Acronym | tepe, K-4.9 (alt: dycuf) |
Name |
tetrahedron prism, line || trip, square - square bi-wedge, digonal orthobicupolaic ring, vertex figure of rix, dyadic cupolafastegium, equatorial cross-section of tet-first hin |
|,>,O device | line pyramid pyramid prism = |>>| |
© | |
Segmentochoron display | |
Cross sections |
© |
Circumradius | sqrt(5/8) = 0.790569 |
Lace city in approx. ASCII-art |
x x x o x o |
o x o x x o x o | |
o3o o3o x3o x3o | |
Coordinates | (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/2) & all even permutations and all even changes of sign in all but last coord., change of sign in last coord. |
Volume | sqrt(2)/12 = 0.117851 |
Dihedral angles | |
Face vector | 8, 16, 14, 6 |
Confer |
|
External links |
Incidence matrix according to Dynkin symbol
x x3o3o . . . . | 8 ♦ 1 3 | 3 3 | 3 1 --------+---+------+-----+---- x . . . | 2 | 4 * | 3 0 | 3 0 . x . . | 2 | * 12 | 1 2 | 2 1 --------+---+------+-----+---- x x . . | 4 | 2 2 | 6 * | 2 0 . x3o . | 3 | 0 3 | * 8 | 1 1 --------+---+------+-----+---- x x3o . ♦ 6 | 3 6 | 3 2 | 4 * . x3o3o ♦ 4 | 0 6 | 0 4 | * 2
x x3o3/2o . . . . | 8 ♦ 1 3 | 3 3 | 3 1 ----------+---+------+-----+---- x . . . | 2 | 4 * | 3 0 | 3 0 . x . . | 2 | * 12 | 1 2 | 2 1 ----------+---+------+-----+---- x x . . | 4 | 2 2 | 6 * | 2 0 . x3o . | 3 | 0 3 | * 8 | 1 1 ----------+---+------+-----+---- x x3o . ♦ 6 | 3 6 | 3 2 | 4 * . x3o3/2o ♦ 4 | 0 6 | 0 4 | * 2
x x3/2o3o . . . . | 8 ♦ 1 3 | 3 3 | 3 1 ----------+---+------+-----+---- x . . . | 2 | 4 * | 3 0 | 3 0 . x . . | 2 | * 12 | 1 2 | 2 1 ----------+---+------+-----+---- x x . . | 4 | 2 2 | 6 * | 2 0 . x3/2o . | 3 | 0 3 | * 8 | 1 1 ----------+---+------+-----+---- x x3/2o . ♦ 6 | 3 6 | 3 2 | 4 * . x3/2o3o ♦ 4 | 0 6 | 0 4 | * 2
x x3/2o3/2o . . . . | 8 ♦ 1 3 | 3 3 | 3 1 ------------+---+------+-----+---- x . . . | 2 | 4 * | 3 0 | 3 0 . x . . | 2 | * 12 | 1 2 | 2 1 ------------+---+------+-----+---- x x . . | 4 | 2 2 | 6 * | 2 0 . x3/2o . | 3 | 0 3 | * 8 | 1 1 ------------+---+------+-----+---- x x3/2o . ♦ 6 | 3 6 | 3 2 | 4 * . x3/2o3/2o ♦ 4 | 0 6 | 0 4 | * 2
x o3o4s . demi( . . . ) | 8 ♦ 1 3 | 3 3 | 3 1 ----------------+---+------+-----+---- x demi( . . . ) | 2 | 4 * | 3 0 | 3 0 . . o4s | 2 | * 12 | 1 2 | 2 1 ----------------+---+------+-----+---- x . o4s | 4 | 2 2 | 6 * | 2 0 . sefa( o3o4s ) | 3 | 0 3 | * 8 | 1 1 ----------------+---+------+-----+---- x sefa( o3o4s ) ♦ 6 | 3 6 | 3 2 | 4 * . o3o4s ♦ 4 | 0 6 | 0 4 | * 2
x s2s4o . demi( . . . ) | 8 ♦ 1 2 1 | 2 1 3 | 1 3 ----------------+---+-------+-------+---- x demi( . . . ) | 2 | 4 * * | 2 1 0 | 0 3 . s2s . | 2 | * 8 * | 1 0 2 | 1 2 . . s4o | 2 | * * 4 | 0 1 2 | 1 2 ----------------+---+-------+-------+---- x s2s . | 4 | 2 2 0 | 4 * * | 0 2 x . s4o | 4 | 2 0 2 | * 2 * | 0 2 . sefa( s2s4o ) | 3 | 0 2 1 | * * 8 | 1 1 ----------------+---+-------+-------+---- . s2s4o ♦ 4 | 0 4 2 | 0 0 4 | 2 * x sefa( s2s4o ) ♦ 6 | 3 4 2 | 2 1 2 | * 4
x s2s2s . demi( . . . ) | 8 ♦ 1 1 1 1 | 1 1 1 3 | 3 1 ----------------+---+---------+---------+---- x demi( . . . ) | 2 | 4 * * * | 1 1 1 0 | 3 0 . s2s . | 2 | * 4 * * | 1 0 0 2 | 2 1 . s 2 s | 2 | * * 4 * | 0 1 0 2 | 2 1 . . s2s | 2 | * * * 4 | 0 0 1 2 | 2 1 ----------------+---+---------+---------+---- x s2s . | 4 | 2 2 0 0 | 2 * * * | 2 0 x s 2 s | 4 | 2 0 2 0 | * 2 * * | 2 0 x . s2s | 4 | 2 0 0 2 | * * 2 * | 2 0 . sefa( s2s2s ) | 3 | 0 1 1 1 | * * * 8 | 1 1 ----------------+---+---------+---------+---- x sefa( s2s2s ) ♦ 6 | 3 2 2 2 | 1 1 1 2 | 4 * . s2s2s ♦ 4 | 0 2 2 2 | 0 0 0 4 | * 2
x2o3o4s demi( . . . . ) | 8 ♦ 1 3 | 3 3 | 1 3 ----------------+---+------+-----+---- demi( x . . . ) | 2 | 4 * | 3 0 | 0 3 . . o4s | 2 | * 12 | 1 2 | 1 2 ----------------+---+------+-----+---- x 2 o4s | 4 | 2 2 | 6 * | 0 2 sefa( . o3o4s ) | 3 | 0 3 | * 8 | 1 1 ----------------+---+------+-----+---- . o3o4s ♦ 4 | 0 6 | 0 4 | 2 * sefa( x2o3o4s ) ♦ 6 | 3 6 | 3 2 | * 4 starting figure: x o3o4x
x2s2s4o demi( . . . . ) | 8 ♦ 1 2 1 | 2 1 3 | 1 3 ----------------+---+-------+-------+---- demi( x . . . ) | 2 | 4 * * | 2 1 0 | 0 3 . s2s . | 2 | * 8 * | 1 0 2 | 1 2 . . s4o | 2 | * * 4 | 0 1 2 | 1 2 ----------------+---+-------+-------+---- x2s2s . | 4 | 2 2 0 | 4 * * | 0 2 x 2 s4o | 4 | 2 0 2 | * 2 * | 0 2 sefa( . s2s4o ) | 3 | 0 2 1 | * * 8 | 1 1 ----------------+---+-------+-------+---- . s2s4o ♦ 4 | 0 4 2 | 0 0 4 | 2 * sefa( x2s2s4o ) ♦ 6 | 3 4 2 | 2 1 2 | * 4 starting figure: x x x4o
x2s2s2s demi( . . . . ) | 8 ♦ 1 1 1 1 | 1 1 1 3 | 1 3 ----------------+---+---------+---------+---- demi( x . . . ) | 2 | 4 * * * | 1 1 1 0 | 0 3 . s2s . | 2 | * 4 * * | 1 0 0 2 | 1 2 . s 2 s | 2 | * * 4 * | 0 1 0 2 | 1 2 . . s2s | 2 | * * * 4 | 0 0 1 2 | 1 2 ----------------+---+---------+---------+---- x2s2s . | 4 | 2 2 0 0 | 2 * * * | 0 2 x2s 2 s | 4 | 2 0 2 0 | * 2 * * | 0 2 x 2 s2s | 4 | 2 0 0 2 | * * 2 * | 0 2 sefa( . s2s2s ) | 3 | 0 1 1 1 | * * * 8 | 1 1 ----------------+---+---------+---------+---- . s2s2s ♦ 4 | 0 2 2 2 | 0 0 0 4 | 2 * sefa( x s2s2s ) ♦ 6 | 3 2 2 2 | 1 1 1 2 | * 4 starting figure: x x x x
xx3oo3oo&#x → height = 1
(tet || tet)
o.3o.3o. | 4 * ♦ 3 1 0 | 3 3 0 | 1 3 0
.o3.o3.o | * 4 ♦ 0 1 3 | 0 3 3 | 0 3 1
------------+-----+-------+-------+------
x. .. .. | 2 0 | 6 * * | 2 1 0 | 1 2 0
oo3oo3oo&#x | 1 1 | * 4 * | 0 3 0 | 0 3 0
.x .. .. | 0 2 | * * 6 | 0 1 2 | 0 2 1
------------+-----+-------+-------+------
x.3o. .. | 3 0 | 3 0 0 | 4 * * | 1 1 0
xx .. ..&#x | 2 2 | 1 2 1 | * 6 * | 0 2 0
.x3.o .. | 0 3 | 0 0 3 | * * 4 | 0 1 1
------------+-----+-------+-------+------
x.3o.3o. ♦ 4 0 | 6 0 0 | 4 0 0 | 1 * *
xx3oo ..&#x ♦ 3 3 | 3 3 3 | 1 3 1 | * 4 *
.x3.o3.o ♦ 0 4 | 0 0 6 | 0 0 4 | * * 1
xx ox3oo&#x → height = sqrt(2/3) = 0.816497
(line || para trip)
o. o.3o. | 2 * ♦ 1 3 0 0 | 3 3 0 0 | 3 1 0
.o .o3.o | * 6 ♦ 0 1 1 2 | 1 2 2 1 | 2 1 1
------------+-----+---------+---------+------
x. .. .. | 2 0 | 1 * * * | 3 0 0 0 | 3 0 0
oo oo3oo&#x | 1 1 | * 6 * * | 1 2 0 0 | 2 1 0
.x .. .. | 0 2 | * * 3 * | 1 0 2 0 | 2 0 1
.. .x .. | 0 2 | * * * 6 | 0 1 1 1 | 1 1 1
------------+-----+---------+---------+------
xx .. ..&#x | 2 2 | 1 2 1 0 | 3 * * * | 2 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 | * 6 * * | 1 1 0
.x .x .. | 0 4 | 0 0 2 2 | * * 3 * | 1 0 1
.. .x3.o | 0 3 | 0 0 0 3 | * * * 2 | 0 1 1
------------+-----+---------+---------+------
xx ox ..&#x ♦ 2 4 | 1 4 2 2 | 2 2 1 0 | 3 * *
.. ox3oo&#x ♦ 1 3 | 0 3 0 3 | 0 3 0 1 | * 2 *
.x .x3.o ♦ 0 6 | 0 0 3 6 | 0 0 3 2 | * * 1
xx xo ox&#x → height = 1/sqrt(2) = 0.707107
({4} || ortho {4})
o. o. o. | 4 * ♦ 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1
.o .o .o | * 4 ♦ 0 0 2 1 1 | 0 2 1 2 1 | 1 2 1
------------+-----+-----------+-----------+------
x. .. .. | 2 0 | 2 * * * * | 1 2 0 0 0 | 2 1 0
.. x. .. | 2 0 | * 2 * * * | 1 0 2 0 0 | 2 0 1
oo oo oo&#x | 1 1 | * * 8 * * | 0 1 1 1 0 | 1 1 1
.x .. .. | 0 2 | * * * 2 * | 0 2 0 0 1 | 1 2 0
.. .. .x | 0 2 | * * * * 2 | 0 0 0 2 1 | 0 2 1
------------+-----+-----------+-----------+------
x. x. .. | 4 0 | 2 2 0 0 0 | 1 * * * * | 2 0 0
xx .. ..&#x | 2 2 | 1 0 2 1 0 | * 4 * * * | 1 1 0
.. xo ..&#x | 2 1 | 0 1 2 0 0 | * * 4 * * | 1 0 1
.. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * 4 * | 0 1 1
.x .. .x | 0 4 | 0 0 0 2 2 | * * * * 1 | 0 2 0
------------+-----+-----------+-----------+------
xx xo ..&#x ♦ 4 2 | 2 2 4 1 0 | 1 2 2 0 0 | 2 * *
xx .. ox&#x ♦ 2 4 | 1 0 4 2 2 | 0 2 0 2 1 | * 2 *
.. xo ox&#x ♦ 2 2 | 0 1 4 0 1 | 0 0 2 2 0 | * * 2
or o. o. o. & | 8 ♦ 1 1 2 | 1 2 3 | 3 1 --------------+---+-------+-------+---- x. .. .. & | 2 | 4 * * | 1 2 0 | 3 0 .. x. .. & | 2 | * 4 * | 1 0 2 | 2 1 oo oo oo&#x | 2 | * * 8 | 0 1 2 | 2 1 --------------+---+-------+-------+---- x. x. .. & | 4 | 2 2 0 | 2 * * | 2 0 xx .. ..&#x | 4 | 2 0 2 | * 4 * | 2 0 .. xo ..&#x & | 3 | 0 1 2 | * * 8 | 1 1 --------------+---+-------+-------+---- xx xo ..&#x & ♦ 6 | 3 2 4 | 1 2 2 | 4 * .. xo ox&#x ♦ 4 | 0 2 4 | 0 0 4 | * 2
oox xxx&#x → height(1,2) = 1 height(1,3) = height(2,3) = sqrt(3)/2 = 0.866025 o.. o.. | 2 * * ♦ 1 1 2 0 0 0 0 | 1 1 2 2 0 0 0 | 1 1 2 0 .o. .o. | * 2 * ♦ 0 1 0 1 2 0 0 | 1 0 0 2 1 2 0 | 0 1 2 1 ..o ..o | * * 4 ♦ 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 -----------+-------+---------------+---------------+-------- ... x.. | 2 0 0 | 1 * * * * * * | 1 0 2 0 0 0 0 | 1 0 2 0 oo. oo.&#x | 1 1 0 | * 2 * * * * * | 1 0 0 2 0 0 0 | 0 1 2 0 o.o o.o&#x | 1 0 1 | * * 4 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 ... .x. | 0 2 0 | * * * 1 * * * | 1 0 0 0 0 2 0 | 0 0 2 1 .oo .oo&#x | 0 1 1 | * * * * 4 * * | 0 0 0 1 1 1 0 | 0 1 1 1 ..x ... | 0 0 2 | * * * * * 2 * | 0 1 0 0 1 0 1 | 1 1 0 1 ... ..x | 0 0 2 | * * * * * * 2 | 0 0 1 0 0 1 1 | 1 0 1 1 -----------+-------+---------------+---------------+-------- ... xx.&#x | 2 2 0 | 1 2 0 1 0 0 0 | 1 * * * * * * | 0 0 2 0 o.x ...&#x | 1 0 2 | 0 0 2 0 0 1 0 | * 2 * * * * * | 1 1 0 0 ... x.x&#x | 2 0 2 | 1 0 2 0 0 0 1 | * * 2 * * * * | 1 0 1 0 ooo ooo&#x | 1 1 1 | 0 1 1 0 1 0 0 | * * * 4 * * * | 0 1 1 0 .ox ...&#x | 0 1 2 | 0 0 0 0 2 1 0 | * * * * 2 * * | 0 1 0 1 ... .xx&#x | 0 2 2 | 0 0 0 1 2 0 1 | * * * * * 2 * | 0 0 1 1 ..x ..x | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * 1 | 1 0 0 1 -----------+-------+---------------+---------------+-------- o.x x.x&#x ♦ 2 0 4 | 1 0 4 0 0 2 2 | 0 2 2 0 0 0 1 | 1 * * * oox ...&#x ♦ 1 1 2 | 0 1 2 0 2 1 0 | 0 1 0 2 1 0 0 | * 2 * * ... xxx&#x ♦ 2 2 2 | 1 2 2 1 2 0 1 | 1 0 1 2 0 1 0 | * * 2 * .ox .xx&#x ♦ 0 2 4 | 0 0 0 1 4 2 2 | 0 0 0 0 2 2 1 | * * * 1
or o.. o.. & | 4 * ♦ 1 1 2 0 0 | 1 1 2 2 0 | 1 1 2 ..o ..o | * 4 ♦ 0 0 2 1 1 | 0 2 2 1 1 | 2 1 1 -------------+-----+-----------+-----------+------ ... x.. & | 2 0 | 2 * * * * | 1 0 2 0 0 | 1 0 2 oo. oo.&#x | 2 0 | * 2 * * * | 1 0 0 2 0 | 0 1 2 o.o o.o&#x & | 1 1 | * * 8 * * | 0 1 1 1 0 | 1 1 1 ..x ... | 0 2 | * * * 2 * | 0 2 0 0 1 | 2 1 0 ... ..x | 0 2 | * * * * 2 | 0 0 2 0 1 | 2 0 1 -------------+-----+-----------+-----------+------ ... xx.&#x | 4 0 | 2 2 0 0 0 | 1 * * * * | 0 0 2 o.x ...&#x & | 1 2 | 0 0 2 1 0 | * 4 * * * | 1 1 0 ... x.x&#x & | 2 2 | 1 0 2 0 1 | * * 4 * * | 1 0 1 ooo ooo&#x | 2 1 | 0 1 2 0 0 | * * * 4 * | 0 1 1 ..x ..x | 0 4 | 0 0 0 2 2 | * * * * 1 | 2 0 0 -------------+-----+-----------+-----------+------ o.x x.x&#x & ♦ 2 4 | 1 0 4 2 2 | 0 2 2 0 1 | 2 * * oox ...&#x ♦ 2 2 | 0 1 4 1 0 | 0 2 0 2 0 | * 2 * ... xxx&#x ♦ 4 2 | 2 2 4 0 1 | 1 0 2 2 0 | * * 2
xxxx&#x → all pairwise heights = 1 o... | 2 * * * ♦ 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 .o.. | * 2 * * ♦ 0 1 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 ..o. | * * 2 * ♦ 0 0 1 0 0 1 0 1 1 0 | 0 1 0 1 1 0 1 1 0 1 | 1 1 0 1 1 ...o | * * * 2 ♦ 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 --------+---------+---------------------+---------------------+---------- x... | 2 0 0 0 | 1 * * * * * * * * * | 1 0 0 1 0 1 0 0 0 0 | 1 0 1 1 0 oo..&#x | 1 1 0 0 | * 2 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 o.o.&#x | 1 0 1 0 | * * 2 * * * * * * * | 0 1 0 1 1 0 0 0 0 0 | 1 1 0 1 0 o..o&#x | 1 0 0 1 | * * * 2 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 .x.. | 0 2 0 0 | * * * * 1 * * * * * | 1 0 0 0 0 0 1 0 1 0 | 1 0 1 0 1 .oo.&#x | 0 1 1 0 | * * * * * 2 * * * * | 0 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 .o.o&#x | 0 1 0 1 | * * * * * * 2 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 ..x. | 0 0 2 0 | * * * * * * * 1 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 ..oo&#x | 0 0 1 1 | * * * * * * * * 2 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 ...x | 0 0 0 2 | * * * * * * * * * 1 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 --------+---------+---------------------+---------------------+---------- xx..&#x | 2 2 0 0 | 1 2 0 0 1 0 0 0 0 0 | 1 * * * * * * * * * | 1 0 1 0 0 ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 0 | * 2 * * * * * * * * | 1 1 0 0 0 oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 1 0 0 0 | * * 2 * * * * * * * | 0 1 1 0 0 x.x.&#x | 2 0 2 0 | 1 0 2 0 0 0 0 1 0 0 | * * * 1 * * * * * * | 1 0 0 1 0 o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 1 0 | * * * * 2 * * * * * | 0 1 0 1 0 x..x&#x | 2 0 0 2 | 1 0 0 2 0 0 0 0 0 1 | * * * * * 1 * * * * | 0 0 1 1 0 .xx.&#x | 0 2 2 0 | 0 0 0 0 1 2 0 1 0 0 | * * * * * * 1 * * * | 1 0 0 0 1 .ooo&#x | 0 1 1 1 | 0 0 0 0 0 1 1 0 1 0 | * * * * * * * 2 * * | 0 1 0 0 1 .x.x&#x | 0 2 0 2 | 0 0 0 0 1 0 2 0 0 1 | * * * * * * * * 1 * | 0 0 1 0 1 ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 0 1 2 1 | * * * * * * * * * 1 | 0 0 0 1 1 --------+---------+---------------------+---------------------+---------- xxx.&#x ♦ 2 2 2 0 | 1 2 2 0 1 2 0 1 0 0 | 1 2 0 1 0 0 1 0 0 0 | 1 * * * * oooo&#x ♦ 1 1 1 1 | 0 1 1 1 0 1 1 0 1 0 | 0 1 1 0 1 0 0 1 0 0 | * 2 * * * xx.x&#x ♦ 2 2 0 2 | 1 2 0 2 1 0 2 0 0 1 | 1 0 2 0 0 1 0 0 1 0 | * * 1 * * x.xx&#x ♦ 2 0 2 2 | 1 0 2 2 0 0 0 1 2 1 | 0 0 0 1 2 1 0 0 0 1 | * * * 1 * .xxx&#x ♦ 0 2 2 2 | 0 0 0 0 1 2 2 1 2 1 | 0 0 0 0 0 0 1 2 1 1 | * * * * 1
xxoo ooxx&#xr → height(1,2) = height(3,4) = 1 height(2,3) = height(4,1) = sqrt(3)/2 = 0.866025 (line || (para line || perp line) || perp line) o(..). o(..). | 2 * * * ♦ 1 1 2 0 0 0 0 0 | 1 2 1 2 0 0 0 | 1 2 1 0 .(o.). .(o.). | * 2 * * ♦ 0 1 0 1 2 0 0 0 | 1 0 0 2 2 1 0 | 0 2 1 1 .(.o). .(.o). | * * 2 * ♦ 0 0 2 0 0 1 1 0 | 0 1 2 2 0 0 1 | 1 1 2 0 .(..)o .(..)o | * * * 2 ♦ 0 0 0 0 2 0 1 1 | 0 0 0 2 1 2 1 | 0 1 2 1 -----------------+---------+-----------------+---------------+-------- x(..). .(..). | 2 0 0 0 | 1 * * * * * * * | 1 2 0 0 0 0 0 | 1 2 0 0 o(o.). o(o.).&#x | 1 1 0 0 | * 2 * * * * * * | 1 0 0 2 0 0 0 | 0 2 1 0 o(.o). o(.o).&#x | 1 0 1 0 | * * 4 * * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 .(x.). .(..). | 0 2 0 0 | * * * 1 * * * * | 1 0 0 0 2 0 0 | 0 2 0 1 .(o.)o .(o.)o&#x | 0 1 0 1 | * * * * 4 * * * | 0 0 0 1 1 1 0 | 0 1 1 1 .(..). .(.x). | 0 0 2 0 | * * * * * 1 * * | 0 0 2 0 0 0 1 | 1 0 2 0 .(.o)o .(.o)o&#x | 0 0 1 1 | * * * * * * 2 * | 0 0 0 2 0 0 1 | 0 1 2 0 .(..). .(..)x | 0 0 0 2 | * * * * * * * 1 | 0 0 0 0 0 2 1 | 0 0 2 1 -----------------+---------+-----------------+---------------+-------- x(x.). .(..).&#x | 2 2 0 0 | 1 2 0 1 0 0 0 0 | 1 * * * * * * | 0 2 0 0 x(.o). .(..).&#x | 2 0 1 0 | 1 0 2 0 0 0 0 0 | * 2 * * * * * | 1 1 0 0 .(..). o(.x).&#x | 1 0 2 0 | 0 0 2 0 0 1 0 0 | * * 2 * * * * | 1 0 1 0 oooo oooo&#xr | 1 1 1 1 | 0 1 1 0 1 0 1 0 | * * * 4 * * * | 0 1 1 0 .(x.)o .(..).&#x | 0 2 0 1 | 0 0 0 1 2 0 0 0 | * * * * 2 * * | 0 1 0 1 .(..). .(o.)x&#x | 0 1 0 2 | 0 0 0 0 2 0 0 1 | * * * * * 2 * | 0 0 1 1 .(..). .(.x)x&#x | 0 0 2 2 | 0 0 0 0 0 1 2 1 | * * * * * * 1 | 0 0 2 0 -----------------+---------+-----------------+---------------+-------- x(.o). o(.x).&#x ♦ 2 0 2 0 | 1 0 4 0 0 1 0 0 | 0 2 2 0 0 0 0 | 1 * * * xxoo ....&#xr ♦ 2 2 1 1 | 1 2 2 1 2 0 1 0 | 1 1 0 2 1 0 0 | * 2 * * .... ooxx&#xr ♦ 1 1 2 2 | 0 1 2 0 2 1 2 1 | 0 0 1 2 0 1 1 | * * 2 * .(x.)o .(o.)x&#x ♦ 0 2 0 2 | 0 0 0 1 4 0 0 1 | 0 0 0 0 2 2 0 | * * * 1
or o(..). o(..). & | 4 * ♦ 1 1 2 0 | 1 2 1 2 | 1 3 .(o.). .(o.). & | * 4 ♦ 0 1 2 1 | 1 1 2 2 | 1 3 -------------------+-----+---------+---------+---- x(..). .(..). & | 2 0 | 2 * * * | 1 2 0 0 | 1 2 o(o.). o(o.).&#x & | 1 1 | * 4 * * | 1 0 0 2 | 0 3 o(.o). o(.o).&#x & | 1 1 | * * 8 * | 0 1 1 1 | 1 2 .(x.). .(..). & | 0 2 | * * * 2 | 1 0 2 0 | 1 2 -------------------+-----+---------+---------+---- x(x.). .(..).&#x & | 2 2 | 1 2 0 1 | 2 * * * | 0 2 x(.o). .(..).&#x & | 2 1 | 1 0 2 0 | * 4 * * | 1 1 .(..). o(.x).&#x & | 1 2 | 0 0 2 1 | * * 4 * | 1 1 oooo oooo&#xr | 2 2 | 0 2 2 0 | * * * 4 | 0 2 -------------------+-----+---------+---------+---- x(.o). o(.x).&#x & ♦ 2 2 | 1 0 4 1 | 0 2 2 0 | 2 * xxoo ....&#xr & ♦ 3 3 | 1 3 4 1 | 1 1 1 2 | * 4
oxxo3oooo&#xr → height(2,3) = height(4,1) = 1 height(1,2) = height(3,4) = sqrt(2/3) = 0.816497 (type: (pt || {3}) || (pt || {3}) ) o...3o... | 1 * * * ♦ 3 1 0 0 0 0 | 3 3 0 0 0 0 | 1 3 0 0 .o..3.o.. | * 3 * * ♦ 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0 ..o.3..o. | * * 3 * ♦ 0 0 0 1 2 1 | 0 1 0 2 1 2 | 0 2 1 1 ...o3...o | * * * 1 ♦ 0 1 0 0 0 3 | 0 3 0 0 0 3 | 0 3 0 1 --------------+---------+-------------+-------------+-------- oo..3oo..&#x | 1 1 0 0 | 3 * * * * * | 2 1 0 0 0 0 | 1 2 0 0 o..o3o..o&#x | 1 0 0 1 | * 1 * * * * | 0 3 0 0 0 0 | 0 3 0 0 .x.. .... | 0 2 0 0 | * * 3 * * * | 1 0 1 1 0 0 | 1 1 1 0 .oo.3.oo.&#x | 0 1 1 0 | * * * 3 * * | 0 1 0 2 0 0 | 0 2 1 0 ..x. .... | 0 0 2 0 | * * * * 3 * | 0 0 0 1 1 1 | 0 1 1 1 ..oo3..oo&#x | 0 0 1 1 | * * * * * 3 | 0 1 0 0 0 2 | 0 2 0 1 --------------+---------+-------------+-------------+-------- ox.. ....&#x | 1 2 0 0 | 2 0 1 0 0 0 | 3 * * * * * | 1 1 0 0 oooo3oooo&#xr | 1 1 1 1 | 1 1 0 1 0 1 | * 3 * * * * | 0 2 0 0 .x..3.o.. | 0 3 0 0 | 0 0 3 0 0 0 | * * 1 * * * | 1 0 1 0 .xx. ....&#x | 0 2 2 0 | 0 0 1 2 1 0 | * * * 3 * * | 0 1 1 0 ..x.3..o. | 0 0 3 0 | 0 0 0 0 3 0 | * * * * 1 * | 0 0 1 1 ..xo ....&#x | 0 0 2 1 | 0 0 0 0 1 2 | * * * * * 3 | 0 1 0 1 --------------+---------+-------------+-------------+-------- ox..3oo..&#x ♦ 1 3 0 0 | 3 0 3 0 0 0 | 3 0 1 0 0 0 | 1 * * * oxxo ....&#xr ♦ 1 2 2 1 | 2 1 1 2 1 2 | 1 2 0 1 0 1 | * 3 * * .xx.3.oo.&#x ♦ 0 3 3 0 | 0 0 3 3 3 0 | 0 0 1 3 1 0 | * * 1 * ..xo3..oo&#x ♦ 0 0 3 1 | 0 0 0 0 3 3 | 0 0 0 0 1 3 | * * * 1
o(xo)x3o(oo)o&#xt (type: pt || ({3} || pt) || para {3}) o(..).3o(..). | 1 * * * ♦ 3 1 0 0 0 0 | 3 3 0 0 0 0 | 1 3 0 0 .(o.).3.(o.). | * 3 * * ♦ 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0 .(.o).3.(.o). | * * 1 * ♦ 0 1 0 0 3 0 | 0 3 0 0 3 0 | 0 3 0 1 .(..)o3.(..)o | * * * 3 ♦ 0 0 0 1 1 1 | 0 1 0 2 2 1 | 0 2 1 1 ------------------+---------+-------------+-------------+-------- o(o.).3o(o.).&#x | 1 1 0 0 | 3 * * * * * | 2 1 0 0 0 0 | 1 2 0 0 o(.o).3o(.o).&#x | 1 0 1 0 | * 1 * * * * | 0 3 0 0 0 0 | 0 3 0 0 .(x.). .(..). | 0 2 0 0 | * * 3 * * * | 1 0 1 1 0 0 | 1 1 1 0 .(o.)o3.(o.)o&#x | 0 1 0 1 | * * * 3 * * | 0 1 0 2 0 0 | 0 2 1 0 .(.o)o3.(.o)o&#x | 0 0 1 1 | * * * * 3 * | 0 1 0 0 2 0 | 0 2 0 1 .(..)x .(..). | 0 0 0 2 | * * * * * 3 | 0 0 0 1 1 1 | 0 1 1 1 ------------------+---------+-------------+-------------+-------- o(x.). .(..).&#x | 1 2 0 0 | 2 0 1 0 0 0 | 3 * * * * * | 1 1 0 0 o(oo)o o(oo)o&#xt | 1 1 1 1 | 1 1 0 1 1 0 | * 3 * * * * | 0 2 0 0 .(x.).3.(o.). | 0 3 0 0 | 0 0 3 0 0 0 | * * 1 * * * | 1 0 1 0 .(x.)x .(..).&#x | 0 2 0 2 | 0 0 1 2 0 1 | * * * 3 * * | 0 1 1 0 .(.o)x .(..).&#x | 0 0 1 2 | 0 0 0 0 2 1 | * * * * 3 * | 0 1 0 1 .(..)x3.(..)o | 0 0 0 3 | 0 0 0 0 0 3 | * * * * * 1 | 0 0 1 1 ------------------+---------+-------------+-------------+-------- o(x.).3o(o.).&#x ♦ 1 3 0 0 | 3 0 3 0 0 0 | 3 0 1 0 0 0 | 1 * * * o(xo)x .(..).&#xt ♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 3 * * .(x.)x3.(o.)o&#x ♦ 0 3 0 3 | 0 0 3 3 0 3 | 0 0 1 3 0 1 | * * 1 * .(.o)x3.(.o)o&#x ♦ 0 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 3 1 | * * * 1
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