Acronym | squete |
Name |
square-pyramidal pyramid pyramid, square-tettene, triangular-square disphenoid, half of the triacontiditeron |
|,>,O device | line prism pyramid pyramid pyramid = ||>>> |
Circumradius | 1/sqrt(2) = 0.707107 |
Lace city in approx. ASCII-art |
x o3o o x3o x o3o |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dual | (topologically selfdual, in different orientation) |
Face vector | 7, 19, 26, 19, 7 |
Confer |
|
External links |
Incidence matrix according to Dynkin symbol
xo3oo ox4oo&#x → height = 1/sqrt(6) = 0.408248 (pyramid product of {3} with {4}) o.3o. o.4o. | 3 * ♦ 2 4 0 | 1 8 4 0 | 4 8 1 | 4 2 .o3.o .o4.o | * 4 | 0 3 2 | 0 3 6 1 | 1 6 3 | 2 3 ---------------+-----+--------+-----------+--------+---- x. .. .. .. | 2 0 | 3 * * ♦ 1 4 0 0 | 4 4 0 | 4 1 oo3oo oo4oo&#x | 1 1 | * 12 * | 0 2 2 0 | 1 4 1 | 2 2 .. .. .x .. | 0 2 | * * 4 | 0 0 3 1 | 0 3 3 | 1 3 ---------------+-----+--------+-----------+--------+---- x.3o. .. .. | 3 0 | 3 0 0 | 1 * * * | 4 0 0 | 4 0 xo .. .. ..&#x | 2 1 | 1 2 0 | * 12 * * | 1 2 0 | 2 1 .. .. ox ..&#x | 1 2 | 0 2 1 | * * 12 * | 0 2 1 | 1 2 .. .. .x4.o | 0 4 | 0 0 4 | * * * 1 | 0 0 3 | 0 3 ---------------+-----+--------+-----------+--------+---- xo3oo .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | 4 * * | 2 0 xo .. ox ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * 12 * | 1 1 .. .. ox4oo&#x ♦ 1 4 | 0 4 4 | 0 0 4 1 | * * 3 | 0 2 ---------------+-----+--------+-----------+--------+---- xo3oo ox ..&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 2 3 0 | 4 * xo .. ox4oo&#x ♦ 2 4 | 1 8 4 | 0 4 8 1 | 0 4 2 | * 3
ox ox xo3oo&#x → height = 1/sqrt(6) = 0.408248 (pyramid product of {3} with {4}) o. o. o.3o. | 3 * ♦ 2 4 0 0 | 1 2 2 8 0 | 1 4 4 4 | 2 2 2 .o .o .o3.o | * 4 | 0 3 1 1 | 0 3 3 3 1 | 3 3 3 1 | 3 1 1 ---------------+-----+----------+------------+---------+------ .. .. x. .. | 2 0 | 3 * * * ♦ 1 0 0 4 0 | 0 2 2 4 | 1 2 2 oo oo oo3oo&#x | 1 1 | * 12 * * | 0 1 1 2 0 | 1 2 2 1 | 2 1 1 .x .. .. .. | 0 2 | * * 2 * | 0 3 0 0 1 | 3 3 0 0 | 3 1 0 .. .x .. .. | 0 2 | * * * 2 | 0 0 3 0 1 | 3 0 3 0 | 3 0 1 ---------------+-----+----------+------------+---------+------ .. .. x.3o. | 3 0 | 3 0 0 0 | 1 * * * * | 0 0 0 4 | 0 2 2 ox .. .. ..&#x | 1 2 | 0 2 1 0 | * 6 * * * | 1 2 0 0 | 2 1 0 .. ox .. ..&#x | 1 2 | 0 2 0 1 | * * 6 * * | 1 0 2 0 | 2 0 1 .. .. xo ..&#x | 2 1 | 1 2 0 0 | * * * 12 * | 0 1 1 1 | 1 1 1 .x .x .. .. | 0 4 | 0 0 2 2 | * * * * 1 | 3 0 0 0 | 3 0 0 ---------------+-----+----------+------------+---------+------ ox ox .. ..&#x ♦ 1 4 | 0 4 2 2 | 0 2 2 0 1 | 3 * * * | 2 0 0 ox .. xo ..&#x ♦ 2 2 | 1 4 1 0 | 0 2 0 2 0 | * 6 * * | 1 1 0 .. ox xo ..&#x ♦ 2 2 | 1 4 0 1 | 0 0 2 2 0 | * * 6 * | 1 0 1 .. .. xo3oo&#x ♦ 3 1 | 3 3 0 0 | 1 0 0 3 0 | * * * 4 | 0 1 1 ---------------+-----+----------+------------+---------+------ ox ox xo ..&#x ♦ 2 4 | 1 8 2 2 | 0 4 4 4 1 | 2 2 2 0 | 3 * * ox .. xo3oo&#x ♦ 3 2 | 3 6 1 0 | 1 3 0 6 0 | 0 3 0 2 | * 2 * .. ox xo3oo&#x ♦ 3 2 | 3 6 0 1 | 1 0 3 6 0 | 0 0 3 2 | * * 2
oox oox oxo&#x → height(1,2) = sqrt(3)/2 = 0.866025 height(1,3) = 1/sqrt(2) = 0.707107 height(2,3) = 1/2 o.. o.. o.. | 1 * * ♦ 2 4 0 0 0 0 | 1 2 2 8 0 0 0 0 | 1 4 4 4 0 0 0 | 2 2 2 0 .o. .o. .o. | * 2 * ♦ 1 0 1 4 0 0 | 1 0 0 4 2 2 4 0 | 0 2 2 4 1 2 2 | 1 2 2 1 ..o ..o ..o | * * 4 | 0 1 0 2 1 1 | 0 1 1 2 2 2 1 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ---------------+-------+-------------+-----------------+---------------+-------- oo. oo. oo.&#x | 1 1 0 | 2 * * * * * ♦ 1 0 0 4 0 0 0 0 | 0 2 2 4 0 0 0 | 1 2 2 0 o.o o.o o.o&#x | 1 0 1 | * 4 * * * * | 0 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 ... ... .x. | 0 2 0 | * * 1 * * * ♦ 1 0 0 0 0 0 4 0 | 0 0 0 4 0 2 2 | 0 2 2 1 .oo .oo .oo&#x | 0 1 1 | * * * 8 * * | 0 0 0 1 1 1 1 0 | 0 1 1 1 1 1 1 | 1 1 1 1 ..x ... ... | 0 0 2 | * * * * 2 * | 0 1 0 0 2 0 0 1 | 1 2 0 0 2 1 0 | 2 1 0 1 ... ..x ... | 0 0 2 | * * * * * 2 | 0 0 1 0 0 2 0 1 | 1 0 2 0 2 0 1 | 2 0 1 1 ---------------+-------+-------------+-----------------+---------------+-------- ... ... ox.&#x | 1 2 0 | 2 0 1 0 0 0 | 1 * * * * * * * | 0 0 0 4 0 0 0 | 0 2 2 0 o.x ... ...&#x | 1 0 2 | 0 2 0 0 1 0 | * 2 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 ... o.x ...&#x | 1 0 2 | 0 2 0 0 0 1 | * * 2 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 ooo ooo ooo&#x | 1 1 1 | 1 1 0 1 0 0 | * * * 8 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 .ox ... ...&#x | 0 1 2 | 0 0 0 2 1 0 | * * * * 4 * * * | 0 1 0 0 1 1 0 | 1 1 0 1 ... .ox ...&#x | 0 1 2 | 0 0 0 2 0 1 | * * * * * 4 * * | 0 0 1 0 1 0 1 | 1 0 1 1 ... ... .xo&#x | 0 2 1 | 0 0 1 2 0 0 | * * * * * * 4 * | 0 0 0 1 0 1 1 | 0 1 1 1 ..x ..x ... | 0 0 4 | 0 0 0 0 2 2 | * * * * * * * 1 | 1 0 0 0 2 0 0 | 2 0 0 1 ---------------+-------+-------------+-----------------+---------------+-------- o.x o.x ...&#x ♦ 1 0 4 | 0 4 0 0 2 2 | 0 2 2 0 0 0 0 1 | 1 * * * * * * | 2 0 0 0 oox ... ...&#x ♦ 1 1 2 | 1 2 0 2 1 0 | 0 1 0 2 1 0 0 0 | * 4 * * * * * | 1 1 0 0 ... oox ...&#x ♦ 1 1 2 | 1 2 0 2 0 1 | 0 0 1 2 0 1 0 0 | * * 4 * * * * | 1 0 1 0 ... ... oxo&#x ♦ 1 2 1 | 2 1 1 2 0 0 | 1 0 0 2 0 0 1 0 | * * * 4 * * * | 0 1 1 0 .ox .ox ...&#x ♦ 0 1 4 | 0 0 0 4 2 2 | 0 0 0 0 2 2 0 1 | * * * * 2 * * | 1 0 0 1 .ox ... .xo&#x ♦ 0 2 2 | 0 0 1 4 1 0 | 0 0 0 0 2 0 2 0 | * * * * * 2 * | 0 1 0 1 ... .ox .xo&#x ♦ 0 2 2 | 0 0 1 4 0 1 | 0 0 0 0 0 2 2 0 | * * * * * * 2 | 0 0 1 1 ---------------+-------+-------------+-----------------+---------------+-------- oox oox ...&#x ♦ 1 1 4 | 1 4 0 4 2 2 | 0 2 2 4 2 2 0 1 | 1 2 2 0 1 0 0 | 2 * * * oox ... oxo&#x ♦ 1 2 2 | 2 2 1 4 1 0 | 1 1 0 4 2 0 2 0 | 0 2 0 2 0 1 0 | * 2 * * ... oox oxo&#x ♦ 1 2 2 | 2 2 1 4 0 1 | 1 0 1 4 0 2 2 0 | 0 0 2 2 0 0 1 | * * 2 * .ox .ox .xo&#x ♦ 0 2 4 | 0 0 1 8 2 2 | 0 0 0 0 4 4 4 1 | 0 0 0 0 2 2 2 | * * * 1
xoo3ooo oxx&#x → height(1,2) = height(1,3) = sqrt(5/12) = 0.645497 height(2,3) = 1 o..3o.. o.. | 3 * * | 2 2 2 0 0 0 | 1 4 1 4 1 2 0 | 2 2 2 2 4 1 | 1 1 2 2 .o.3.o. .o. | * 2 * | 0 3 0 1 1 0 | 0 3 3 0 0 3 1 | 1 3 0 0 3 3 | 1 0 1 3 ..o3..o ..o | * * 2 | 0 0 3 0 1 1 | 0 0 0 3 3 3 1 | 0 0 1 3 3 3 | 0 1 1 3 ---------------+-------+-------------+---------------+-------------+-------- x.. ... ... | 2 0 0 | 3 * * * * * | 1 2 0 2 0 0 0 | 2 1 2 1 2 0 | 1 1 2 1 oo.3oo. oo.&#x | 1 1 0 | * 6 * * * * | 0 2 1 0 0 1 0 | 1 2 0 0 2 1 | 1 0 1 2 o.o3o.o o.o&#x | 1 0 1 | * * 6 * * * | 0 0 0 2 1 1 0 | 0 0 1 2 2 1 | 0 1 1 2 ... ... .x. | 0 2 0 | * * * 1 * * | 0 0 3 0 0 0 1 | 0 3 0 0 0 3 | 1 0 0 3 .oo3.oo .oo&#x | 0 1 1 | * * * * 2 * | 0 0 0 0 0 3 1 | 0 0 0 0 3 3 | 0 0 1 3 ... ... ..x | 0 0 2 | * * * * * 1 | 0 0 0 0 3 0 1 | 0 0 0 3 0 3 | 0 1 0 3 ---------------+-------+-------------+---------------+-------------+-------- x..3o.. ... | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * | 2 0 2 0 0 0 | 1 1 2 0 xo. ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 6 * * * * * | 1 1 0 0 1 0 | 1 0 1 1 ... ... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 3 * * * * | 0 2 0 0 0 1 | 1 0 0 2 x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 6 * * * | 0 0 1 1 1 0 | 0 1 1 1 ... ... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 3 * * | 0 0 0 2 0 1 | 0 1 0 2 ooo3ooo ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 6 * | 0 0 0 0 2 1 | 0 0 1 2 ... ... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * 1 | 0 0 0 0 0 3 | 0 0 0 3 ---------------+-------+-------------+---------------+-------------+-------- xo.3oo. ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 | 1 3 0 0 0 0 0 | 2 * * * * * | 1 0 1 0 xo. ... ox.&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2 2 0 0 0 0 | * 3 * * * * | 1 0 0 1 x.o3o.o ...&#x ♦ 3 0 1 | 3 0 3 0 0 0 | 1 0 0 3 0 0 0 | * * 2 * * * | 0 1 1 0 x.o ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 0 2 2 0 0 | * * * 3 * * | 0 1 0 1 xoo ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 | * * * * 6 * | 0 0 1 1 ... ... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 1 | * * * * * 3 | 0 0 0 2 ---------------+-------+-------------+---------------+-------------+-------- xo.3oo. ox.&#x ♦ 3 2 0 | 3 6 0 1 0 0 | 1 6 3 0 0 0 0 | 2 3 0 0 0 0 | 1 * * * x.o3o.o o.x&#x ♦ 3 0 2 | 3 0 6 0 0 1 | 1 0 0 6 3 0 0 | 0 0 2 3 0 0 | * 1 * * xoo3ooo ...&#x ♦ 3 1 1 | 3 3 3 0 1 0 | 1 3 0 3 0 3 0 | 1 0 1 0 3 0 | * * 2 * xoo ... oxx&#x ♦ 2 2 2 | 1 4 4 1 2 1 | 0 2 2 2 2 4 1 | 0 1 0 1 2 2 | * * * 3
or o..3o.. o.. | 3 * | 2 4 0 0 | 1 8 2 2 0 | 4 4 4 1 | 2 2 2 .o.3.o. .o. & | * 4 | 0 3 1 1 | 0 3 3 3 1 | 1 3 3 3 | 1 1 3 -----------------+-----+----------+------------+---------+------ x.. ... ... | 2 0 | 3 * * * | 1 4 0 0 0 | 4 2 2 0 | 2 2 1 oo.3oo. oo.&#x & | 1 1 | * 12 * * | 0 2 1 1 0 | 1 2 2 1 | 1 1 2 ... ... .x. & | 0 2 | * * 2 * | 0 0 3 0 1 | 0 3 0 3 | 1 0 3 .oo3.oo .oo&#x | 0 2 | * * * 2 | 0 0 0 3 1 | 0 0 3 3 | 0 1 3 -----------------+-----+----------+------------+---------+------ x..3o.. ... | 3 0 | 3 0 0 0 | 1 * * * * | 4 0 0 0 | 2 2 0 xo. ... ...&#x & | 2 1 | 1 2 0 0 | * 12 * * * | 1 1 1 0 | 1 1 1 ... ... ox.&#x & | 1 2 | 0 2 1 0 | * * 6 * * | 0 2 0 1 | 1 0 2 ooo3ooo ooo&#x | 1 2 | 0 2 0 1 | * * * 6 * | 0 0 2 1 | 0 1 2 ... ... .xx&#x | 0 4 | 0 0 2 2 | * * * * 1 | 0 0 0 3 | 0 0 3 -----------------+-----+----------+------------+---------+------ xo.3oo. ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 | 4 * * * | 1 1 0 xo. ... ox.&#x & ♦ 2 2 | 1 4 1 0 | 0 2 2 0 0 | * 6 * * | 1 0 1 xoo ... ...&#x ♦ 2 2 | 1 4 0 1 | 0 2 0 2 0 | * * 6 * | 0 1 1 ... ... oxx&#x ♦ 1 4 | 0 4 2 2 | 0 0 2 2 1 | * * * 3 | 0 0 2 -----------------+-----+----------+------------+---------+------ xo.3oo. ox.&#x & ♦ 3 2 | 3 6 1 0 | 1 6 3 0 0 | 2 3 0 0 | 2 * * xoo3ooo ...&#x ♦ 3 2 | 3 6 0 1 | 1 6 0 3 0 | 2 0 3 0 | * 2 * xoo ... oxx&#x ♦ 2 4 | 1 8 2 2 | 0 4 4 4 1 | 0 2 2 2 | * * 3
ooox4oooo&#x → height(1,2) = height(1,3) = height(2,3) = 1 height(1,4) = height(2,4) = height(3,4) = 1/sqrt(2) = 0.707107 o...4o... | 1 * * * ♦ 1 1 4 0 0 0 0 | 1 4 4 4 0 0 0 0 | 4 4 4 1 0 0 0 | 4 1 1 0 .o..4.o.. | * 1 * * ♦ 1 0 0 1 4 0 0 | 1 4 0 0 4 4 0 0 | 4 4 0 0 4 1 0 | 4 1 0 1 ..o.4..o. | * * 1 * ♦ 0 1 0 1 0 4 0 | 1 0 4 0 4 0 4 0 | 4 0 4 0 4 0 1 | 4 0 1 1 ...o4...o | * * * 4 | 0 0 1 0 1 1 2 | 0 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1 -------------+---------+---------------+-----------------+---------------+-------- oo..4oo..&#x | 1 1 0 0 | 1 * * * * * * ♦ 1 4 0 0 0 0 0 0 | 4 4 0 0 0 0 0 | 4 1 0 0 o.o.4o.o.&#x | 1 0 1 0 | * 1 * * * * * ♦ 1 0 4 0 0 0 0 0 | 4 0 4 0 0 0 0 | 4 0 1 0 o..o4o..o&#x | 1 0 0 1 | * * 4 * * * * | 0 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 .oo.4.oo.&#x | 0 1 1 0 | * * * 1 * * * ♦ 1 0 0 0 4 0 0 0 | 4 0 0 0 4 0 0 | 4 0 0 1 .o.o4.o.o&#x | 0 1 0 1 | * * * * 4 * * | 0 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 ..oo4..oo&#x | 0 0 1 1 | * * * * * 4 * | 0 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 ...x .... | 0 0 0 2 | * * * * * * 4 | 0 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 -------------+---------+---------------+-----------------+---------------+-------- ooo.4ooo.&#x | 1 1 1 0 | 1 1 0 1 0 0 0 | 1 * * * * * * * | 4 0 0 0 0 0 0 | 4 0 0 0 oo.o4oo.o&#x | 1 1 0 1 | 1 0 1 0 1 0 0 | * 4 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 o.oo4o.oo&#x | 1 0 1 1 | 0 1 1 0 0 1 0 | * * 4 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 o..x ....&#x | 1 0 0 2 | 0 0 2 0 0 0 1 | * * * 4 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 .ooo4.ooo&#x | 0 1 1 1 | 0 0 0 1 1 1 0 | * * * * 4 * * * | 1 0 0 0 2 0 0 | 2 0 0 1 .o.x ....&#x | 0 1 0 2 | 0 0 0 0 2 0 1 | * * * * * 4 * * | 0 1 0 0 1 1 0 | 1 1 0 1 ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * 4 * | 0 0 1 0 1 0 1 | 1 0 1 1 ...x4...o | 0 0 0 4 | 0 0 0 0 0 0 4 | * * * * * * * 1 | 0 0 0 1 0 1 1 | 0 1 1 1 -------------+---------+---------------+-----------------+---------------+-------- oooo4oooo&#x ♦ 1 1 1 1 | 1 1 1 1 1 1 0 | 1 1 1 0 1 0 0 0 | 4 * * * * * * | 2 0 0 0 oo.x ....&#x ♦ 1 1 0 2 | 1 0 2 0 2 0 1 | 0 2 0 1 0 1 0 0 | * 4 * * * * * | 1 1 0 0 o.ox ....&#x ♦ 1 0 1 2 | 0 1 2 0 0 2 1 | 0 0 2 1 0 0 1 0 | * * 4 * * * * | 1 0 1 0 o..x4o..o&#x ♦ 1 0 0 4 | 0 0 4 0 0 0 4 | 0 0 0 4 0 0 0 1 | * * * 1 * * * | 0 1 1 0 .oox ....&#x ♦ 0 1 1 2 | 0 0 0 1 2 2 1 | 0 0 0 0 2 1 1 0 | * * * * 4 * * | 1 0 0 1 .o.x4.o.o&#x ♦ 0 1 0 4 | 0 0 0 0 4 0 4 | 0 0 0 0 0 4 0 1 | * * * * * 1 * | 0 1 0 1 ..ox4..oo&#x ♦ 0 0 1 4 | 0 0 0 0 0 4 4 | 0 0 0 0 0 0 4 1 | * * * * * * 1 | 0 0 1 1 -------------+---------+---------------+-----------------+---------------+-------- ooox ....&#x ♦ 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 0 | 2 1 1 0 1 0 0 | 4 * * * oo.x4oo.o&#x ♦ 1 1 0 4 | 1 0 4 0 4 0 4 | 0 4 0 4 0 4 0 1 | 0 4 0 1 0 1 0 | * 1 * * o.ox4o.oo&#x ♦ 1 0 1 4 | 0 1 4 0 0 4 4 | 0 0 4 4 0 0 4 1 | 0 0 4 1 0 0 1 | * * 1 * .oox4.ooo&#x ♦ 0 1 1 4 | 0 0 0 1 4 4 4 | 0 0 0 0 4 4 4 1 | 0 0 0 0 4 1 1 | * * * 1
ooox ooox&#x → height(1,2) = height(1,3) = height(2,3) = 1 height(1,4) = height(2,4) = height(3,4) = 1/sqrt(2) = 0.707107 o... o... | 1 * * * ♦ 1 1 4 0 0 0 0 0 | 1 4 4 2 2 0 0 0 0 0 0 | 4 2 2 2 2 1 0 0 0 0 | 2 2 1 1 0 .o.. .o.. | * 1 * * ♦ 1 0 0 1 4 0 0 0 | 1 4 0 0 0 4 2 2 0 0 0 | 4 2 2 0 0 0 2 2 1 0 | 2 2 1 0 1 ..o. ..o. | * * 1 * ♦ 0 1 0 1 0 4 0 0 | 1 0 4 0 0 4 0 0 2 2 0 | 4 0 0 2 2 0 2 2 0 1 | 2 2 0 1 1 ...o ...o | * * * 4 | 0 0 1 0 1 1 1 1 | 0 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 -------------+---------+-----------------+-----------------------+---------------------+---------- oo.. oo..&#x | 1 1 0 0 | 1 * * * * * * * ♦ 1 4 0 0 0 0 0 0 0 0 0 | 4 2 2 0 0 0 0 0 0 0 | 2 2 1 0 0 o.o. o.o.&#x | 1 0 1 0 | * 1 * * * * * * ♦ 1 0 4 0 0 0 0 0 0 0 0 | 4 0 0 2 2 0 0 0 0 0 | 2 2 0 1 0 o..o o..o&#x | 1 0 0 1 | * * 4 * * * * * | 0 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0 .oo. .oo.&#x | 0 1 1 0 | * * * 1 * * * * ♦ 1 0 0 0 0 4 0 0 0 0 0 | 4 0 0 0 0 0 2 2 0 0 | 2 2 0 0 1 .o.o .o.o&#x | 0 1 0 1 | * * * * 4 * * * | 0 1 0 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 ..oo ..oo&#x | 0 0 1 1 | * * * * * 4 * * | 0 0 1 0 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 ...x .... | 0 0 0 2 | * * * * * * 2 * | 0 0 0 1 0 0 1 0 1 0 1 | 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1 .... ...x | 0 0 0 2 | * * * * * * * 2 | 0 0 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 -------------+---------+-----------------+-----------------------+---------------------+---------- ooo. ooo.&#x | 1 1 1 0 | 1 1 0 1 0 0 0 0 | 1 * * * * * * * * * * | 4 0 0 0 0 0 0 0 0 0 | 2 2 0 0 0 oo.o oo.o&#x | 1 1 0 1 | 1 0 1 0 1 0 0 0 | * 4 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 o.oo o.oo&#x | 1 0 1 1 | 0 1 1 0 0 1 0 0 | * * 4 * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 o..x ....&#x | 1 0 0 2 | 0 0 2 0 0 0 1 0 | * * * 2 * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0 .... o..x&#x | 1 0 0 2 | 0 0 2 0 0 0 0 1 | * * * * 2 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 .ooo .ooo&#x | 0 1 1 1 | 0 0 0 1 1 1 0 0 | * * * * * 4 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 .o.x ....&#x | 0 1 0 2 | 0 0 0 0 2 0 1 0 | * * * * * * 2 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 .... .o.x&#x | 0 1 0 2 | 0 0 0 0 2 0 0 1 | * * * * * * * 2 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 2 1 0 | * * * * * * * * 2 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * * * * * 2 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 ...x ...x | 0 0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * * * 1 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 -------------+---------+-----------------+-----------------------+---------------------+---------- oooo oooo&#x ♦ 1 1 1 1 | 1 1 1 1 1 1 0 0 | 1 1 1 0 0 1 0 0 0 0 0 | 4 * * * * * * * * * | 1 1 0 0 0 oo.x ....&#x ♦ 1 1 0 2 | 1 0 2 0 2 0 1 0 | 0 2 0 1 0 0 1 0 0 0 0 | * 2 * * * * * * * * | 1 0 1 0 0 .... oo.x&#x ♦ 1 1 0 2 | 1 0 2 0 2 0 0 1 | 0 2 0 0 1 0 0 1 0 0 0 | * * 2 * * * * * * * | 0 1 1 0 0 o.ox ....&#x ♦ 1 0 1 2 | 0 1 2 0 0 2 1 0 | 0 0 2 1 0 0 0 0 1 0 0 | * * * 2 * * * * * * | 1 0 0 1 0 .... o.ox&#x ♦ 1 0 1 2 | 0 1 2 0 0 2 0 1 | 0 0 2 0 1 0 0 0 0 1 0 | * * * * 2 * * * * * | 0 1 0 1 0 o..x o..x&#x ♦ 1 0 0 4 | 0 0 4 0 0 0 2 2 | 0 0 0 2 2 0 0 0 0 0 1 | * * * * * 1 * * * * | 0 0 1 1 0 .oox ....&#x ♦ 0 1 1 2 | 0 0 0 1 2 2 1 0 | 0 0 0 0 0 2 1 0 1 0 0 | * * * * * * 2 * * * | 1 0 0 0 1 .... .oox&#x ♦ 0 1 1 2 | 0 0 0 1 2 2 0 1 | 0 0 0 0 0 2 0 1 0 1 0 | * * * * * * * 2 * * | 0 1 0 0 1 .o.x .o.x&#x ♦ 0 1 0 4 | 0 0 0 0 4 0 2 2 | 0 0 0 0 0 0 2 2 0 0 1 | * * * * * * * * 1 * | 0 0 1 0 1 ..ox ..ox&#x ♦ 0 0 1 4 | 0 0 0 0 0 4 2 2 | 0 0 0 0 0 0 0 0 2 2 1 | * * * * * * * * * 1 | 0 0 0 1 1 -------------+---------+-----------------+-----------------------+---------------------+---------- ooox ....&#x ♦ 1 1 1 2 | 1 1 2 1 2 2 1 0 | 1 2 2 1 0 2 1 0 1 0 0 | 2 1 0 1 0 0 1 0 0 0 | 2 * * * * .... ooox&#x ♦ 1 1 1 2 | 1 1 2 1 2 2 0 1 | 1 2 2 0 1 2 0 1 0 1 0 | 2 0 1 0 1 0 0 1 0 0 | * 2 * * * oo.x oo.x&#x ♦ 1 1 0 4 | 1 0 4 0 4 0 2 2 | 0 4 0 2 2 0 2 2 0 0 1 | 0 2 2 0 0 1 0 0 1 0 | * * 1 * * o.ox o.ox&#x ♦ 1 0 1 4 | 0 1 4 0 0 4 2 2 | 0 0 4 2 2 0 0 0 2 2 1 | 0 0 0 2 2 1 0 0 0 1 | * * * 1 * .oox .oox&#x ♦ 0 1 1 4 | 0 0 0 1 4 4 2 2 | 0 0 0 0 0 4 2 2 2 2 1 | 0 0 0 0 0 0 2 2 1 1 | * * * * 1
ooox oxxo&#x → height(1,2) = height(1,3) = height(1,4) = sqrt(3)/2 = 0.866025 height(2,3) = 1 height(2,4) = height(3,4) = 1/sqrt(2) = 0.707107 o... o... | 1 * * * ♦ 2 2 2 0 0 0 0 0 0 | 1 2 4 1 4 1 0 0 0 0 0 0 | 1 4 2 2 2 2 0 0 0 0 | 2 2 1 1 0 .o.. .o.. | * 2 * * | 1 0 0 1 1 2 0 0 0 | 1 1 2 0 0 0 1 2 1 2 0 0 | 1 2 1 2 0 0 1 2 1 0 | 1 2 1 0 1 ..o. ..o. | * * 2 * | 0 1 0 0 1 0 1 2 0 | 0 1 0 1 2 0 1 2 0 0 1 2 | 1 2 0 0 1 2 1 2 0 1 | 1 2 0 1 1 ...o ...o | * * * 2 ♦ 0 0 1 0 0 2 0 2 1 | 0 0 2 0 2 1 0 2 2 1 2 1 | 0 2 2 1 2 1 2 1 1 1 | 2 1 1 1 1 -------------+---------+-------------------+-------------------------+---------------------+---------- oo.. oo..&#x | 1 1 0 0 | 2 * * * * * * * * | 1 1 2 0 0 0 0 0 0 0 0 0 | 1 2 1 2 0 0 0 0 0 0 | 1 2 1 0 0 o.o. o.o.&#x | 1 0 1 0 | * 2 * * * * * * * | 0 1 0 1 2 0 0 0 0 0 0 0 | 1 2 0 0 1 2 0 0 0 0 | 1 2 0 1 0 o..o o..o&#x | 1 0 0 1 | * * 2 * * * * * * ♦ 0 0 2 0 2 1 0 0 0 0 0 0 | 0 2 2 1 2 1 0 0 0 0 | 2 1 1 1 0 .... .x.. | 0 2 0 0 | * * * 1 * * * * * | 1 0 0 0 0 0 1 0 0 2 0 0 | 1 0 0 2 0 0 0 2 1 0 | 0 2 1 0 1 .oo. .oo.&#x | 0 1 1 0 | * * * * 2 * * * * | 0 1 0 0 0 0 1 2 0 0 0 0 | 1 2 0 0 0 0 1 2 0 0 | 1 2 0 0 1 .o.o .o.o&#x | 0 1 0 1 | * * * * * 4 * * * | 0 0 1 0 0 0 0 1 1 1 0 0 | 0 1 1 1 0 0 1 1 1 0 | 1 1 1 0 1 .... ..x. | 0 0 2 0 | * * * * * * 1 * * | 0 0 0 1 0 0 1 0 0 0 0 2 | 1 0 0 0 0 2 0 2 0 1 | 0 2 0 1 1 ..oo ..oo&#x | 0 0 1 1 | * * * * * * * 4 * | 0 0 0 0 1 0 0 1 0 0 1 1 | 0 1 0 0 1 1 1 1 0 1 | 1 1 0 1 1 ...x .... | 0 0 0 2 | * * * * * * * * 1 ♦ 0 0 0 0 0 1 0 0 2 0 2 0 | 0 0 2 0 2 0 2 0 1 1 | 2 0 1 1 1 -------------+---------+-------------------+-------------------------+---------------------+---------- .... ox..&#x | 1 2 0 0 | 2 0 0 1 0 0 0 0 0 | 1 * * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 0 2 1 0 0 ooo. ooo.&#x | 1 1 1 0 | 1 1 0 0 1 0 0 0 0 | * 2 * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 | 1 2 0 0 0 oo.o oo.o&#x | 1 1 0 1 | 1 0 1 0 0 1 0 0 0 | * * 4 * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 .... o.x.&#x | 1 0 2 0 | 0 2 0 0 0 0 1 0 0 | * * * 1 * * * * * * * * | 1 0 0 0 0 2 0 0 0 0 | 0 2 0 1 0 o.oo o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 0 1 0 | * * * * 4 * * * * * * * | 0 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0 o..x ....&#x | 1 0 0 2 | 0 0 2 0 0 0 0 0 1 | * * * * * 1 * * * * * * | 0 0 2 0 2 0 0 0 0 0 | 2 0 1 1 0 .... .xx.&#x | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 | * * * * * * 1 * * * * * | 1 0 0 0 0 0 0 2 0 0 | 0 2 0 0 1 .ooo .ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 | * * * * * * * 4 * * * * | 0 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 .o.x ....&#x | 0 1 0 2 | 0 0 0 0 0 2 0 0 1 | * * * * * * * * 2 * * * | 0 0 1 0 0 0 1 0 1 0 | 1 0 1 0 1 .... .x.o&#x | 0 2 0 1 | 0 0 0 1 0 2 0 0 0 | * * * * * * * * * 2 * * | 0 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1 ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * 2 * | 0 0 0 0 1 0 1 0 0 1 | 1 0 0 1 1 .... ..xo&#x | 0 0 2 1 | 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * 2 | 0 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1 -------------+---------+-------------------+-------------------------+---------------------+---------- .... oxx.&#x ♦ 1 2 2 0 | 2 2 0 1 2 0 1 0 0 | 1 2 0 1 0 0 1 0 0 0 0 0 | 1 * * * * * * * * * | 0 2 0 0 0 oooo oooo&#x ♦ 1 1 1 1 | 1 1 1 0 1 1 0 1 0 | 0 1 1 0 1 0 0 1 0 0 0 0 | * 4 * * * * * * * * | 1 1 0 0 0 oo.x ....&#x ♦ 1 1 0 2 | 1 0 2 0 0 2 0 0 1 | 0 0 2 0 0 1 0 0 1 0 0 0 | * * 2 * * * * * * * | 1 0 1 0 0 .... ox.o&#x ♦ 1 2 0 1 | 2 0 1 1 0 2 0 0 0 | 1 0 2 0 0 0 0 0 0 1 0 0 | * * * 2 * * * * * * | 0 1 1 0 0 o.ox ....&#x ♦ 1 0 1 2 | 0 1 2 0 0 0 0 2 1 | 0 0 0 0 2 1 0 0 0 0 1 0 | * * * * 2 * * * * * | 1 0 0 1 0 .... o.xo&#x ♦ 1 0 2 1 | 0 2 1 0 0 0 1 2 0 | 0 0 0 1 2 0 0 0 0 0 0 1 | * * * * * 2 * * * * | 0 1 0 1 0 .oox ....&#x ♦ 0 1 1 2 | 0 0 0 0 1 2 0 2 1 | 0 0 0 0 0 0 0 2 1 0 1 0 | * * * * * * 2 * * * | 1 0 0 0 1 .... .xxo&#x ♦ 0 2 2 1 | 0 0 0 1 2 2 1 2 0 | 0 0 0 0 0 0 1 2 0 1 0 1 | * * * * * * * 2 * * | 0 1 0 0 1 .o.x .x.o&#x ♦ 0 2 0 2 | 0 0 0 1 0 4 0 0 1 | 0 0 0 0 0 0 0 0 2 2 0 0 | * * * * * * * * 1 * | 0 0 1 0 1 ..ox ..xo&#x ♦ 0 0 2 2 | 0 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * 1 | 0 0 0 1 1 -------------+---------+-------------------+-------------------------+---------------------+---------- ooox ....&#x ♦ 1 1 1 2 | 1 1 2 0 1 2 0 2 1 | 0 1 2 0 2 1 0 2 1 0 1 0 | 0 2 1 0 1 0 1 0 0 0 | 2 * * * * .... oxxo&#x ♦ 1 2 2 1 | 2 2 1 1 2 2 1 2 0 | 1 2 2 1 2 0 1 2 0 1 0 1 | 1 2 0 1 0 1 0 1 0 0 | * 2 * * * oo.x ox.o&#x ♦ 1 2 0 2 | 2 0 2 1 0 4 0 0 1 | 1 0 4 0 0 1 0 0 2 2 0 0 | 0 0 2 2 0 0 0 0 1 0 | * * 1 * * o.ox o.xo&#x ♦ 1 0 2 2 | 0 2 2 0 0 0 1 4 1 | 0 0 0 1 4 1 0 0 0 0 2 2 | 0 0 0 0 2 2 0 0 0 1 | * * * 1 * .oox .xxo&#x ♦ 0 2 2 2 | 0 0 0 1 2 4 1 4 1 | 0 0 0 0 0 0 1 4 2 2 2 2 | 0 0 0 0 0 0 2 2 1 1 | * * * * 1
oooxx&#x → height(1,2) = height(1,3) = height(2,3) = height(4,5) = 1 height(1,4) = height(1,5) = height(2,4) = height(2,5) = height(3,4) = height(3,5) = sqrt(3)/2 = 0.866025 o.... | 1 * * * * ♦ 1 1 2 2 0 0 0 0 0 0 0 0 | 1 2 2 2 2 1 2 1 0 0 0 0 0 0 0 0 0 | 2 2 1 2 1 1 2 1 1 0 0 0 0 0 | 1 2 1 1 1 0 .o... | * 1 * * * ♦ 1 0 0 0 1 2 2 0 0 0 0 0 | 1 2 2 0 0 0 0 0 2 2 1 2 1 0 0 0 0 | 2 2 1 2 1 0 0 0 0 1 2 1 1 0 | 1 2 1 1 0 1 ..o.. | * * 1 * * ♦ 0 1 0 0 1 0 0 2 2 0 0 0 | 1 0 0 2 2 0 0 0 2 2 0 0 0 1 2 1 0 | 2 2 0 0 0 1 2 1 0 1 2 1 0 1 | 1 2 1 0 1 1 ...o. | * * * 2 * | 0 0 1 0 0 1 0 1 0 1 1 0 | 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 | 1 0 1 1 0 1 1 0 1 1 1 0 1 1 | 1 1 0 1 1 1 ....o | * * * * 2 | 0 0 0 1 0 0 1 0 1 0 1 1 | 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 | 0 1 0 1 1 0 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1 ---------+-----------+-------------------------+-----------------------------------+-----------------------------+------------ oo...&#x | 1 1 0 0 0 | 1 * * * * * * * * * * * ♦ 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 2 1 2 1 0 0 0 0 0 0 0 0 0 | 1 2 1 1 0 0 o.o..&#x | 1 0 1 0 0 | * 1 * * * * * * * * * * ♦ 1 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 | 2 2 0 0 0 1 2 1 0 0 0 0 0 0 | 1 2 1 0 1 0 o..o.&#x | 1 0 0 1 0 | * * 2 * * * * * * * * * | 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 1 1 0 1 0 0 0 0 0 | 1 1 0 1 1 0 o...o&#x | 1 0 0 0 1 | * * * 2 * * * * * * * * | 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 | 0 1 0 1 1 0 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0 .oo..&#x | 0 1 1 0 0 | * * * * 1 * * * * * * * ♦ 1 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 | 2 2 0 0 0 0 0 0 0 1 2 1 0 0 | 1 2 1 0 0 1 .o.o.&#x | 0 1 0 1 0 | * * * * * 2 * * * * * * | 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 | 1 0 1 1 0 0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1 .o..o&#x | 0 1 0 0 1 | * * * * * * 2 * * * * * | 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 | 0 1 0 1 1 0 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1 ..oo.&#x | 0 0 1 1 0 | * * * * * * * 2 * * * * | 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 | 1 0 0 0 0 1 1 0 0 1 1 0 0 1 | 1 1 0 0 1 1 ..o.o&#x | 0 0 1 0 1 | * * * * * * * * 2 * * * | 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 | 0 1 0 0 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1 ...x. | 0 0 0 2 0 | * * * * * * * * * 1 * * | 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 | 0 0 1 0 0 1 0 0 1 1 0 0 1 1 | 1 0 0 1 1 1 ...oo&#x | 0 0 0 1 1 | * * * * * * * * * * 2 * | 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 | 0 0 0 1 0 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1 ....x | 0 0 0 0 2 | * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 | 0 0 0 0 1 0 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1 ---------+-----------+-------------------------+-----------------------------------+-----------------------------+------------ ooo..&#x | 1 1 1 0 0 | 1 1 0 0 1 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 oo.o.&#x | 1 1 0 1 0 | 1 0 1 0 0 1 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * * | 1 0 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 oo..o&#x | 1 1 0 0 1 | 1 0 0 1 0 0 1 0 0 0 0 0 | * * 2 * * * * * * * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 o.oo.&#x | 1 0 1 1 0 | 0 1 1 0 0 0 0 1 0 0 0 0 | * * * 2 * * * * * * * * * * * * * | 1 0 0 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0 o.o.o&#x | 1 0 1 0 1 | 0 1 0 1 0 0 0 0 1 0 0 0 | * * * * 2 * * * * * * * * * * * * | 0 1 0 0 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0 o..x.&#x | 1 0 0 2 0 | 0 0 2 0 0 0 0 0 0 1 0 0 | * * * * * 1 * * * * * * * * * * * | 0 0 1 0 0 1 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0 o..oo&#x | 1 0 0 1 1 | 0 0 1 1 0 0 0 0 0 0 1 0 | * * * * * * 2 * * * * * * * * * * | 0 0 0 1 0 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0 o...x&#x | 1 0 0 0 2 | 0 0 0 2 0 0 0 0 0 0 0 1 | * * * * * * * 1 * * * * * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0 .ooo.&#x | 0 1 1 1 0 | 0 0 0 0 1 1 0 1 0 0 0 0 | * * * * * * * * 2 * * * * * * * * | 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1 .oo.o&#x | 0 1 1 0 1 | 0 0 0 0 1 0 1 0 1 0 0 0 | * * * * * * * * * 2 * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1 .o.x.&#x | 0 1 0 2 0 | 0 0 0 0 0 2 0 0 0 1 0 0 | * * * * * * * * * * 1 * * * * * * | 0 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1 .o.oo&#x | 0 1 0 1 1 | 0 0 0 0 0 1 1 0 0 0 1 0 | * * * * * * * * * * * 2 * * * * * | 0 0 0 1 0 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1 .o..x&#x | 0 1 0 0 2 | 0 0 0 0 0 0 2 0 0 0 0 1 | * * * * * * * * * * * * 1 * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1 ..ox.&#x | 0 0 1 2 0 | 0 0 0 0 0 0 0 2 0 1 0 0 | * * * * * * * * * * * * * 1 * * * | 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1 ..ooo&#x | 0 0 1 1 1 | 0 0 0 0 0 0 0 1 1 0 1 0 | * * * * * * * * * * * * * * 2 * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1 ..o.x&#x | 0 0 1 0 2 | 0 0 0 0 0 0 0 0 2 0 0 1 | * * * * * * * * * * * * * * * 1 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1 ...xx&#x | 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 1 2 1 | * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1 ---------+-----------+-------------------------+-----------------------------------+-----------------------------+------------ oooo.&#x ♦ 1 1 1 1 0 | 1 1 1 0 1 1 0 1 0 0 0 0 | 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * | 1 1 0 0 0 0 ooo.o&#x ♦ 1 1 1 0 1 | 1 1 0 1 1 0 1 0 1 0 0 0 | 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * | 0 1 1 0 0 0 oo.x.&#x ♦ 1 1 0 2 0 | 1 0 2 0 0 2 0 0 0 1 0 0 | 0 2 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 | * * 1 * * * * * * * * * * * | 1 0 0 1 0 0 oo.oo&#x ♦ 1 1 0 1 1 | 1 0 1 1 0 1 1 0 0 0 1 0 | 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 | * * * 2 * * * * * * * * * * | 0 1 0 1 0 0 oo..x&#x ♦ 1 1 0 0 2 | 1 0 0 2 0 0 2 0 0 0 0 1 | 0 0 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0 | * * * * 1 * * * * * * * * * | 0 0 1 1 0 0 o.ox.&#x ♦ 1 0 1 2 0 | 0 1 2 0 0 0 0 2 0 1 0 0 | 0 0 0 2 0 1 0 0 0 0 0 0 0 1 0 0 0 | * * * * * 1 * * * * * * * * | 1 0 0 0 1 0 o.ooo&#x ♦ 1 0 1 1 1 | 0 1 1 1 0 0 0 1 1 0 1 0 | 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 | * * * * * * 2 * * * * * * * | 0 1 0 0 1 0 o.o.x&#x ♦ 1 0 1 0 2 | 0 1 0 2 0 0 0 0 2 0 0 1 | 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 1 0 | * * * * * * * 1 * * * * * * | 0 0 1 0 1 0 o..xx&#x ♦ 1 0 0 2 2 | 0 0 2 2 0 0 0 0 0 1 2 1 | 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 | * * * * * * * * 1 * * * * * | 0 0 0 1 1 0 .oox.&#x ♦ 0 1 1 2 0 | 0 0 0 0 1 2 0 2 0 1 0 0 | 0 0 0 0 0 0 0 0 2 0 1 0 0 1 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1 .oooo&#x ♦ 0 1 1 1 1 | 0 0 0 0 1 1 1 1 1 0 1 0 | 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 | * * * * * * * * * * 2 * * * | 0 1 0 0 0 1 .oo.x&#x ♦ 0 1 1 0 2 | 0 0 0 0 1 0 2 0 2 0 0 1 | 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 1 0 | * * * * * * * * * * * 1 * * | 0 0 1 0 0 1 .o.xx&#x ♦ 0 1 0 2 2 | 0 0 0 0 0 2 2 0 0 1 2 1 | 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 1 | * * * * * * * * * * * * 1 * | 0 0 0 1 0 1 ..oxx&#x ♦ 0 0 1 2 2 | 0 0 0 0 0 0 0 2 2 1 2 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 1 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 1 ---------+-----------+-------------------------+-----------------------------------+-----------------------------+------------ ooox.&#x ♦ 1 1 1 2 0 | 1 1 2 0 1 2 0 2 0 1 0 0 | 1 2 0 2 0 1 0 0 2 0 1 0 0 1 0 0 0 | 2 0 1 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * * ooooo&#x ♦ 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 0 1 0 | 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 | 1 1 0 1 0 0 1 0 0 0 1 0 0 0 | * 2 * * * * ooo.x&#x ♦ 1 1 1 0 2 | 1 1 0 2 1 0 2 0 2 0 0 1 | 1 0 2 0 2 0 0 1 0 2 0 0 1 0 0 1 0 | 0 2 0 0 1 0 0 1 0 0 0 1 0 0 | * * 1 * * * oo.xx&#x ♦ 1 1 0 2 2 | 1 0 2 2 0 2 2 0 0 1 2 1 | 0 2 2 0 0 1 2 1 0 0 1 2 1 0 0 0 1 | 0 0 1 2 1 0 0 0 1 0 0 0 1 0 | * * * 1 * * o.oxx&#x ♦ 1 0 1 2 2 | 0 1 2 2 0 0 0 2 2 1 2 1 | 0 0 0 2 2 1 2 1 0 0 0 0 0 1 2 1 1 | 0 0 0 0 0 1 2 1 1 0 0 0 0 1 | * * * * 1 * .ooxx&#x ♦ 0 1 1 2 2 | 0 0 0 0 1 2 2 2 2 1 2 1 | 0 0 0 0 0 0 0 0 2 2 1 2 1 1 2 1 1 | 0 0 0 0 0 0 0 0 0 1 2 1 1 1 | * * * * * 1
pt || squasc → height = 1/sqrt(2) = 0.707107
o...4o... | 1 * * * ♦ 1 1 4 0 0 0 0 | 1 4 4 4 0 0 0 0 | 4 4 4 1 0 0 0 | 4 1 1 0
.o..4.o.. | * 1 * * ♦ 1 0 0 1 4 0 0 | 1 4 0 0 4 4 0 0 | 4 4 0 0 4 1 0 | 4 1 0 1
..o.4..o. | * * 1 * ♦ 0 1 0 1 0 4 0 | 1 0 4 0 4 0 4 0 | 4 0 4 0 4 0 1 | 4 0 1 1
...o4...o | * * * 4 | 0 0 1 0 1 1 2 | 0 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1
-------------+---------+---------------+-----------------+---------------+--------
oo..4oo..&#x | 1 1 0 0 | 1 * * * * * * ♦ 1 4 0 0 0 0 0 0 | 4 4 0 0 0 0 0 | 4 1 0 0
o.o.4o.o.&#x | 1 0 1 0 | * 1 * * * * * ♦ 1 0 4 0 0 0 0 0 | 4 0 4 0 0 0 0 | 4 0 1 0
o..o4o..o&#x | 1 0 0 1 | * * 4 * * * * | 0 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0
.oo.4.oo.&#x | 0 1 1 0 | * * * 1 * * * ♦ 1 0 0 0 4 0 0 0 | 4 0 0 0 4 0 0 | 4 0 0 1
.o.o4.o.o&#x | 0 1 0 1 | * * * * 4 * * | 0 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1
..oo4..oo&#x | 0 0 1 1 | * * * * * 4 * | 0 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1
...x .... | 0 0 0 2 | * * * * * * 4 | 0 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
-------------+---------+---------------+-----------------+---------------+--------
ooo.4ooo.&#x | 1 1 1 0 | 1 1 0 1 0 0 0 | 1 * * * * * * * | 4 0 0 0 0 0 0 | 4 0 0 0
oo.o4oo.o&#x | 1 1 0 1 | 1 0 1 0 1 0 0 | * 4 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
o.oo4o.oo&#x | 1 0 1 1 | 0 1 1 0 0 1 0 | * * 4 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0
o..x ....&#x | 1 0 0 2 | 0 0 2 0 0 0 1 | * * * 4 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0
.ooo4.ooo&#x | 0 1 1 1 | 0 0 0 1 1 1 0 | * * * * 4 * * * | 1 0 0 0 2 0 0 | 2 0 0 1
.o.x ....&#x | 0 1 0 2 | 0 0 0 0 2 0 1 | * * * * * 4 * * | 0 1 0 0 1 1 0 | 1 1 0 1
..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * 4 * | 0 0 1 0 1 0 1 | 1 0 1 1
...x4...o | 0 0 0 4 | 0 0 0 0 0 0 4 | * * * * * * * 1 | 0 0 0 1 0 1 1 | 0 1 1 1
-------------+---------+---------------+-----------------+---------------+--------
oooo4oooo&#x ♦ 1 1 1 1 | 1 1 1 1 1 1 0 | 1 1 1 0 1 0 0 0 | 4 * * * * * * | 2 0 0 0
oo.x ....&#x ♦ 1 1 0 2 | 1 0 2 0 2 0 1 | 0 2 0 1 0 1 0 0 | * 4 * * * * * | 1 1 0 0
o.ox ....&#x ♦ 1 0 1 2 | 0 1 2 0 0 2 1 | 0 0 2 1 0 0 1 0 | * * 4 * * * * | 1 0 1 0
o..x4o..o&#x ♦ 1 0 0 4 | 0 0 4 0 0 0 4 | 0 0 0 4 0 0 0 1 | * * * 1 * * * | 0 1 1 0
.oox ....&#x ♦ 0 1 1 2 | 0 0 0 1 2 2 1 | 0 0 0 0 2 1 1 0 | * * * * 4 * * | 1 0 0 1
.o.x4.o.o&#x ♦ 0 1 0 4 | 0 0 0 0 4 0 4 | 0 0 0 0 0 4 0 1 | * * * * * 1 * | 0 1 0 1
..ox4..oo&#x ♦ 0 0 1 4 | 0 0 0 0 0 4 4 | 0 0 0 0 0 0 4 1 | * * * * * * 1 | 0 0 1 1
-------------+---------+---------------+-----------------+---------------+--------
ooox ....&#x ♦ 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 0 | 2 1 1 0 1 0 0 | 4 * * *
oo.x4oo.o&#x ♦ 1 1 0 4 | 1 0 4 0 4 0 4 | 0 4 0 4 0 4 0 1 | 0 4 0 1 0 1 0 | * 1 * *
o.ox4o.oo&#x ♦ 1 0 1 4 | 0 1 4 0 0 4 4 | 0 0 4 4 0 0 4 1 | 0 0 4 1 0 0 1 | * * 1 *
.oox4.ooo&#x ♦ 0 1 1 4 | 0 0 0 1 4 4 4 | 0 0 0 0 4 4 4 1 | 0 0 0 0 4 1 1 | * * * 1
pyramid product of line with squippy → height = 1/2 o...4o... & | 2 * * ♦ 1 1 4 0 0 | 1 4 4 4 0 0 | 4 4 4 1 0 | 4 1 1 ..o.4..o. | * 1 * ♦ 0 2 0 4 0 | 1 0 8 0 4 0 | 4 0 8 0 1 | 4 0 2 ...o4...o | * * 4 | 0 0 2 1 2 | 0 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2 ---------------+-------+-----------+-------------+-----------+------ oo..4oo..&#x | 2 0 0 | 1 * * * * ♦ 1 4 0 0 0 0 | 4 4 0 0 0 | 4 1 0 o.o.4o.o.&#x & | 1 1 0 | * 2 * * * ♦ 1 0 4 0 0 0 | 4 0 4 0 0 | 4 0 1 o..o4o..o&#x & | 1 0 1 | * * 8 * * | 0 1 1 2 0 0 | 1 2 2 1 0 | 1 2 1 ..oo4..oo&#x | 0 1 1 | * * * 4 * | 0 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2 ...x .... | 0 0 2 | * * * * 4 | 0 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2 ---------------+-------+-----------+-------------+-----------+------ ooo.4ooo.&#x | 2 1 0 | 1 2 0 0 0 | 1 * * * * * | 4 0 0 0 0 | 4 0 0 oo.o4oo.o&#x | 2 0 1 | 1 0 2 0 0 | * 4 * * * * | 1 2 0 0 0 | 2 1 0 o.oo4o.oo&#x & | 1 1 1 | 0 1 1 1 0 | * * 8 * * * | 1 0 2 0 0 | 2 0 1 o..x ....&#x & | 1 0 2 | 0 0 2 0 1 | * * * 8 * * | 0 1 1 1 0 | 1 1 1 ..ox ....&#x | 0 1 2 | 0 0 0 2 1 | * * * * 4 * | 0 0 2 0 1 | 1 0 2 ...x4...o | 0 0 4 | 0 0 0 0 4 | * * * * * 1 | 0 0 0 2 1 | 0 1 2 ---------------+-------+-----------+-------------+-----------+------ oooo4oooo&#x ♦ 2 1 1 | 1 2 2 1 0 | 1 1 2 0 0 0 | 4 * * * * | 2 0 0 oo.x ....&#x ♦ 2 0 2 | 1 0 4 0 1 | 0 2 0 2 0 0 | * 4 * * * | 1 1 0 o.ox ....&#x & ♦ 1 1 2 | 0 1 2 2 1 | 0 0 2 1 1 0 | * * 8 * * | 1 0 1 o..x4o..o&#x & ♦ 1 0 4 | 0 0 4 0 4 | 0 0 0 4 0 1 | * * * 2 * | 0 1 1 ..ox4..oo&#x ♦ 0 1 4 | 0 0 0 4 4 | 0 0 0 0 4 1 | * * * * 1 | 0 0 2 ---------------+-------+-----------+-------------+-----------+------ ooox ....&#x ♦ 2 1 2 | 1 2 4 2 1 | 1 2 4 2 1 0 | 2 1 2 0 0 | 4 * * oo.x4oo.o&#x ♦ 2 0 4 | 1 0 8 0 4 | 0 4 0 8 0 1 | 0 4 0 2 0 | * 1 * o.ox4o.oo&#x & ♦ 1 1 4 | 0 1 4 4 4 | 0 0 4 4 4 1 | 0 0 4 1 1 | * * 2
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