. .... .... ....&#x | 2 2 0 0 | 1 2 0 1 0 0 0 0 | * 6 * * * * * * *♦ 0 2 2 0 0 0 0 0 0 | 1 4 1 0 0 0 0 | 2 2 0 0oooo3oooo3oooo oooo&#xr | 1 1 1 1 | 0 1 1 0 1 0 1 0 | * * 8 * * * * * *♦ 0 0 3 1 0 0 0 0 0 | 0 3 3 0 0 0 0 | 1 3 0 0x..o .... .... ....&#x | 2 0 0 1 | 1 0 2 0 0 0 0 0 | * * * 12 * * * * * | 0 0 1 0 2 1 0 0 0 | 0 2 1 1 2 0 0 | 1 2 1 0.... .... .... o..x&#x | 1 0 0 2 | 0 0 2 0 0 0 0 1 | * * * * 4 * * * * | 0 0 0 1 0 3 0 0 0 | 0 0 3 0 3 0 0 | 0 3 1 0.x..3.o.. .... .... | 0 3 0 0 | 0 0 0 3 0 0 0 0 | * * * * * 4 * * * | 0 1 0 0 0 0 1 2 0 | 1 2 0 0 0 2 1 | 2 1 0 1.xo. .... .... ....&#x | 0 2 1 0 | 0 0 0 1 2 0 0 0 | * * * * * * 12 * * | 0 0 1 0 0 0 0 2 1 | 0 2 1 0 0 1 2 | 1 2 0 1.... .... .... .ox.&#x | 0 1 2 0 | 0 0 0 0 2 1 0 0 | * * * * * * * 4 * | 0 0 0 1 0 0 0 0 3 | 0 0 3 0 0 0 3 | 0 3 0 1.... .... .... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 1 2 1 | * * * * * * * * 1♦ 0 0 0 4 0 0 0 0 0 | 0 0 6 0 0 0 0 | 0 4 0 0------------------------+---------+-----------------+---------------------+--------------------+---------------+--------x...3o...3o... ....♦ 4 0 0 0 | 6 0 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 |1 * * * * * * * * | 1 0 0 2 0 0 0 | 2 0 1 0xx..3oo.. .... ....&#x♦ 3 3 0 0 | 3 3 0 3 0 0 0 0 | 1 3 0 0 0 1 0 0 0 | * 4 * * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0xxoo .... .... ....&#xr♦ 2 2 1 1 | 1 2 2 1 2 0 1 0 | 0 1 2 1 0 0 1 0 0 | * * 12 * * * * * * | 0 2 1 0 0 0 0 | 1 2 0 0.... .... .... ooxx&#xr♦ 1 1 2 2 | 0 1 2 0 2 1 2 1 | 0 0 2 0 1 0 0 1 1 | * * * 4 * * * * * | 0 0 3 0 0 0 0 | 0 3 0 0x..o3o..o .... ....&#x♦ 3 0 0 1 | 3 0 3 0 0 0 0 0 | 1 0 0 3 0 0 0 0 0 | * * * * 8 * * * * | 0 1 0 1 1 0 0 | 1 1 1 0x..o .... .... o..x&#x♦ 2 0 0 2 | 1 0 4 0 0 0 0 1 | 0 0 0 2 2 0 0 0 0 | * * * * * 6 * * * | 0 0 1 0 2 0 0 | 0 2 1 0.x..3.o..3.o.. ....♦ 0 4 0 0 | 0 0 0 6 0 0 0 0 | 0 0 0 0 0 4 0 0 0 | * * * * * *1 * * | 1 0 0 0 0 2 0 | 2 0 0 1.xo.3.oo. .... ....&#x♦ 0 3 1 0 | 0 0 0 3 3 0 0 0 | 0 0 0 0 0 1 3 0 0 | * * * * * * * 8 * | 0 1 0 0 0 1 1 | 1 1 0 1.xo. .... .... .ox.&#x♦ 0 2 2 0 | 0 0 0 1 4 1 0 0 | 0 0 0 0 0 0 2 2 0 | * * * * * * * * 6 | 0 0 1 0 0 0 2 | 0 2 0 1------------------------+---------+-----------------+---------------------+--------------------+---------------+--------xx..3oo..3oo.. ....&#x♦ 4 4 0 0 | 6 4 0 6 0 0 0 0 | 4 6 0 0 0 4 0 0 0 | 1 4 0 0 0 0 1 0 0 | 1 * * * * * * | 2 0 0 0xxoo3oooo .... ....&#xr♦ 3 3 1 1 | 3 3 3 3 3 0 1 0 | 1 3 3 3 0 1 3 0 0 | 0 1 3 0 1 0 0 1 0 | * 8 * * * * * | 1 1 0 0xxoo .... .... ooxx&#xr♦ 2 2 2 2 | 1 2 4 1 4 1 2 1 | 0 1 4 2 2 0 2 2 1 | 0 0 2 2 0 1 0 0 1 | * * 6 * * * * | 0 2 0 0x..o3o..o3o..o ....&#x♦ 4 0 0 1 | 6 0 4 0 0 0 0 0 | 4 0 0 6 0 0 0 0 0 | 1 0 0 0 4 0 0 0 0 | * * * 2 * * * | 1 0 1 0x..o3o..o .... o..x&#x♦ 3 0 0 2 | 3 0 6 0 0 0 0 1 | 1 0 0 6 3 0 0 0 0 | 0 0 0 0 2 3 0 0 0 | * * * * 4 * * | 0 1 1 0.xo.3.oo.3.oo. ....&#x♦ 0 4 1 0 | 0 0 0 6 4 0 0 0 | 0 0 0 0 0 4 6 0 0 | 0 0 0 0 0 0 1 4 0 | * * * * * 2 * | 1 0 0 1.xo.3.oo. .... .ox.&#x♦ 0 3 2 0 | 0 0 0 3 6 1 0 0 | 0 0 0 0 0 1 6 3 0 | 0 0 0 0 0 0 0 2 3 | * * * * * * 4 | 0 1 0 1------------------------+---------+-----------------+---------------------+--------------------+---------------+--------xxoo3oooo3oooo ....&#xr♦ 4 4 1 1 | 6 4 4 6 4 0 1 0 | 4 6 4 6 0 4 6 0 0 | 1 4 6 0 4 0 1 4 0 | 1 4 0 1 0 1 0 | 2 * * *xxoo3oooo .... ooxx&#xr♦ 3 3 2 2 | 3 3 6 3 6 1 2 1 | 1 3 6 6 3 1 6 3 1 | 0 1 6 3 2 3 0 2 3 | 0 2 3 0 1 0 1 | * 4 * *x..o3o..o3o..o o..x&#x♦ 4 0 0 2 | 6 0 8 0 0 0 0 1 | 4 0 0 12 4 0 0 0 0 | 1 0 0 0 8 6 0 0 0 | 0 0 0 2 4 0 0 | * * 1 *.xo.3.oo.3.oo. .ox.&#x♦ 0 4 2 0 | 0 0 0 6 8 1 0 0 | 0 0 0 0 0 4 12 4 0 | 0 0 0 0 0 0 1 8 6 | 0 0 0 0 0 2 4 | * * * 1
xxoo3oooo ooxx3oooo&#xr → height(1,2) = height(3,4) = 1 height(1,4) = height(2,3) = 1/sqrt(3) = 0.577350o...3o... o...3o... | 3 * * * | 2 1 3 0 0 0 0 0 | 1 2 3 6 3 0 0 0 0 0 0 | 1 6 3 3 6 1 0 0 0 0 | 3 6 1 3 2 0 0 | 3 2 1 0.o..3.o.. .o..3.o.. | * 3 * * | 0 1 0 2 3 0 0 0 | 0 2 3 0 0 1 6 3 0 0 0 | 1 6 3 0 0 0 3 6 1 0 | 3 6 1 0 0 3 2 | 3 2 0 1..o.3..o. ..o.3..o. | * * 3 * | 0 0 0 0 3 2 1 0 | 0 0 3 0 0 0 3 6 1 2 0 | 0 3 6 0 0 0 1 6 3 1 | 1 6 3 0 0 2 3 | 2 3 0 1...o3...o ...o3...o | * * * 3 | 0 0 3 0 0 0 1 2 | 0 0 3 3 6 0 0 0 0 2 1 | 0 3 6 1 6 3 0 0 0 1 | 1 6 3 2 3 0 0 | 2 3 1 0------------------------+---------+-----------------+-----------------------+---------------------+---------------+--------x... .... .... .... | 2 0 0 0 | 3 * * * * * * * | 1 1 0 3 0 0 0 0 0 0 0 | 1 3 0 3 3 0 0 0 0 0 | 3 3 0 3 1 0 0 | 3 1 1 0oo..3oo.. oo..3oo..&#x | 1 1 0 0 | * 3 * * * * * *♦ 0 2 3 0 0 0 0 0 0 0 0 | 1 6 3 0 0 0 0 0 0 0 | 3 6 1 0 0 0 0 | 3 2 0 0o..o3o..o o..o3o..o&#x | 1 0 0 1 | * * 9 * * * * * | 0 0 1 2 2 0 0 0 0 0 0 | 0 2 2 1 4 1 0 0 0 0 | 1 4 1 2 2 0 0 | 2 2 1 0.x.. .... .... .... | 0 2 0 0 | * * * 3 * * * * | 0 1 0 0 0 1 3 0 0 0 0 | 1 3 0 0 0 0 3 3 0 0 | 3 3 0 0 0 3 1 | 3 1 0 1.oo.3.oo. .oo.3.oo.&#x | 0 1 1 0 | * * * * 9 * * * | 0 0 1 0 0 0 2 2 0 0 0 | 0 2 2 0 0 0 1 4 1 0 | 1 4 1 0 0 2 2 | 2 2 0 1.... .... ..x. .... | 0 0 2 0 | * * * * * 3 * * | 0 0 0 0 0 0 0 3 1 1 0 | 0 0 3 0 0 0 0 3 3 1 | 0 3 3 0 0 1 3 | 1 3 0 1..oo3..oo ..oo3..oo&#x | 0 0 1 1 | * * * * * * 3 *♦ 0 0 3 0 0 0 0 0 0 2 0 | 0 3 6 0 0 0 0 0 0 1 | 1 6 3 0 0 0 0 | 2 3 0 0.... .... ...x .... | 0 0 0 2 | * * * * * * * 3 | 0 0 0 0 3 0 0 0 0 1 1 | 0 0 3 0 3 3 0 0 0 1 | 0 3 3 1 3 0 0 | 1 3 1 0------------------------+---------+-----------------+-----------------------+---------------------+---------------+--------x...3o... .... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 |1 * * * * * * * * * * | 1 0 0 3 0 0 0 0 0 0 | 3 0 0 3 0 0 0 | 3 0 1 0xx.. .... .... ....&#x | 2 2 0 0 | 1 2 0 1 0 0 0 0 | * 3 * * * * * * * * *♦ 1 3 0 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 | 3 1 0 0oooo3oooo oooo3oooo&#xr | 1 1 1 1 | 0 1 1 0 1 0 1 0 | * * 9 * * * * * * * *♦ 0 2 2 0 0 0 0 0 0 0 | 1 4 1 0 0 0 0 | 2 2 0 0x..o .... .... ....&#x | 2 0 0 1 | 1 0 2 0 0 0 0 0 | * * * 9 * * * * * * * | 0 1 0 1 2 0 0 0 0 0 | 1 2 0 2 1 0 0 | 2 1 1 0.... .... o..x ....&#x | 1 0 0 2 | 0 0 2 0 0 0 0 1 | * * * * 9 * * * * * * | 0 0 1 0 2 1 0 0 0 0 | 0 2 1 1 2 0 0 | 1 2 1 0.x..3.o.. .... .... | 0 3 0 0 | 0 0 0 3 0 0 0 0 | * * * * *1 * * * * * | 1 0 0 0 0 0 3 0 0 0 | 3 0 0 0 0 3 0 | 3 0 0 1.xo. .... .... ....&#x | 0 2 1 0 | 0 0 0 1 2 0 0 0 | * * * * * * 9 * * * * | 0 1 0 0 0 0 1 2 0 0 | 1 2 0 0 0 2 1 | 2 1 0 1.... .... .ox. ....&#x | 0 1 2 0 | 0 0 0 0 2 1 0 0 | * * * * * * * 9 * * * | 0 0 1 0 0 0 0 2 1 0 | 0 2 1 0 0 1 2 | 1 2 0 1.... .... ..x.3..o. | 0 0 3 0 | 0 0 0 0 0 3 0 0 | * * * * * * * *1 * * | 0 0 0 0 0 0 0 0 3 1 | 0 0 3 0 0 0 3 | 0 3 0 1.... .... ..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 1 2 1 | * * * * * * * * * 3 *♦ 0 0 3 0 0 0 0 0 0 1 | 0 3 3 0 0 0 0 | 1 3 0 0.... .... ...x3...o | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * *1 | 0 0 0 0 0 3 0 0 0 1 | 0 0 3 0 3 0 0 | 0 3 1 0------------------------+---------+-----------------+-----------------------+---------------------+---------------+--------xx..3oo.. .... ....&#x♦ 3 3 0 0 | 3 3 0 3 0 0 0 0 | 1 3 0 0 0 1 0 0 0 0 0 | 1 * * * * * * * * * | 3 0 0 0 0 0 0 | 3 0 0 0xxoo .... .... ....&#xr♦ 2 2 1 1 | 1 2 2 1 2 0 1 0 | 0 1 2 1 0 0 1 0 0 0 0 | * 9 * * * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0.... .... ooxx ....&#xr♦ 1 1 2 2 | 0 1 2 0 2 1 2 1 | 0 0 2 0 1 0 0 1 0 1 0 | * * 9 * * * * * * * | 0 2 1 0 0 0 0 | 1 2 0 0x..o3o..o .... ....&#x♦ 3 0 0 1 | 3 0 3 0 0 0 0 0 | 1 0 0 3 0 0 0 0 0 0 0 | * * * 3 * * * * * * | 1 0 0 2 0 0 0 | 2 0 1 0x..o .... o..x ....&#x♦ 2 0 0 2 | 1 0 4 0 0 0 0 1 | 0 0 0 2 2 0 0 0 0 0 0 | * * * * 9 * * * * * | 0 1 0 1 1 0 0 | 1 1 1 0.... .... o..x3o..o&#x♦ 1 0 0 3 | 0 0 3 0 0 0 0 3 | 0 0 0 0 3 0 0 0 0 0 1 | * * * * * 3 * * * * | 0 0 1 0 2 0 0 | 0 2 1 0.xo.3.oo. .... ....&#x♦ 0 3 1 0 | 0 0 0 3 3 0 0 0 | 0 0 0 0 0 1 3 0 0 0 0 | * * * * * * 3 * * * | 1 0 0 0 0 2 0 | 2 0 0 1.xo. .... .ox. ....&#x♦ 0 2 2 0 | 0 0 0 1 4 1 0 0 | 0 0 0 0 0 0 2 2 0 0 0 | * * * * * * * 9 * * | 0 1 0 0 0 1 1 | 1 1 0 1.... .... .ox.3.oo.&#x♦ 0 1 3 0 | 0 0 0 0 3 3 0 0 | 0 0 0 0 0 0 0 3 1 0 0 | * * * * * * * * 3 * | 0 0 1 0 0 0 2 | 0 2 0 1.... .... ..xx3..oo&#x♦ 0 0 3 3 | 0 0 0 0 0 1 3 1 | 0 0 0 0 0 0 0 0 1 3 1 | * * * * * * * * * 1 | 0 0 3 0 0 0 0 | 0 3 0 0------------------------+---------+-----------------+-----------------------+---------------------+---------------+--------xxoo3oooo .... ....&#xr♦ 3 3 1 1 | 3 3 3 3 3 0 1 0 | 1 3 3 3 0 1 3 0 0 0 0 | 1 3 0 1 0 0 1 0 0 0 | 3 * * * * * * | 2 0 0 0xxoo .... ooxx ....&#xr♦ 2 2 2 2 | 1 2 4 1 4 1 2 1 | 0 1 4 2 2 0 2 2 0 1 0 | 0 2 2 0 1 0 0 1 0 0 | * 9 * * * * * | 1 1 0 0.... .... ooxx3oooo&#xr♦ 1 1 3 3 | 0 1 3 0 3 3 3 3 | 0 0 3 0 3 0 0 3 1 3 1 | 0 0 3 0 0 1 0 0 1 1 | * * 3 * * * * | 0 2 0 0x..o3o..o o..x ....&#x♦ 3 0 0 2 | 3 0 6 0 0 0 0 1 | 1 0 0 6 3 0 0 0 0 0 0 | 0 0 0 2 3 0 0 0 0 0 | * * * 3 * * * | 1 0 1 0x..o .... o..x3o..o&#x♦ 2 0 0 3 | 1 0 6 0 0 0 0 3 | 0 0 0 3 6 0 0 0 0 0 1 | 0 0 0 0 3 2 0 0 0 0 | * * * * 3 * * | 0 1 1 0.xo.3.oo. .ox. ....&#x♦ 0 3 2 0 | 0 0 0 3 6 1 0 0 | 0 0 0 0 0 1 6 3 0 0 0 | 0 0 0 0 0 0 2 3 0 0 | * * * * * 3 * | 1 0 0 1.xo. .... .ox.3.oo.&#x♦ 0 2 3 0 | 0 0 0 1 6 3 0 0 | 0 0 0 0 0 0 3 6 1 0 0 | 0 0 0 0 0 0 0 3 2 0 | * * * * * * 3 | 0 1 0 1------------------------+---------+-----------------+-----------------------+---------------------+---------------+--------xxoo3oooo ooxx ....&#xr♦ 3 3 2 2 | 3 3 6 3 6 1 2 1 | 1 3 6 6 3 1 6 3 0 1 0 | 1 6 3 2 3 0 2 3 0 0 | 2 3 0 1 0 1 0 | 3 * * *xxoo .... ooxx3oooo&#xr♦ 2 2 3 3 | 1 2 6 1 6 3 3 3 | 0 1 6 3 6 0 3 6 1 3 1 | 0 3 6 0 3 2 0 3 2 1 | 0 3 2 0 1 0 1 | * 3 * *x..o3o..o o..x3o..o&#x♦ 3 0 0 3 | 3 0 9 0 0 0 0 3 | 1 0 0 9 9 0 0 0 0 0 1 | 0 0 0 3 9 3 0 0 0 0 | 0 0 0 3 3 0 0 | * * 1 *.xo.3.oo. .ox.3.oo.&#x♦ 0 3 3 0 | 0 0 0 3 9 3 0 0 | 0 0 0 0 0 1 9 9 1 0 0 | 0 0 0 0 0 0 3 9 3 0 | 0 0 0 0 0 3 3 | * * * 1
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