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
|,>,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
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.
Dihedral angles
  • at {3} between tet and trip:   90°
  • at {4} between trip and trip:   arccos(1/3) = 70.528779°
Confer
variations:
q x3o3o  
more general:
n-cuf
general polytopal classes:
segmentochora  
External
links
hedrondude   wikipedia

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 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

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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