Acronym ...
Name hex atop octaco,
rap atop alt. tetaco,
0.323792-lune of rat,
tet-first lune of rat,
(oct,tet,dual tet,co)-cycle lace ring
Circumradius 1
Lace city
in approx. ASCII-art 
o3x3o   x3o3o   
                
                
   x3o3x   o3o3x
Dihedral angles
  • at oct between rap and rap:   arccos(-3/5) = 126.869898°
  • at co between octaco and tetaco:   arccos[-1/sqrt(5)] = 116.565051°
  • at tet between hex and rap:   arccos[-1/sqrt(5)] = 116.565051°
  • at oct between octaco and rap:   arccos(1/sqrt(5)) = 63.434949°
  • at tet between hex and tetaco:   arccos(1/sqrt(5)) = 63.434949°
  • ...
Face vector 26, 120, 180, 106, 22
Confer
uniform relative:
rat  
related segmentotera:
rapaspid   hexaico  
general polytopal classes:
segmentotera  

The dihedral angle at co between octaco and tetaco is arccos[-1/sqrt(5)] = 116.565051°, which is 0.323792 of the full circle.


Incidence matrix according to Dynkin symbol

oxox3xooo3ooxx&#xr   → height(1,2) = height(3,4) = sqrt(5/8) = 0.790569
                       height(1,4) = height(2,3) = 1/sqrt(2) = 0.707107
                       height(12,34) = sqrt(2/5) = 0.632456 (as: rap || alt. tetaco)
                       height(14,23) = 1/sqrt(2) = 0.707107 (as: hex || octaco)
(cycle of oct, tet, dual tet, co)

o...3o...3o...     | 6 * *  * |  4  2  4 0  0  0 0  0  0  0 | 2 2 1  4  4  2  4  2 0  0  0  0  0 0  0  0 0 0 0 | 1 2 2  2  4  2 2 1 2 0 0 0 0  0 0 0 0 0 0 0 | 1 2 1 2 1 0 0 0
.o..3.o..3.o..     | * 4 *  * ♦  0  3  0 3  3  3 0  0  0  0 | 0 0 3  3  6  0  0  0 3  6  3  3  3 0  0  0 0 0 0 | 0 3 1  6  3  3 0 0 0 1 3 3 1  3 1 0 0 0 0 0 | 1 3 3 1 0 1 1 0
..o.3..o.3..o.     | * * 4  * |  0  0  0 0  3  0 3  3  0  0 | 0 0 0  0  0  0  0  0 0  3  6  3  0 3  3  6 0 0 0 | 0 0 0  3  0  0 0 0 0 0 1 3 3  6 0 1 1 3 3 0 | 0 1 3 0 0 1 3 1
...o3...o3...o     | * * * 12 |  0  0  2 0  0  1 0  1  2  2 | 0 0 0  0  2  2  1  2 0  0  0  1  2 0  2  2 1 2 1 | 0 0 0  2  1  2 1 2 1 0 0 0 0  2 1 0 1 2 1 1 | 0 1 2 1 1 0 1 1
-------------------+----------+-----------------------------+--------------------------------------------------+---------------------------------------------+----------------
.... x... ....     | 2 0 0  0 | 12  *  * *  *  * *  *  *  * | 1 1 0  1  0  0  1  0 0  0  0  0  0 0  0  0 0 0 0 | 1 1 1  0  1  0 1 0 1 0 0 0 0  0 0 0 0 0 0 0 | 1 1 0 1 1 0 0 0
oo..3oo..3oo..&#x  | 1 1 0  0 |  * 12  * *  *  * *  *  *  * | 0 0 1  2  2  0  0  0 0  0  0  0  0 0  0  0 0 0 0 | 0 2 1  2  2  1 0 0 0 0 0 0 0  0 0 0 0 0 0 0 | 1 2 1 1 0 0 0 0
o..o3o..o3o..o&#x  | 1 0 0  1 |  *  * 24 *  *  * *  *  *  * | 0 0 0  0  1  1  1  1 0  0  0  0  0 0  0  0 0 0 0 | 0 0 0  1  1  1 1 1 1 0 0 0 0  0 0 0 0 0 0 0 | 0 1 1 1 1 0 0 0
.x.. .... ....     | 0 2 0  0 |  *  *  * 6  *  * *  *  *  * | 0 0 1  0  0  0  0  0 2  2  0  0  0 0  0  0 0 0 0 | 0 2 0  2  0  0 0 0 0 1 2 1 0  0 0 0 0 0 0 0 | 1 2 1 0 0 1 0 0
.oo.3.oo.3.oo.&#x  | 0 1 1  0 |  *  *  * * 12  * *  *  *  * | 0 0 0  0  0  0  0  0 0  2  2  1  0 0  0  0 0 0 0 | 0 0 0  2  0  0 0 0 0 0 1 2 1  2 0 0 0 0 0 0 | 0 1 2 0 0 1 1 0
.o.o3.o.o3.o.o&#x  | 0 1 0  1 |  *  *  * *  * 12 *  *  *  * | 0 0 0  0  2  0  0  0 0  0  0  1  2 0  0  0 0 0 0 | 0 0 0  2  1  2 0 0 0 0 0 0 0  2 1 0 0 0 0 0 | 0 1 2 1 0 0 1 0
.... .... ..x.     | 0 0 2  0 |  *  *  * *  *  * 6  *  *  * | 0 0 0  0  0  0  0  0 0  0  2  0  0 2  0  2 0 0 0 | 0 0 0  0  0  0 0 0 0 0 0 1 2  2 0 1 0 1 2 0 | 0 0 1 0 0 1 2 1
..oo3..oo3..oo&#x  | 0 0 1  1 |  *  *  * *  *  * * 12  *  * | 0 0 0  0  0  0  0  0 0  0  0  1  0 0  2  2 0 0 0 | 0 0 0  2  0  0 0 0 0 0 0 0 0  2 0 0 1 2 1 0 | 0 1 2 0 0 0 1 1
...x .... ....     | 0 0 0  2 |  *  *  * *  *  * *  * 12  * | 0 0 0  0  0  1  0  0 0  0  0  0  0 0  1  0 1 1 0 | 0 0 0  1  0  0 1 1 0 0 0 0 0  0 0 0 1 1 0 1 | 0 1 1 0 1 0 0 1
.... .... ...x     | 0 0 0  2 |  *  *  * *  *  * *  *  * 12 | 0 0 0  0  0  0  0  1 0  0  0  0  1 0  0  1 0 1 1 | 0 0 0  0  0  1 0 1 1 0 0 0 0  1 1 0 0 1 1 1 | 0 0 1 1 1 0 1 1
-------------------+----------+-----------------------------+--------------------------------------------------+---------------------------------------------+----------------
o...3x... ....     | 3 0 0  0 |  3  0  0 0  0  0 0  0  0  0 | 4 * *  *  *  *  *  * *  *  *  *  * *  *  * * * * | 1 1 0  0  0  0 1 0 0 0 0 0 0  0 0 0 0 0 0 0 | 1 1 0 0 1 0 0 0
.... x...3o...     | 3 0 0  0 |  3  0  0 0  0  0 0  0  0  0 | * 4 *  *  *  *  *  * *  *  *  *  * *  *  * * * * | 1 0 1  0  0  0 0 0 1 0 0 0 0  0 0 0 0 0 0 0 | 1 0 0 1 1 0 0 0
ox.. .... ....&#x  | 1 2 0  0 |  0  2  0 1  0  0 0  0  0  0 | * * 6  *  *  *  *  * *  *  *  *  * *  *  * * * * | 0 2 0  2  0  0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0
.... xo.. ....&#x  | 2 1 0  0 |  1  2  0 0  0  0 0  0  0  0 | * * * 12  *  *  *  * *  *  *  *  * *  *  * * * * | 0 1 1  0  1  0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 | 1 1 0 1 0 0 0 0
oo.o3oo.o3oo.o&#x  | 1 1 0  1 |  0  1  1 0  0  1 0  0  0  0 | * * *  * 24  *  *  * *  *  *  *  * *  *  * * * * | 0 0 0  1  1  1 0 0 0 0 0 0 0  0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
o..x .... ....&#x  | 1 0 0  2 |  0  0  2 0  0  0 0  0  1  0 | * * *  *  * 12  *  * *  *  *  *  * *  *  * * * * | 0 0 0  1  0  0 1 1 0 0 0 0 0  0 0 0 0 0 0 0 | 0 1 1 0 1 0 0 0
.... x..o ....&#x  | 2 0 0  1 |  1  0  2 0  0  0 0  0  0  0 | * * *  *  *  * 12  * *  *  *  *  * *  *  * * * * | 0 0 0  0  1  0 1 0 1 0 0 0 0  0 0 0 0 0 0 0 | 0 1 0 1 1 0 0 0
.... .... o..x&#x  | 1 0 0  2 |  0  0  2 0  0  0 0  0  0  1 | * * *  *  *  *  * 12 *  *  *  *  * *  *  * * * * | 0 0 0  0  0  1 0 1 1 0 0 0 0  0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 0
.x..3.o.. ....     | 0 3 0  0 |  0  0  0 3  0  0 0  0  0  0 | * * *  *  *  *  *  * 4  *  *  *  * *  *  * * * * | 0 1 0  0  0  0 0 0 0 1 1 0 0  0 0 0 0 0 0 0 | 1 1 0 0 0 1 0 0
.xo. .... ....&#x  | 0 2 1  0 |  0  0  0 1  2  0 0  0  0  0 | * * *  *  *  *  *  * * 12  *  *  * *  *  * * * * | 0 0 0  1  0  0 0 0 0 0 1 1 0  0 0 0 0 0 0 0 | 0 1 1 0 0 1 0 0
.... .... .ox.&#x  | 0 1 2  0 |  0  0  0 0  2  0 1  0  0  0 | * * *  *  *  *  *  * *  * 12  *  * *  *  * * * * | 0 0 0  0  0  0 0 0 0 0 0 1 1  1 0 0 0 0 0 0 | 0 0 1 0 0 1 1 0
.ooo3.ooo3.ooo&#x  | 0 1 1  1 |  0  0  0 0  1  1 0  1  0  0 | * * *  *  *  *  *  * *  *  * 12  * *  *  * * * * | 0 0 0  2  0  0 0 0 0 0 0 0 0  2 0 0 0 0 0 0 | 0 1 2 0 0 0 1 0
.... .... .o.x&#x  | 0 1 0  2 |  0  0  0 0  0  2 0  0  0  1 | * * *  *  *  *  *  * *  *  *  * 12 *  *  * * * * | 0 0 0  0  0  1 0 0 0 0 0 0 0  1 1 0 0 0 0 0 | 0 0 1 1 0 0 1 0
.... ..o.3..x.     | 0 0 3  0 |  0  0  0 0  0  0 3  0  0  0 | * * *  *  *  *  *  * *  *  *  *  * 4  *  * * * * | 0 0 0  0  0  0 0 0 0 0 0 0 1  0 0 1 0 0 1 0 | 0 0 0 0 0 1 1 1
..ox .... ....&#x  | 0 0 1  2 |  0  0  0 0  0  0 0  2  1  0 | * * *  *  *  *  *  * *  *  *  *  * * 12  * * * * | 0 0 0  1  0  0 0 0 0 0 0 0 0  0 0 0 1 1 0 0 | 0 1 1 0 0 0 0 1
.... .... ..xx&#x  | 0 0 2  2 |  0  0  0 0  0  0 1  2  0  1 | * * *  *  *  *  *  * *  *  *  *  * *  * 12 * * * | 0 0 0  0  0  0 0 0 0 0 0 0 0  1 0 0 0 1 1 0 | 0 0 1 0 0 0 1 1
...x3...o ....     | 0 0 0  3 |  0  0  0 0  0  0 0  0  3  0 | * * *  *  *  *  *  * *  *  *  *  * *  *  * 4 * * | 0 0 0  0  0  0 1 0 0 0 0 0 0  0 0 0 1 0 0 1 | 0 1 0 0 1 0 0 1
...x .... ...x     | 0 0 0  4 |  0  0  0 0  0  0 0  0  2  2 | * * *  *  *  *  *  * *  *  *  *  * *  *  * * 6 * | 0 0 0  0  0  0 0 1 0 0 0 0 0  0 0 0 0 1 0 1 | 0 0 1 0 1 0 0 1
.... ...o3...x     | 0 0 0  3 |  0  0  0 0  0  0 0  0  0  3 | * * *  *  *  *  *  * *  *  *  *  * *  *  * * * 4 | 0 0 0  0  0  0 0 0 1 0 0 0 0  0 1 0 0 0 1 1 | 0 0 0 1 1 0 1 1
-------------------+----------+-----------------------------+--------------------------------------------------+---------------------------------------------+----------------
o...3x...3o...     ♦ 6 0 0  0 | 12  0  0 0  0  0 0  0  0  0 | 4 4 0  0  0  0  0  0 0  0  0  0  0 0  0  0 0 0 0 | 1 * *  *  *  * * * * * * * *  * * * * * * * | 1 0 0 0 1 0 0 0
ox..3xo.. ....&#x  ♦ 3 3 0  0 |  3  6  0 3  0  0 0  0  0  0 | 1 0 3  3  0  0  0  0 1  0  0  0  0 0  0  0 0 0 0 | * 4 *  *  *  * * * * * * * *  * * * * * * * | 1 1 0 0 0 0 0 0
.... xo..3oo..&#x  ♦ 3 1 0  0 |  3  3  0 0  0  0 0  0  0  0 | 0 1 0  3  0  0  0  0 0  0  0  0  0 0  0  0 0 0 0 | * * 4  *  *  * * * * * * * *  * * * * * * * | 1 0 0 1 0 0 0 0
oxox .... ....&#xr ♦ 1 2 1  2 |  0  2  2 1  2  2 0  2  1  0 | 0 0 1  0  2  1  0  0 0  1  0  2  0 0  1  0 0 0 0 | * * * 12  *  * * * * * * * *  * * * * * * * | 0 1 1 0 0 0 0 0
.... xo.o ....&#x  ♦ 2 1 0  1 |  1  2  2 0  0  1 0  0  0  0 | 0 0 0  1  2  0  1  0 0  0  0  0  0 0  0  0 0 0 0 | * * *  * 12  * * * * * * * *  * * * * * * * | 0 1 0 1 0 0 0 0
.... .... oo.x&#x  ♦ 1 1 0  2 |  0  1  2 0  0  2 0  0  0  1 | 0 0 0  0  2  0  0  1 0  0  0  0  1 0  0  0 0 0 0 | * * *  *  * 12 * * * * * * *  * * * * * * * | 0 0 1 1 0 0 0 0
o..x3x..o ....&#x  ♦ 3 0 0  3 |  3  0  6 0  0  0 0  0  3  0 | 1 0 0  0  0  3  3  0 0  0  0  0  0 0  0  0 1 0 0 | * * *  *  *  * 4 * * * * * *  * * * * * * * | 0 1 0 0 1 0 0 0
o..x .... o..x&#x  ♦ 1 0 0  4 |  0  0  4 0  0  0 0  0  2  2 | 0 0 0  0  0  2  0  2 0  0  0  0  0 0  0  0 0 1 0 | * * *  *  *  * * 6 * * * * *  * * * * * * * | 0 0 1 0 1 0 0 0
.... x..o3o..x&#x  ♦ 3 0 0  3 |  3  0  6 0  0  0 0  0  0  3 | 0 1 0  0  0  0  3  3 0  0  0  0  0 0  0  0 0 0 1 | * * *  *  *  * * * 4 * * * *  * * * * * * * | 0 0 0 1 1 0 0 0
.x..3.o..3.o..     ♦ 0 4 0  0 |  0  0  0 6  0  0 0  0  0  0 | 0 0 0  0  0  0  0  0 4  0  0  0  0 0  0  0 0 0 0 | * * *  *  *  * * * * 1 * * *  * * * * * * * | 1 0 0 0 0 1 0 0
.xo.3.oo. ....&#x  ♦ 0 3 1  0 |  0  0  0 3  3  0 0  0  0  0 | 0 0 0  0  0  0  0  0 1  3  0  0  0 0  0  0 0 0 0 | * * *  *  *  * * * * * 4 * *  * * * * * * * | 0 1 0 0 0 1 0 0
.xo. .... .ox.&#x  ♦ 0 2 2  0 |  0  0  0 1  4  0 1  0  0  0 | 0 0 0  0  0  0  0  0 0  2  2  0  0 0  0  0 0 0 0 | * * *  *  *  * * * * * * 6 *  * * * * * * * | 0 0 1 0 0 1 0 0
.... .oo.3.ox.&#x  ♦ 0 1 3  0 |  0  0  0 0  3  0 3  0  0  0 | 0 0 0  0  0  0  0  0 0  0  3  0  0 1  0  0 0 0 0 | * * *  *  *  * * * * * * * 4  * * * * * * * | 0 0 0 0 0 1 1 0
.... .... .oxx&#x  ♦ 0 1 2  2 |  0  0  0 0  2  2 1  2  0  1 | 0 0 0  0  0  0  0  0 0  0  1  2  1 0  0  1 0 0 0 | * * *  *  *  * * * * * * * * 12 * * * * * * | 0 0 1 0 0 0 1 0
.... .o.o3.o.x&#x  ♦ 0 1 0  3 |  0  0  0 0  0  3 0  0  0  3 | 0 0 0  0  0  0  0  0 0  0  0  0  3 0  0  0 0 0 1 | * * *  *  *  * * * * * * * *  * 4 * * * * * | 0 0 0 1 0 0 1 0
..o.3..o.3..x.     ♦ 0 0 4  0 |  0  0  0 0  0  0 6  0  0  0 | 0 0 0  0  0  0  0  0 0  0  0  0  0 4  0  0 0 0 0 | * * *  *  *  * * * * * * * *  * * 1 * * * * | 0 0 0 0 0 1 0 1
..ox3..oo ....&#x  ♦ 0 0 1  3 |  0  0  0 0  0  0 0  3  3  0 | 0 0 0  0  0  0  0  0 0  0  0  0  0 0  3  0 1 0 0 | * * *  *  *  * * * * * * * *  * * * 4 * * * | 0 1 0 0 0 0 0 1
..ox .... ..xx&#x  ♦ 0 0 2  4 |  0  0  0 0  0  0 1  4  2  2 | 0 0 0  0  0  0  0  0 0  0  0  0  0 0  2  2 0 1 0 | * * *  *  *  * * * * * * * *  * * * * 6 * * | 0 0 1 0 0 0 0 1
.... ..oo3..xx&#x  ♦ 0 0 3  3 |  0  0  0 0  0  0 3  3  0  3 | 0 0 0  0  0  0  0  0 0  0  0  0  0 1  0  3 0 0 1 | * * *  *  *  * * * * * * * *  * * * * * 4 * | 0 0 0 0 0 0 1 1
...x3...o3...x     ♦ 0 0 0 12 |  0  0  0 0  0  0 0  0 12 12 | 0 0 0  0  0  0  0  0 0  0  0  0  0 0  0  0 4 6 4 | * * *  *  *  * * * * * * * *  * * * * * * 1 | 0 0 0 0 1 0 0 1
-------------------+----------+-----------------------------+--------------------------------------------------+---------------------------------------------+----------------
ox..3xo..3oo..&#x  ♦ 6 4 0  0 | 12 12  0 6  0  0 0  0  0  0 | 4 4 6 12  0  0  0  0 4  0  0  0  0 0  0  0 0 0 0 | 1 4 4  0  0  0 0 0 0 1 0 0 0  0 0 0 0 0 0 0 | 1 * * * * * * *
oxox3xooo ....&#xr ♦ 3 3 1  3 |  3  6  6 3  3  3 0  3  3  0 | 1 0 3  3  6  3  3  0 1  3  0  3  0 0  3  0 1 0 0 | 0 1 0  3  3  0 1 0 0 0 1 0 0  0 0 0 1 0 0 0 | * 4 * * * * * *
oxox .... ooxx&#xr ♦ 1 2 2  4 |  0  2  4 1  4  4 1  4  2  2 | 0 0 1  0  4  2  0  2 0  2  2  4  2 0  2  2 0 1 0 | 0 0 0  2  0  2 0 1 0 0 0 1 0  2 0 0 0 1 0 0 | * * 6 * * * * *
.... xo.o3oo.x&#x  ♦ 3 1 0  3 |  3  3  6 0  0  3 0  0  0  3 | 0 1 0  3  6  0  3  3 0  0  0  0  3 0  0  0 0 0 1 | 0 0 1  0  3  3 0 0 1 0 0 0 0  0 1 0 0 0 0 0 | * * * 4 * * * *
o..x3x..o3o..x&#x  ♦ 6 0 0 12 | 12  0 24 0  0  0 0  0 12 12 | 4 4 0  0  0 12 12 12 0  0  0  0  0 0  0  0 4 6 4 | 1 0 0  0  0  0 4 6 4 0 0 0 0  0 0 0 0 0 0 1 | * * * * 1 * * *
.xo.3.oo.3.ox.&#x  ♦ 0 4 4  0 |  0  0  0 6 12  0 6  0  0  0 | 0 0 0  0  0  0  0  0 4 12 12  0  0 4  0  0 0 0 0 | 0 0 0  0  0  0 0 0 0 1 4 6 4  0 0 1 0 0 0 0 | * * * * * 1 * *
.... .ooo3.oxx&#x  ♦ 0 1 3  3 |  0  0  0 0  3  3 3  3  0  3 | 0 0 0  0  0  0  0  0 0  0  3  3  3 1  0  3 0 0 1 | 0 0 0  0  0  0 0 0 0 0 0 0 1  3 1 0 0 0 1 0 | * * * * * * 4 *
..ox3..oo3..xx&#x  ♦ 0 0 4 12 |  0  0  0 0  0  0 6 12 12 12 | 0 0 0  0  0  0  0  0 0  0  0  0  0 4 12 12 4 6 4 | 0 0 0  0  0  0 0 0 0 0 0 0 0  0 0 1 4 6 4 1 | * * * * * * * 1

© 2004-2025
top of page