Acronym squaw, K-4.64, {8} || squap
Name antitetrawedge,
octagon - square-antiprismatic wedge,
square gyrobicupolaic ring,
{8} || squap,
{4} || gyrated squacu
Segmentochoron display
Circumradius (1+sqrt(8))/sqrt(7) = 1.447009
Lace city
in approx. ASCII-art
    x4x    
           
x4o     o4x
Confer
related segmentochora:
coasirco  
segmentochora family:
{2n} || n-ap  
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

xxo4oxx&#x   → height(1,2) = height(2,3) = 1/sqrt(2) = 0.707107
               height(1,3) = 1/sqrt(sqrt(2)) = 0.840896

o..4o..    | 4 * * | 2 2 2 0 0 0 0 | 1 2 1 2 1 2 0 0 0 0 | 1 1 2 1 0
.o.4.o.    | * 8 * | 0 1 0 1 1 1 0 | 0 1 1 0 0 1 1 1 1 0 | 1 0 1 1 1
..o4..o    | * * 4 | 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 | 4 * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0
oo.4oo.&#x | 1 1 0 | * 8 * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
o.o4o.o&#x | 1 0 1 | * * 8 * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.x. ...    | 0 2 0 | * * * 4 * * * | 0 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0 2 0 | * * * * 4 * * | 0 0 1 0 0 0 1 0 1 0 | 1 0 0 1 1
.oo4.oo&#x | 0 1 1 | * * * * * 8 * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
... ..x    | 0 0 2 | * * * * * * 4 | 0 0 0 0 1 0 0 0 1 1 | 0 1 0 1 1
-----------+-------+---------------+---------------------+----------
x..4o..    | 4 0 0 | 4 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * 4 * * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * 4 * * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 0 | * * * 4 * * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 0 1 | * * * * 4 * * * * * | 0 1 0 1 0
ooo4ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * * 8 * * * * | 0 0 1 1 0
.x.4.x.    | 0 8 0 | 0 0 0 4 4 0 0 | * * * * * * 1 * * * | 1 0 0 0 1
.xo ...&#x | 0 2 1 | 0 0 0 1 0 2 0 | * * * * * * * 4 * * | 0 0 1 0 1
... .xx&#x | 0 2 2 | 0 0 0 0 1 2 1 | * * * * * * * * 4 * | 0 0 0 1 1
..o4..x    | 0 0 4 | 0 0 0 0 0 0 4 | * * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+---------------+---------------------+----------
xx.4ox.&#x  4 8 0 | 4 8 0 4 4 0 0 | 1 4 4 0 0 0 1 0 0 0 | 1 * * * *
x.o4o.x&#x  4 0 4 | 4 0 8 0 0 0 4 | 1 0 0 4 4 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 | * * 4 * *
... oxx&#x  1 2 2 | 0 2 2 0 1 2 1 | 0 0 1 0 1 2 0 0 1 0 | * * * 4 *
.xo4.xx&#x  0 8 4 | 0 0 0 4 4 8 4 | 0 0 0 0 0 0 1 4 4 1 | * * * * 1

os2xo8os&#x   → height = sqrt[(4-sqrt(2))/8] = 0.568527
({8} || squap)

      o.2o.8o.      | 8 * | 2  2 0 0 | 1 1 2 0 2 0 | 2 0 2
demi( .o2.o8.o    ) | * 8 | 0  2 2 2 | 0 2 1 1 2 3 | 1 1 3
--------------------+-----+----------+-------------+------
      .. x. ..      | 2 0 | 8  * * * | 1 0 1 0 1 0 | 2 0 1
demi( oo2oo8oo&#x ) | 1 1 | * 16 * * | 0 1 1 0 1 0 | 1 0 2
      .s .2 .s      | 0 2 | *  * 8 * | 0 1 0 0 0 2 | 0 1 2
sefa( .. .o8.s    ) | 0 2 | *  * * 8 | 0 0 0 1 1 1 | 1 1 1
--------------------+-----+----------+-------------+------
      .. x.8o.      | 8 0 | 8  0 0 0 | 1 * * * * * | 2 0 0
      os .2 os&#x   | 1 2 | 0  2 1 0 | * 8 * * * * | 0 0 2
demi( .. xo ..&#x ) | 2 1 | 1  2 0 0 | * * 8 * * * | 1 0 1
      .. .o8.s      | 0 4 | 0  0 0 4 | * * * 2 * * | 1 1 0
sefa( .. xo8os&#x ) | 2 2 | 1  2 0 1 | * * * * 8 * | 1 0 1
sefa( .s2.o8.s    ) | 0 3 | 0  0 2 1 | * * * * * 8 | 0 1 1
--------------------+-----+----------+-------------+------
      .. xo8os&#x    8 4 | 8  8 0 4 | 1 0 4 1 4 0 | 2 * *
      .s2.o8.s       0 8 | 0  0 8 8 | 0 0 0 2 0 8 | * 1 *
sefa( os2xo8os&#x )  2 3 | 1  4 2 1 | 0 2 1 0 1 1 | * * 8

starting figure: ox xo8ox&#x

{4} || gyro squacu   → height = sqrt[sqrt(8)-1]/2 = 0.676097

  4 * * | 2 2 2 0 0 0 0 | 1 2 2 1 2 1 0 0 0 0 | 1 1 2 1 0
  * 4 * | 0 2 0 2 2 0 0 | 0 1 0 2 2 0 1 2 1 0 | 1 0 1 2 1
  * * 8 | 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 | 4 * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
  1 1 0 | * 8 * * * * * | 0 1 0 1 1 0 0 0 0 0 | 1 0 1 1 0
  1 0 1 | * * 8 * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
  0 2 0 | * * * 4 * * * | 0 0 0 1 0 0 1 1 0 0 | 1 0 0 1 1
  0 1 1 | * * * * 8 * * | 0 0 0 0 1 0 0 1 1 0 | 0 0 1 1 1
  0 0 2 | * * * * * 4 * | 0 0 1 0 0 0 0 0 1 1 | 0 1 1 0 1
  0 0 2 | * * * * * * 4 | 0 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
--------+---------------+---------------------+----------
  4 0 0 | 4 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0
  2 1 0 | 1 2 0 0 0 0 0 | * 4 * * * * * * * * | 1 0 1 0 0
  2 0 2 | 1 0 2 0 0 1 0 | * * 4 * * * * * * * | 0 1 1 0 0
  1 2 0 | 0 2 0 1 0 0 0 | * * * 4 * * * * * * | 1 0 0 1 0
  1 1 1 | 0 1 1 0 1 0 0 | * * * * 8 * * * * * | 0 0 1 1 0
  1 0 2 | 0 0 2 0 0 0 1 | * * * * * 4 * * * * | 0 1 0 1 0
  0 4 0 | 0 0 0 4 0 0 0 | * * * * * * 1 * * * | 1 0 0 0 1
  0 2 2 | 0 0 0 1 2 0 1 | * * * * * * * 4 * * | 0 0 0 1 1
  0 1 2 | 0 0 0 0 2 1 0 | * * * * * * * * 4 * | 0 0 1 0 1
  0 0 8 | 0 0 0 0 0 4 4 | * * * * * * * * * 1 | 0 1 0 0 1
--------+---------------+---------------------+----------
 4 4 0 | 4 8 0 4 0 0 0 | 1 4 0 4 0 0 1 0 0 0 | 1 * * * *
 4 0 8 | 4 0 8 0 0 4 4 | 1 0 4 0 0 4 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 | * * 4 * *
 1 2 2 | 0 2 2 1 2 0 1 | 0 0 0 1 2 1 0 1 0 0 | * * * 4 *
 0 4 8 | 0 0 0 4 8 4 4 | 0 0 0 0 0 0 1 4 4 1 | * * * * 1

© 2004-2019
top of page