Acronym ..., K-4.27
Name antitriwedge,
hexagon - octahedral wedge,
triangular gyrobicupolaic ring,
{6} || oct,
{3} || gyrated tricu,
1/6-luna of ico
Segmentochoron display
Circumradius 1
Lace city
in approx. ASCII-art
o3x   x3o
         
   x3x   
Dihedral angles
Confer
segmentochora family:
{2n} || n-ap  
related segmentochora:
oct || tricu   oct || co  
uniform relative:
ico  
general polytopal classes:
luna   segmentochora  

Incidence matrix according to Dynkin symbol

xxo3oxx&#x   → all heights = sqrt(2/3) = 0.816497

o..3o..    | 3 * * | 2 2 2 0 0 0 0 | 1 2 1 2 1 2 0 0 0 0 | 1 1 2 1 0
.o.3.o.    | * 6 * | 0 1 0 1 1 1 0 | 0 1 1 0 0 1 1 1 1 0 | 1 0 1 1 1
..o3..o    | * * 3 | 0 0 2 0 0 2 2 | 0 0 0 1 2 2 0 1 2 1 | 0 1 1 2 1
-----------+-------+---------------+---------------------+----------
x.. ...    | 2 0 0 | 3 * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
oo.3oo.&#x | 1 1 0 | * 6 * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
o.o3o.o&#x | 1 0 1 | * * 6 * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.x. ...    | 0 2 0 | * * * 3 * * * | 0 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0 2 0 | * * * * 3 * * | 0 0 1 0 0 0 1 0 1 0 | 1 0 0 1 1
.oo3.oo&#x | 0 1 1 | * * * * * 6 * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
... ..x    | 0 0 2 | * * * * * * 3 | 0 0 0 0 1 0 0 0 1 1 | 0 1 0 1 1
-----------+-------+---------------+---------------------+----------
x..3o..    | 3 0 0 | 3 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * 3 * * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * 3 * * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 0 | * * * 3 * * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 0 1 | * * * * 3 * * * * * | 0 1 0 1 0
ooo3ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * * 6 * * * * | 0 0 1 1 0
.x.3.x.    | 0 6 0 | 0 0 0 3 3 0 0 | * * * * * * 1 * * * | 1 0 0 0 1
.xo ...&#x | 0 2 1 | 0 0 0 1 0 2 0 | * * * * * * * 3 * * | 0 0 1 0 1
... .xx&#x | 0 2 2 | 0 0 0 0 1 2 1 | * * * * * * * * 3 * | 0 0 0 1 1
..o3..x    | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+---------------+---------------------+----------
xx.3ox.&#x  3 6 0 | 3 6 0 3 3 0 0 | 1 3 3 0 0 0 1 0 0 0 | 1 * * * *
x.o3o.x&#x  3 0 3 | 3 0 6 0 0 0 3 | 1 0 0 3 3 0 0 0 0 1 | * 1 * * *
xxo ...&#x  2 2 1 | 1 2 2 1 0 2 0 | 0 1 0 1 0 2 0 1 0 0 | * * 3 * *
... oxx&#x  1 2 2 | 0 2 2 0 1 2 1 | 0 0 1 0 1 2 0 0 1 0 | * * * 3 *
.xo3.xx&#x  0 6 3 | 0 0 0 3 3 6 3 | 0 0 0 0 0 0 1 3 3 1 | * * * * 1

os2xo6os&#x   → height = 1/sqrt(2) = 0.707107
({6} || oct)

      o.2o.6o.      | 6 * | 2  2 0 0 | 1 1 2 0 2 0 | 2 0 2
demi( .o2.o6.o    ) | * 6 | 0  2 2 2 | 0 2 1 1 2 3 | 1 1 3
--------------------+-----+----------+-------------+------
      .. x. ..      | 2 0 | 6  * * * | 1 0 1 0 1 0 | 2 0 1
demi( oo2oo6oo&#x ) | 1 1 | * 12 * * | 0 1 1 0 1 0 | 1 0 2
      .s .2 .s      | 0 2 | *  * 6 * | 0 1 0 0 0 2 | 0 1 2
sefa( .. .o6.s    ) | 0 2 | *  * * 6 | 0 0 0 1 1 1 | 1 1 1
--------------------+-----+----------+-------------+------
      .. x.6o.      | 6 0 | 6  0 0 0 | 1 * * * * * | 2 0 0
      os .2 os&#x   | 1 2 | 0  2 1 0 | * 6 * * * * | 0 0 2
demi( .. xo ..&#x ) | 2 1 | 1  2 0 0 | * * 6 * * * | 1 0 1
      .. .o6.s      | 0 3 | 0  0 0 3 | * * * 2 * * | 1 1 0
sefa( .. xo6os&#x ) | 2 2 | 1  2 0 1 | * * * * 6 * | 1 0 1
sefa( .s2.o6.s    ) | 0 3 | 0  0 2 1 | * * * * * 6 | 0 1 1
--------------------+-------+----------+-------------+------
      .. xo6os&#x    6 3 | 6  6 0 3 | 1 0 3 1 3 0 | 2 * *
      .s2.o6.s       0 6 | 0  0 6 6 | 0 0 0 2 0 6 | * 1 *
sefa( os2xo6os&#x )  2 3 | 1  4 2 1 | 0 2 1 0 1 1 | * * 6

starting figure: ox xo6ox&#x

{3} || gyro tricu   → height = 1/sqrt(2) = 0.707107

  3 * * | 2 2 2 0 0 0 0 | 1 2 2 1 2 1 0 0 0 0 | 1 1 2 1 0
  * 3 * | 0 2 0 2 2 0 0 | 0 1 0 2 2 0 1 2 1 0 | 1 0 1 2 1
  * * 6 | 0 0 1 0 1 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
--------+---------------+---------------------+----------
  2 0 0 | 3 * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
  1 1 0 | * 6 * * * * * | 0 1 0 1 1 0 0 0 0 0 | 1 0 1 1 0
  1 0 1 | * * 6 * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
  0 2 0 | * * * 3 * * * | 0 0 0 1 0 0 1 1 0 0 | 1 0 0 1 1
  0 1 1 | * * * * 6 * * | 0 0 0 0 1 0 0 1 1 0 | 0 0 1 1 1
  0 0 2 | * * * * * 3 * | 0 0 1 0 0 0 0 0 1 1 | 0 1 1 0 1
  0 0 2 | * * * * * * 3 | 0 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
--------+---------------+---------------------+----------
  3 0 0 | 3 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
  2 1 0 | 1 2 0 0 0 0 0 | * 3 * * * * * * * * | 1 0 1 0 0
  2 0 2 | 1 0 2 0 0 1 0 | * * 3 * * * * * * * | 0 1 1 0 0
  1 2 0 | 0 2 0 1 0 0 0 | * * * 3 * * * * * * | 1 0 0 1 0
  1 1 1 | 0 1 1 0 1 0 0 | * * * * 6 * * * * * | 0 0 1 1 0
  1 0 2 | 0 0 2 0 0 0 1 | * * * * * 3 * * * * | 0 1 0 1 0
  0 3 0 | 0 0 0 3 0 0 0 | * * * * * * 1 * * * | 1 0 0 0 1
  0 2 2 | 0 0 0 1 2 0 1 | * * * * * * * 3 * * | 0 0 0 1 1
  0 1 2 | 0 0 0 0 2 1 0 | * * * * * * * * 3 * | 0 0 1 0 1
  0 0 6 | 0 0 0 0 0 3 3 | * * * * * * * * * 1 | 0 1 0 0 1
--------+---------------+---------------------+----------
 3 3 0 | 3 6 0 3 0 0 0 | 1 3 0 3 0 0 1 0 0 0 | 1 * * * *
 3 0 6 | 3 0 6 0 0 3 3 | 1 0 3 0 0 3 0 0 0 1 | * 1 * * *
 2 1 2 | 1 2 2 0 2 1 0 | 0 1 1 0 2 0 0 0 1 0 | * * 3 * *
 1 2 2 | 0 2 2 1 2 0 1 | 0 0 0 1 2 1 0 1 0 0 | * * * 3 *
 0 3 6 | 0 0 0 3 6 3 3 | 0 0 0 0 0 0 1 3 3 1 | * * * * 1

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