Acronym | cubasc |
Name |
(degenerate) cubical scalene, line atop fully orthogonal cube |
|,>,O device | line prism prism pyramid pyramid = |||>> |
Circumradius | ∞ i.e. flat in euclidean space |
Face vector | 10, 29, 38, 25, 8 |
Confer |
|
The hull of this degenerate shape is cute. In fact, the latter provides 2 different decompositions, either into 6 squascs (kind in the sense of a 4D orange) or equatorially into 2 cubpies. The blend of these 2 decompositions, blending out right those cute cells each, then would result in cubasc again.
In fact, it is only this degeneracy, which lets become here the hull of a scalene to be a mere bipyramid.
Incidence matrix according to Dynkin symbol
xo oo3oo4ox&#x → height = 0 (pyramid product of line with cube) o. o.3o.4o. | 2 * ♦ 1 8 0 | 8 12 0 | 12 6 0 | 6 1 .o .o3.o4.o | * 8 | 0 2 3 | 1 6 3 | 3 6 1 | 3 2 ---------------+-----+---------+--------+---------+---- x. .. .. .. | 2 0 | 1 * * ♦ 8 0 0 | 12 0 0 | 6 0 oo oo3oo4oo&#x | 1 1 | * 16 * | 1 3 0 | 3 3 0 | 3 1 .. .. .. .x | 0 2 | * * 12 | 0 2 2 | 1 4 1 | 2 2 ---------------+-----+---------+--------+---------+---- xo .. .. ..&#x | 2 1 | 1 2 0 | 8 * * | 3 0 0 | 3 0 .. .. .. ox&#x | 1 2 | 0 2 1 | * 24 * | 1 2 0 | 2 1 .. .. .o4.x | 0 4 | 0 0 4 | * * 6 | 0 2 1 | 1 2 ---------------+-----+---------+--------+---------+---- xo .. .. ox&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 12 * * | 2 0 .. .. oo4ox&#x ♦ 1 4 | 0 4 4 | 0 4 1 | * 12 * | 1 1 .. .o3.o4.x ♦ 0 8 | 0 0 12 | 0 0 6 | * * 1 | 0 2 ---------------+-----+---------+--------+---------+---- xo .. oo4ox&#x ♦ 2 4 | 1 8 4 | 4 8 1 | 4 2 0 | 6 * .. oo3oo4ox&#x ♦ 1 8 | 0 8 12 | 0 12 6 | 0 6 1 | * 2
ooo3ooo4oox&#x → height(1,2) = 1 height(1,3) = height(2,3) = 1/2 o..3o..4o.. | 1 * * ♦ 1 8 0 0 | 8 12 0 0 | 12 6 0 0 | 6 1 0 .o.3.o.4.o. | * 1 * ♦ 1 0 8 0 | 8 0 12 0 | 12 0 6 0 | 6 0 1 ..o3..o4..o | * * 8 | 0 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1 ---------------+-------+----------+-----------+----------+------ oo.3oo.4oo.&#x | 1 1 0 | 1 * * * ♦ 8 0 0 0 | 12 0 0 0 | 6 0 0 o.o3o.o4o.o&#x | 1 0 1 | * 8 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0 .oo3.oo4.oo&#x | 0 1 1 | * * 8 * | 1 0 3 0 | 3 0 3 0 | 3 0 1 ... ... ..x | 0 0 2 | * * * 12 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ---------------+-------+----------+-----------+----------+------ ooo3ooo4ooo&#x | 1 1 1 | 1 1 1 0 | 8 * * * | 3 0 0 0 | 3 0 0 ... ... o.x&#x | 1 0 2 | 0 2 0 1 | * 12 * * | 1 2 0 0 | 2 1 0 ... ... .ox&#x | 0 1 2 | 0 0 2 1 | * * 12 * | 1 0 2 0 | 2 0 1 ... ..o4..x | 0 0 4 | 0 0 0 4 | * * * 6 | 0 1 1 1 | 1 1 1 ---------------+-------+----------+-----------+----------+------ ... ... oox&#x ♦ 1 1 2 | 1 2 2 1 | 2 1 1 0 | 12 * * * | 2 0 0 ... o.o4o.x&#x ♦ 1 0 4 | 0 4 0 4 | 0 4 0 1 | * 6 * * | 1 1 0 ... .oo4.ox&#x ♦ 0 1 4 | 0 0 4 4 | 0 0 4 1 | * * 6 * | 1 0 1 ..o3..o4..x ♦ 0 0 8 | 0 0 0 12 | 0 0 0 6 | * * * 1 | 0 1 1 ---------------+-------+----------+-----------+----------+------ ... ooo4oox&#x ♦ 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 0 | 6 * * o.o3o.o4o.x&#x ♦ 1 0 8 | 0 8 0 12 | 0 12 0 6 | 0 6 0 1 | * 1 * .oo3.oo4.ox&#x ♦ 0 1 8 | 0 0 8 12 | 0 0 12 6 | 0 0 6 1 | * * 1
or o..3o..4o.. & | 2 * ♦ 1 8 0 | 8 12 0 | 12 6 0 | 6 1 ..o3..o4..o | * 8 | 0 2 3 | 1 6 3 | 3 6 1 | 3 2 -----------------+-----+---------+--------+---------+---- oo.3oo.4oo.&#x | 2 0 | 1 * * ♦ 8 0 0 | 12 0 0 | 6 0 o.o3o.o4o.o&#x & | 1 1 | * 16 * | 1 3 0 | 3 3 0 | 3 1 ... ... ..x | 0 2 | * * 12 | 0 2 2 | 1 4 1 | 2 2 -----------------+-----+---------+--------+---------+---- ooo3ooo4ooo&#x | 2 1 | 1 2 0 | 8 * * | 3 0 0 | 3 0 ... ... o.x&#x & | 1 2 | 0 2 1 | * 24 * | 1 2 0 | 2 1 ... ..o4..x | 0 4 | 0 0 4 | * * 6 | 0 2 1 | 1 2 -----------------+-----+---------+--------+---------+---- ... ... oox&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 12 * * | 2 0 ... o.o4o.x&#x & ♦ 1 4 | 0 4 4 | 0 4 1 | * 12 * | 1 1 ..o3..o4..x ♦ 0 8 | 0 0 12 | 0 0 6 | * * 1 | 0 2 -----------------+-----+---------+--------+---------+---- ... ooo4oox&#x ♦ 2 4 | 1 8 4 | 4 8 1 | 4 2 0 | 6 * o.o3o.o4o.x&#x & ♦ 1 8 | 0 8 12 | 0 12 6 | 0 6 1 | * 2
pt || cubpy → height = 0
o..3o..4o.. | 1 * * ♦ 1 8 0 0 | 8 12 0 0 | 12 6 0 0 | 6 1 0
.o.3.o.4.o. | * 1 * ♦ 1 0 8 0 | 8 0 12 0 | 12 0 6 0 | 6 0 1
..o3..o4..o | * * 8 | 0 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1
---------------+-------+----------+-----------+----------+------
oo.3oo.4oo.&#x | 1 1 0 | 1 * * * ♦ 8 0 0 0 | 12 0 0 0 | 6 0 0
o.o3o.o4o.o&#x | 1 0 1 | * 8 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0
.oo3.oo4.oo&#x | 0 1 1 | * * 8 * | 1 0 3 0 | 3 0 3 0 | 3 0 1
... ... ..x | 0 0 2 | * * * 12 | 0 1 1 2 | 1 2 2 1 | 2 1 1
---------------+-------+----------+-----------+----------+------
ooo3ooo4ooo&#x | 1 1 1 | 1 1 1 0 | 8 * * * | 3 0 0 0 | 3 0 0
... ... o.x&#x | 1 0 2 | 0 2 0 1 | * 12 * * | 1 2 0 0 | 2 1 0
... ... .ox&#x | 0 1 2 | 0 0 2 1 | * * 12 * | 1 0 2 0 | 2 0 1
... ..o4..x | 0 0 4 | 0 0 0 4 | * * * 6 | 0 1 1 1 | 1 1 1
---------------+-------+----------+-----------+----------+------
... ... oox&#x ♦ 1 1 2 | 1 2 2 1 | 2 1 1 0 | 12 * * * | 2 0 0
... o.o4o.x&#x ♦ 1 0 4 | 0 4 0 4 | 0 4 0 1 | * 6 * * | 1 1 0
... .oo4.ox&#x ♦ 0 1 4 | 0 0 4 4 | 0 0 4 1 | * * 6 * | 1 0 1
..o3..o4..x ♦ 0 0 8 | 0 0 0 12 | 0 0 0 6 | * * * 1 | 0 1 1
---------------+-------+----------+-----------+----------+------
... ooo4oox&#x ♦ 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 0 | 6 * *
o.o3o.o4o.x&#x ♦ 1 0 8 | 0 8 0 12 | 0 12 0 6 | 0 6 0 1 | * 1 *
.oo3.oo4.ox&#x ♦ 0 1 8 | 0 0 8 12 | 0 0 12 6 | 0 0 6 1 | * * 1
oox oox oox&#x → height(1,2) = 1 height(1,3) = height(2,3) = 1/2 o.. o.. o.. | 1 * * ♦ 1 8 0 0 0 0 | 4 4 4 8 0 0 0 0 0 0 | 2 2 2 4 4 4 0 0 0 0 | 1 2 2 2 0 .o. .o. .o. | * 1 * ♦ 1 0 8 0 0 0 | 0 0 0 8 4 4 4 0 0 0 | 0 0 0 4 4 4 2 2 2 0 | 0 2 2 2 1 ..o ..o ..o | * * 8 | 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 | 1 1 1 1 1 ---------------+-------+-------------+---------------------+---------------------+---------- oo. oo. oo.&#x | 1 1 0 | 1 * * * * * ♦ 0 0 0 8 0 0 0 0 0 0 | 0 0 0 4 4 4 0 0 0 0 | 0 2 2 2 0 o.o o.o o.o&#x | 1 0 1 | * 8 * * * * | 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 .oo&#x | 0 1 1 | * * 8 * * * | 0 0 0 1 1 1 1 0 0 0 | 0 0 0 1 1 1 1 1 1 0 | 0 1 1 1 1 ..x ... ... | 0 0 2 | * * * 4 * * | 1 0 0 0 1 0 0 1 1 0 | 1 1 0 1 0 0 1 1 0 1 | 1 1 1 0 1 ... ..x ... | 0 0 2 | * * * * 4 * | 0 1 0 0 0 1 0 1 0 1 | 1 0 1 0 1 0 1 0 1 1 | 1 1 0 1 1 ... ... ..x | 0 0 2 | * * * * * 4 | 0 0 1 0 0 0 1 0 1 1 | 0 1 1 0 0 1 0 1 1 1 | 1 0 1 1 1 ---------------+-------+-------------+---------------------+---------------------+---------- o.x ... ...&#x | 1 0 2 | 0 2 0 1 0 0 | 4 * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0 ... o.x ...&#x | 1 0 2 | 0 2 0 0 1 0 | * 4 * * * * * * * * | 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0 ... ... o.x&#x | 1 0 2 | 0 2 0 0 0 1 | * * 4 * * * * * * * | 1 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0 ooo ooo ooo&#x | 1 1 1 | 1 1 1 0 0 0 | * * * 8 * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 .ox ... ...&#x | 0 1 2 | 0 0 2 1 0 0 | * * * * 4 * * * * * | 0 0 0 1 0 0 1 1 0 0 | 0 1 1 0 1 ... .ox ...&#x | 0 1 2 | 0 0 2 0 1 0 | * * * * * 4 * * * * | 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 1 ... ... .ox&#x | 0 1 2 | 0 0 2 0 0 1 | * * * * * * 4 * * * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1 ..x ..x ... | 0 0 4 | 0 0 0 2 2 0 | * * * * * * * 2 * * | 1 0 0 0 0 0 1 0 0 1 | 1 1 0 0 1 ..x ... ..x | 0 0 4 | 0 0 0 2 0 2 | * * * * * * * * 2 * | 0 1 0 0 0 0 0 1 0 1 | 1 0 1 0 1 ... ..x ..x | 0 0 4 | 0 0 0 0 2 2 | * * * * * * * * * 2 | 0 0 1 0 0 0 0 0 1 1 | 1 0 0 1 1 ---------------+-------+-------------+---------------------+---------------------+---------- o.x o.x ...&#x ♦ 1 0 4 | 0 4 0 2 2 0 | 2 2 0 0 0 0 0 1 0 0 | 2 * * * * * * * * * | 1 1 0 0 0 o.x ... o.x&#x ♦ 1 0 4 | 0 4 0 2 0 2 | 2 0 2 0 0 0 0 0 1 0 | * 2 * * * * * * * * | 1 0 1 0 0 ... o.x o.x&#x ♦ 1 0 4 | 0 4 0 0 2 2 | 0 2 2 0 0 0 0 0 0 1 | * * 2 * * * * * * * | 1 0 0 1 0 oox ... ...&#x ♦ 1 1 2 | 1 2 2 1 0 0 | 1 0 0 2 1 0 0 0 0 0 | * * * 4 * * * * * * | 0 1 1 0 0 ... oox ...&#x ♦ 1 1 2 | 1 2 2 0 1 0 | 0 1 0 2 0 1 0 0 0 0 | * * * * 4 * * * * * | 0 1 0 1 0 ... ... oox&#x ♦ 1 1 2 | 1 2 2 0 0 1 | 0 0 1 2 0 0 1 0 0 0 | * * * * * 4 * * * * | 0 0 1 1 0 .ox .ox ...&#x ♦ 0 1 4 | 0 0 4 2 2 0 | 0 0 0 0 2 2 0 1 0 0 | * * * * * * 2 * * * | 0 1 0 0 1 .ox ... .ox&#x ♦ 0 1 4 | 0 0 4 2 0 2 | 0 0 0 0 2 0 2 0 1 0 | * * * * * * * 2 * * | 0 0 1 0 1 ... .ox .ox&#x ♦ 0 1 4 | 0 0 4 0 2 2 | 0 0 0 0 0 2 2 0 0 1 | * * * * * * * * 2 * | 0 0 0 1 1 ..x ..x ..x ♦ 0 0 8 | 0 0 0 4 4 4 | 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * 1 | 1 0 0 0 1 ---------------+-------+-------------+---------------------+---------------------+---------- o.x o.x o.x&#x ♦ 1 0 8 | 0 8 0 4 4 4 | 4 4 4 0 0 0 0 2 2 2 | 2 2 2 0 0 0 0 0 0 1 | 1 * * * * oox oox ...&#x ♦ 1 1 4 | 1 4 4 2 2 0 | 2 2 0 4 2 2 0 1 0 0 | 1 0 0 2 2 0 1 0 0 0 | * 2 * * * oox ... oox&#x ♦ 1 1 4 | 1 4 4 2 0 2 | 2 0 2 4 2 0 2 0 1 0 | 0 1 0 2 0 2 0 1 0 0 | * * 2 * * ... oox oox&#x ♦ 1 1 4 | 1 4 4 0 2 2 | 0 2 2 4 0 2 2 0 0 1 | 0 0 1 0 2 2 0 0 1 0 | * * * 2 * .ox .ox .ox&#x ♦ 0 1 8 | 0 0 8 4 4 4 | 0 0 0 0 4 4 4 2 2 2 | 0 0 0 0 0 0 2 2 2 1 | * * * * 1
oox xxo xxo&#x → height(1,2) = 1 height(1,3) = height(2,3) = 1/2 o.. o.. o.. | 4 * * | 1 1 1 2 0 0 0 0 | 1 1 1 1 2 2 2 0 0 0 0 | 1 1 1 2 1 2 2 0 0 0 | 1 1 1 2 0 .o. .o. .o. | * 4 * | 0 0 1 0 1 1 2 0 | 0 1 1 0 0 0 2 1 1 2 2 | 1 0 0 0 1 2 2 1 1 2 | 0 1 1 2 1 ..o ..o ..o | * * 2 ♦ 0 0 0 4 0 0 4 1 | 0 0 0 4 2 2 4 0 4 2 2 | 0 2 2 1 4 2 2 2 2 1 | 1 2 2 1 1 ---------------+-------+-----------------+-----------------------+---------------------+---------- ... x.. ... | 2 0 0 | 2 * * * * * * * | 1 1 0 0 2 0 0 0 0 0 0 | 1 1 0 2 0 2 0 0 0 0 | 1 1 0 2 0 ... ... x.. | 2 0 0 | * 2 * * * * * * | 1 0 1 0 0 2 0 0 0 0 0 | 1 0 1 2 0 0 2 0 0 0 | 1 0 1 2 0 oo. oo. oo.&#x | 1 1 0 | * * 4 * * * * * | 0 1 1 0 0 0 2 0 0 0 0 | 1 0 0 0 1 2 2 0 0 0 | 0 1 1 2 0 o.o o.o o.o&#x | 1 0 1 | * * * 8 * * * * | 0 0 0 1 1 1 1 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0 ... .x. ... | 0 2 0 | * * * * 2 * * * | 0 1 0 0 0 0 0 1 0 2 0 | 1 0 0 0 0 2 0 1 0 2 | 0 1 0 2 1 ... ... .x. | 0 2 0 | * * * * * 2 * * | 0 0 1 0 0 0 0 1 0 0 2 | 1 0 0 0 0 0 2 0 1 2 | 0 0 1 2 1 .oo .oo .oo&#x | 0 1 1 | * * * * * * 8 * | 0 0 0 0 0 0 1 0 1 1 1 | 0 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1 ..x ... ... | 0 0 2 | * * * * * * * 1 ♦ 0 0 0 4 0 0 0 0 4 0 0 | 0 2 2 0 4 0 0 2 2 0 | 1 2 2 0 1 ---------------+-------+-----------------+-----------------------+---------------------+---------- ... x.. x.. | 4 0 0 | 2 2 0 0 0 0 0 0 | 1 * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 1 0 0 2 0 ... xx. ...&#x | 2 2 0 | 1 0 2 0 1 0 0 0 | * 2 * * * * * * * * * | 1 0 0 0 0 2 0 0 0 0 | 0 1 0 2 0 ... ... xx.&#x | 2 2 0 | 0 1 2 0 0 1 0 0 | * * 2 * * * * * * * * | 1 0 0 0 0 0 2 0 0 0 | 0 0 1 2 0 o.x ... ...&#x | 1 0 2 | 0 0 0 2 0 0 0 1 | * * * 4 * * * * * * * | 0 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0 ... x.o ...&#x | 2 0 1 | 1 0 0 2 0 0 0 0 | * * * * 4 * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0 ... ... x.o&#x | 2 0 1 | 0 1 0 2 0 0 0 0 | * * * * * 4 * * * * * | 0 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0 ooo ooo ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 0 | * * * * * * 8 * * * * | 0 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 ... .x. .x. | 0 4 0 | 0 0 0 0 2 2 0 0 | * * * * * * * 1 * * * | 1 0 0 0 0 0 0 0 0 2 | 0 0 0 2 1 .ox ... ...&#x | 0 1 2 | 0 0 0 0 0 0 2 1 | * * * * * * * * 4 * * | 0 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1 ... .xo ...&#x | 0 2 1 | 0 0 0 0 1 0 2 0 | * * * * * * * * * 4 * | 0 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1 ... ... .xo&#x | 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1 ---------------+-------+-----------------+-----------------------+---------------------+---------- ... xx. xx.&#x ♦ 4 4 0 | 2 2 4 0 2 2 0 0 | 1 2 2 0 0 0 0 1 0 0 0 | 1 * * * * * * * * * | 0 0 0 2 0 o.x x.o ...&#x ♦ 2 0 2 | 1 0 0 4 0 0 0 1 | 0 0 0 2 2 0 0 0 0 0 0 | * 2 * * * * * * * * | 1 1 0 0 0 o.x ... x.o&#x ♦ 2 0 2 | 0 1 0 4 0 0 0 1 | 0 0 0 2 0 2 0 0 0 0 0 | * * 2 * * * * * * * | 1 0 1 0 0 ... x.o x.o&#x ♦ 4 0 1 | 2 2 0 4 0 0 0 0 | 1 0 0 0 2 2 0 0 0 0 0 | * * * 2 * * * * * * | 1 0 0 1 0 oox ... ...&#x ♦ 1 1 2 | 0 0 1 2 0 0 2 1 | 0 0 0 1 0 0 2 0 1 0 0 | * * * * 4 * * * * * | 0 1 1 0 0 ... xxo ...&#x ♦ 2 2 1 | 1 0 2 2 1 0 2 0 | 0 1 0 0 1 0 2 0 0 1 0 | * * * * * 4 * * * * | 0 1 0 1 0 ... ... xxo&#x ♦ 2 2 1 | 0 1 2 2 0 1 2 0 | 0 0 1 0 0 1 2 0 0 0 1 | * * * * * * 4 * * * | 0 0 1 1 0 .ox .xo ...&#x ♦ 0 2 2 | 0 0 0 0 1 0 4 1 | 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * 2 * * | 0 1 0 0 1 .ox ... .xo&#x ♦ 0 2 2 | 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 2 0 2 | * * * * * * * * 2 * | 0 0 1 0 1 ... .xo .xo&#x ♦ 0 4 1 | 0 0 0 0 2 2 4 0 | 0 0 0 0 0 0 0 1 0 2 2 | * * * * * * * * * 2 | 0 0 0 1 1 ---------------+-------+-----------------+-----------------------+---------------------+---------- o.x x.o x.o&#x ♦ 4 0 2 | 2 2 0 8 0 0 0 1 | 1 0 0 4 4 4 0 0 0 0 0 | 0 2 2 2 0 0 0 0 0 0 | 1 * * * * oox xxo ...&#x ♦ 2 2 2 | 1 0 2 4 1 0 4 1 | 0 1 0 2 2 0 4 0 2 2 0 | 0 1 0 0 2 2 0 1 0 0 | * 2 * * * oox ... xxo&#x ♦ 2 2 2 | 0 1 2 4 0 1 4 1 | 0 0 1 2 0 2 4 0 2 0 2 | 0 0 1 0 2 0 2 0 1 0 | * * 2 * * ... xxo xxo&#x ♦ 4 4 1 | 2 2 4 4 2 2 4 0 | 1 2 2 0 2 2 4 1 0 2 2 | 1 0 0 1 0 2 2 0 0 1 | * * * 2 * .ox .xo .xo&#x ♦ 0 4 2 | 0 0 0 0 2 2 8 1 | 0 0 0 0 0 0 0 1 4 4 4 | 0 0 0 0 0 0 0 2 2 2 | * * * * 1
ooxx ooxx&#x → height(1,2) = height(3,4) = 1 height(1,3) = height(1,4) = height(2,3) = height(2,4) = 1/sqrt(2) = 0.707107 o... o... | 1 * * * ♦ 1 4 4 0 0 0 0 0 0 0 | 4 4 2 2 4 2 2 0 0 0 0 0 0 0 0 0 | 2 2 4 2 2 1 2 2 1 0 0 0 0 0 | 1 2 2 1 1 0 .o.. .o.. | * 1 * * ♦ 1 0 0 4 4 0 0 0 0 0 | 4 4 0 0 0 0 0 2 2 4 2 2 0 0 0 0 | 2 2 4 2 2 0 0 0 0 1 2 2 1 0 | 1 2 2 1 0 1 ..o. ..o. | * * 4 * | 0 1 0 1 0 1 1 1 0 0 | 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 | 1 1 1 0 0 1 1 1 0 1 1 1 0 1 | 1 1 1 0 1 1 ...o ...o | * * * 4 | 0 0 1 0 1 0 0 1 1 1 | 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 | 0 0 1 1 1 0 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1 -------------+---------+---------------------+---------------------------------+-----------------------------+------------ oo.. oo..&#x | 1 1 0 0 | 1 * * * * * * * * * ♦ 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 2 4 2 2 0 0 0 0 0 0 0 0 0 | 1 2 2 1 0 0 o.o. o.o.&#x | 1 0 1 0 | * 4 * * * * * * * * | 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 1 0 o..o o..o&#x | 1 0 0 1 | * * 4 * * * * * * * | 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0 .oo. .oo.&#x | 0 1 1 0 | * * * 4 * * * * * * | 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1 .o.o .o.o&#x | 0 1 0 1 | * * * * 4 * * * * * | 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 1 1 1 0 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1 ..x. .... | 0 0 2 0 | * * * * * 2 * * * * | 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 .... ..x. | 0 0 2 0 | * * * * * * 2 * * * | 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 | 0 1 0 0 0 1 0 1 0 1 0 1 0 1 | 1 0 1 0 1 1 ..oo ..oo&#x | 0 0 1 1 | * * * * * * * 4 * * | 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 | 0 0 1 0 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1 ...x .... | 0 0 0 2 | * * * * * * * * 2 * | 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 2 | * * * * * * * * * 2 | 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. ooo.&#x | 1 1 1 0 | 1 1 0 1 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 oo.o oo.o&#x | 1 1 0 1 | 1 0 1 0 1 0 0 0 0 0 | * 4 * * * * * * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 o.x. ....&#x | 1 0 2 0 | 0 2 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.x.&#x | 1 0 2 0 | 0 2 0 0 0 0 1 0 0 0 | * * * 2 * * * * * * * * * * * * | 0 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0 o.oo o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 0 1 0 0 | * * * * 4 * * * * * * * * * * * | 0 0 1 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 2 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 2 | 0 0 2 0 0 0 0 0 0 1 | * * * * * * 2 * * * * * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0 .ox. ....&#x | 0 1 2 0 | 0 0 0 2 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 .... .ox.&#x | 0 1 2 0 | 0 0 0 2 0 0 1 0 0 0 | * * * * * * * * 2 * * * * * * * | 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1 .ooo .ooo&#x | 0 1 1 1 | 0 0 0 1 1 0 0 1 0 0 | * * * * * * * * * 4 * * * * * * | 0 0 1 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 2 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 2 | 0 0 0 0 2 0 0 0 0 1 | * * * * * * * * * * * 2 * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1 ..x. ..x. | 0 0 4 0 | 0 0 0 0 0 2 2 0 0 0 | * * * * * * * * * * * * 1 * * * | 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1 ..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 1 0 2 1 0 | * * * * * * * * * * * * * 2 * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1 .... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * * * 2 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1 ...x ...x | 0 0 0 4 | 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1 -------------+---------+---------------------+---------------------------------+-----------------------------+------------ oox. ....&#x ♦ 1 1 2 0 | 1 2 0 2 0 1 0 0 0 0 | 2 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * | 1 1 0 0 0 0 .... oox.&#x ♦ 1 1 2 0 | 1 2 0 2 0 0 1 0 0 0 | 2 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * | 1 0 1 0 0 0 oooo oooo&#x ♦ 1 1 1 1 | 1 1 1 1 1 0 0 1 0 0 | 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * | 0 1 1 0 0 0 oo.x ....&#x ♦ 1 1 0 2 | 1 0 2 0 2 0 0 0 1 0 | 0 2 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 2 | 1 0 2 0 2 0 0 0 0 1 | 0 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0 | * * * * 2 * * * * * * * * * | 0 0 1 1 0 0 o.x. o.x.&#x ♦ 1 0 4 0 | 0 4 0 0 0 2 2 0 0 0 | 0 0 2 2 0 0 0 0 0 0 0 0 1 0 0 0 | * * * * * 1 * * * * * * * * | 1 0 0 0 1 0 o.xx ....&#x ♦ 1 0 2 2 | 0 2 2 0 0 1 0 2 1 0 | 0 0 1 0 2 1 0 0 0 0 0 0 0 1 0 0 | * * * * * * 2 * * * * * * * | 0 1 0 0 1 0 .... o.xx&#x ♦ 1 0 2 2 | 0 2 2 0 0 0 1 2 0 1 | 0 0 0 1 2 0 1 0 0 0 0 0 0 0 1 0 | * * * * * * * 2 * * * * * * | 0 0 1 0 1 0 o..x o..x&#x ♦ 1 0 0 4 | 0 0 4 0 0 0 0 0 2 2 | 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 1 | * * * * * * * * 1 * * * * * | 0 0 0 1 1 0 .ox. .ox.&#x ♦ 0 1 4 0 | 0 0 0 4 0 2 2 0 0 0 | 0 0 0 0 0 0 0 2 2 0 0 0 1 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1 .oxx ....&#x ♦ 0 1 2 2 | 0 0 0 2 2 1 0 2 1 0 | 0 0 0 0 0 0 0 1 0 2 1 0 0 1 0 0 | * * * * * * * * * * 2 * * * | 0 1 0 0 0 1 .... .oxx&#x ♦ 0 1 2 2 | 0 0 0 2 2 0 1 2 0 1 | 0 0 0 0 0 0 0 0 1 2 0 1 0 0 1 0 | * * * * * * * * * * * 2 * * | 0 0 1 0 0 1 .o.x .o.x&#x ♦ 0 1 0 4 | 0 0 0 0 4 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 1 | * * * * * * * * * * * * 1 * | 0 0 0 1 0 1 ..xx ..xx&#x ♦ 0 0 4 4 | 0 0 0 0 0 2 2 4 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 1 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 1 -------------+---------+---------------------+---------------------------------+-----------------------------+------------ oox. oox.&#x ♦ 1 1 4 0 | 1 4 0 4 0 2 2 0 0 0 | 4 0 2 2 0 0 0 2 2 0 0 0 1 0 0 0 | 2 2 0 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * * ooxx ....&#x ♦ 1 1 2 2 | 1 2 2 2 2 1 0 2 1 0 | 2 2 1 0 2 1 0 1 0 2 1 0 0 1 0 0 | 1 0 2 1 0 0 1 0 0 0 1 0 0 0 | * 2 * * * * .... ooxx&#x ♦ 1 1 2 2 | 1 2 2 2 2 0 1 2 0 1 | 2 2 0 1 2 0 1 0 1 2 0 1 0 0 1 0 | 0 1 2 0 1 0 0 1 0 0 0 1 0 0 | * * 2 * * * oo.x oo.x&#x ♦ 1 1 0 4 | 1 0 4 0 4 0 0 0 2 2 | 0 4 0 0 0 2 2 0 0 0 2 2 0 0 0 1 | 0 0 0 2 2 0 0 0 1 0 0 0 1 0 | * * * 1 * * o.xx o.xx&#x ♦ 1 0 4 4 | 0 4 4 0 0 2 2 4 2 2 | 0 0 2 2 4 2 2 0 0 0 0 0 1 2 2 1 | 0 0 0 0 0 1 2 2 1 0 0 0 0 1 | * * * * 1 * .oxx .oxx&#x ♦ 0 1 4 4 | 0 0 0 4 4 2 2 4 2 2 | 0 0 0 0 0 0 0 2 2 4 2 2 1 2 2 1 | 0 0 0 0 0 0 0 0 0 1 2 2 1 1 | * * * * * 1
© 2004-2024 | top of page |