Acronym toagircoatic
Name toe atop girco atop tic
Lace city
in approx. ASCII-art
    o4x   o4u   q4x   o4u   o4x    
                                   
x4x   x4u   w4x     w4x   x4u   x4x
                                   
                                   
      x4x   w4o     w4o   x4x      
Dihedral angles
(at margins)
  • at {4} between hip and trip (within upper segment):   arccos(-sqrt[8/9]) = 160.528779°
  • at {6} between hip and toe:   150°
  • at {3} between squacu and trip:   150°
  • at {3} between tricu and trip (within lower segment):   150°
  • at {4} between hip and squacu:   arccos(-sqrt[2/3]) = 144.735610°
  • at {4} between op and trip:   arccos(-sqrt[2/3]) = 144.735610°
  • at {8} between op and tic:   135°
  • at {4} between op and tricu:   135°
  • at {4} between squacu and toe:   135°
  • at {3} between tic and tricu:   120°
  • at {6} between hip and tricu (across rim):   90°
  • at {8} between op and squacu (across rim):   90°
  • at {4} between trip and trip (across rim):   90°
Confer
segmentochora:
toagirco   ticagirco  
general polytopal classes:
bistratic lace towers  

This polychoron is a mere stack of 2 segmentochora. None the less it is special in that all dihedrals of the rim independently equate to 90°.


Incidence matrix according to Dynkin symbol

xxo3xxx4oxx&#xt   → height(1,2) = 1/2
                    height(2,3) = 1/sqrt(2) = 0.707107
(toe || pseudo girco || tic)

o..3o..4o..    | 24  *  * |  1  2  2  0  0  0  0  0  0 | 2 1  2  2  1 0  0 0  0  0  0 0 0 | 1 2  1 1 0  0 0 0
.o.3.o.4.o.    |  * 48  * |  0  0  1  1  1  1  1  0  0 | 0 0  1  1  1 1  1 1  1  1  1 0 0 | 0 1  1 1 1  1 1 0
..o3..o4..o    |  *  * 24 |  0  0  0  0  0  0  2  2  1 | 0 0  0  0  0 0  0 0  1  2  2 1 2 | 0 0  0 0 1  1 2 1
---------------+----------+----------------------------+----------------------------------+------------------
x.. ... ...    |  2  0  0 | 12  *  *  *  *  *  *  *  * | 2 0  2  0  0 0  0 0  0  0  0 0 0 | 1 2  1 0 0  0 0 0
... x.. ...    |  2  0  0 |  * 24  *  *  *  *  *  *  * | 1 1  0  1  0 0  0 0  0  0  0 0 0 | 1 1  0 1 0  0 0 0
oo.3oo.4oo.&#x |  1  1  0 |  *  * 48  *  *  *  *  *  * | 0 0  1  1  1 0  0 0  0  0  0 0 0 | 0 1  1 1 0  0 0 0
.x. ... ...    |  0  2  0 |  *  *  * 24  *  *  *  *  * | 0 0  1  0  0 1  1 0  1  0  0 0 0 | 0 1  1 0 1  1 0 0
... .x. ...    |  0  2  0 |  *  *  *  * 24  *  *  *  * | 0 0  0  1  0 1  0 1  0  1  0 0 0 | 0 1  0 1 1  0 1 0
... ... .x.    |  0  2  0 |  *  *  *  *  * 24  *  *  * | 0 0  0  0  1 0  1 1  0  0  1 0 0 | 0 0  1 1 0  1 1 0
.oo3.oo4.oo&#x |  0  1  1 |  *  *  *  *  *  * 48  *  * | 0 0  0  0  0 0  0 0  1  1  1 0 0 | 0 0  0 0 1  1 1 0
... ..x ...    |  0  0  2 |  *  *  *  *  *  *  * 24  * | 0 0  0  0  0 0  0 0  0  1  0 1 1 | 0 0  0 0 1  0 1 1
... ... ..x    |  0  0  2 |  *  *  *  *  *  *  *  * 12 | 0 0  0  0  0 0  0 0  0  0  2 0 2 | 0 0  0 0 0  1 2 1
---------------+----------+----------------------------+----------------------------------+------------------
x..3x.. ...    |  6  0  0 |  3  3  0  0  0  0  0  0  0 | 8 *  *  *  * *  * *  *  *  * * * | 1 1  0 0 0  0 0 0
... x..4o..    |  4  0  0 |  0  4  0  0  0  0  0  0  0 | * 6  *  *  * *  * *  *  *  * * * | 1 0  0 1 0  0 0 0
xx. ... ...&#x |  2  2  0 |  1  0  2  1  0  0  0  0  0 | * * 24  *  * *  * *  *  *  * * * | 0 1  1 0 0  0 0 0
... xx. ...&#x |  2  2  0 |  0  1  2  0  1  0  0  0  0 | * *  * 24  * *  * *  *  *  * * * | 0 1  0 1 0  0 0 0
... ... ox.&#x |  1  2  0 |  0  0  2  0  0  1  0  0  0 | * *  *  * 24 *  * *  *  *  * * * | 0 0  1 1 0  0 0 0
.x.3.x. ...    |  0  6  0 |  0  0  0  3  3  0  0  0  0 | * *  *  *  * 8  * *  *  *  * * * | 0 1  0 0 1  0 0 0
.x. ... .x.    |  0  4  0 |  0  0  0  2  0  2  0  0  0 | * *  *  *  * * 12 *  *  *  * * * | 0 0  1 0 0  1 0 0
... .x.4.x.    |  0  8  0 |  0  0  0  0  4  4  0  0  0 | * *  *  *  * *  * 6  *  *  * * * | 0 0  0 1 0  0 1 0
.xo ... ...&#x |  0  2  1 |  0  0  0  1  0  0  2  0  0 | * *  *  *  * *  * * 24  *  * * * | 0 0  0 0 1  1 0 0
... .xx ...&#x |  0  2  2 |  0  0  0  0  1  0  2  1  0 | * *  *  *  * *  * *  * 24  * * * | 0 0  0 0 1  0 1 0
... ... .xx&#x |  0  2  2 |  0  0  0  0  0  1  2  0  1 | * *  *  *  * *  * *  *  * 24 * * | 0 0  0 0 0  1 1 0
..o3..x ...    |  0  0  3 |  0  0  0  0  0  0  0  3  0 | * *  *  *  * *  * *  *  *  * 8 * | 0 0  0 0 1  0 0 1
... ..x4..x    |  0  0  8 |  0  0  0  0  0  0  0  4  4 | * *  *  *  * *  * *  *  *  * * 6 | 0 0  0 0 0  0 1 1
---------------+----------+----------------------------+----------------------------------+------------------
x..3x..4o..     24  0  0 | 12 24  0  0  0  0  0  0  0 | 8 6  0  0  0 0  0 0  0  0  0 0 0 | 1 *  * * *  * * *
xx.3xx. ...&#x   6  6  0 |  3  3  6  3  3  0  0  0  0 | 1 0  3  3  0 1  0 0  0  0  0 0 0 | * 8  * * *  * * *
xx. ... ox.&#x   2  4  0 |  1  0  4  2  0  2  0  0  0 | 0 0  2  0  2 0  1 0  0  0  0 0 0 | * * 12 * *  * * *
... xx.4ox.&#x   4  8  0 |  0  4  8  0  4  4  0  0  0 | 0 1  0  4  4 0  0 1  0  0  0 0 0 | * *  * 6 *  * * *
.xo3.xx ...&#x   0  6  3 |  0  0  0  3  3  0  6  3  0 | 0 0  0  0  0 1  0 0  3  3  0 1 0 | * *  * * 8  * * *
.xo ... .xx&#x   0  4  2 |  0  0  0  2  0  2  4  0  1 | 0 0  0  0  0 0  1 0  2  0  2 0 0 | * *  * * * 12 * *
... .xx4.xx&#x   0  8  8 |  0  0  0  0  4  4  8  4  4 | 0 0  0  0  0 0  0 1  0  4  4 0 1 | * *  * * *  * 6 *
..o3..x4..x      0  0 24 |  0  0  0  0  0  0  0 24 12 | 0 0  0  0  0 0  0 0  0  0  0 8 6 | * *  * * *  * * 1

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