| Acronym | ... |
| Name | FAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx |
|
Lace city in approx. ASCII-art |
x3x
J
o3x F3x x3F x3o
H F G I
x3x F3x o3A A3o x3F x3x
D E
x3F A3x x3A F3x
B C
x3o A3o x3A F3F A3x o3A o3x
A
x3F A3x x3A F3x
x3x F3x o3A A3o x3F x3x
o3x F3x x3F x3o
x3x
|
o3o
A
x3o o3x
B C
x3o o3f f3x x3f f3o o3x
E F G D
o3o f3x x3f o3o
f3f
J
o3x x3f f3f o3F F3o f3f f3x x3o
I H
f3o F3o o3F o3f
o3x x3f f3f o3F F3o f3f f3x x3o
f3f
o3o f3x x3f o3o
x3o o3f f3x x3f f3o o3x
x3o o3x
o3o
| |
| Face vector | 186, 612, 600, 174 |
| Confer |
|
The relation to ex runs as follows: ex in triangular duoprismatic subsymmetry can be given as fFoxffooxo 3 foFfxofxoo 2 oxofofxFof 3 ooxofxfoFf &#zx (F = ff = f+x). That will be transformed finally into fFo(-x)Ffo(-x)oo 3 foFF(-x)ofo(-x)o 2 oxofofxFof 3 ooxofxfoFf &#zx. Then a Stott expansion wrt. the first and second nodes produces this polychoron (A = F+x = f+2x).
Incidence matrix according to Dynkin symbol
FAxoAFxoxx3FxAAoxFxox oxofofxFof3ooxofxfoFf&#zx → all heights = 0 – but not all lacings exist o.........3o......... o.........3o......... | 6 * * * * * | 6 0 0 0 0 0 0 0 0 0 0 0 0 | 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 6 0 0 0 0 0 0 0 A .o........3.o........ .o........3.o........ & | * 36 * * * * | 1 1 2 2 2 0 0 0 0 0 0 0 0 | 2 2 2 1 2 2 2 1 2 0 0 0 0 0 0 0 0 0 0 | 1 3 1 2 1 2 0 0 0 B,C ...o......3...o...... ...o......3...o...... & | * * 18 * * * | 0 0 0 4 0 4 0 0 0 0 0 0 0 | 0 0 0 0 2 2 0 0 4 2 2 0 0 0 0 0 0 0 0 | 0 2 0 1 0 2 1 0 0 D,E .....o....3.....o.... .....o....3.....o.... & | * * * 72 * * | 0 0 0 0 1 1 1 1 1 1 0 0 0 | 0 1 0 0 0 0 1 1 1 1 2 1 1 1 1 0 0 0 0 | 0 2 0 0 1 1 2 1 0 F,G .......o..3.......o.. .......o..3.......o.. & | * * * * 18 * | 0 0 0 0 0 0 0 0 0 0 2 4 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 2 4 0 | 0 0 0 0 0 0 1 2 2 H,I .........o3.........o .........o3.........o | * * * * * 36 | 0 0 0 0 0 0 0 0 0 2 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 2 2 1 | 0 0 0 0 0 0 2 2 2 J --------------------------------------------------+------------------+----------------------------------------+--------------------------------------------------------+-------------------------- oo........3oo........ oo........3oo........&#x & | 1 1 0 0 0 0 | 36 * * * * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 3 0 0 0 0 0 0 0 .......... .x........ .......... .......... & | 0 2 0 0 0 0 | * 18 * * * * * * * * * * * | 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 2 1 2 0 0 0 .......... .......... .x........ .......... & | 0 2 0 0 0 0 | * * 36 * * * * * * * * * * | 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0 0 0 0 .o..o.....3.o..o..... .o..o.....3.o..o.....&#x & | 0 1 1 0 0 0 | * * * 72 * * * * * * * * * | 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 0 1 0 0 0 .o...o....3.o...o.... .o...o....3.o...o....&#x & | 0 1 0 1 0 0 | * * * * 72 * * * * * * * * | 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 2 0 0 1 1 0 0 0 ...o..o...3...o..o... ...o..o...3...o..o...&#x & | 0 0 1 1 0 0 | * * * * * 72 * * * * * * * | 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 1 0 0 0 1 1 0 0 .......... .....x.... .......... .......... & | 0 0 0 2 0 0 | * * * * * * 36 * * * * * * | 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 | 0 0 0 0 1 1 1 1 0 .......... .......... .......... .....x.... & | 0 0 0 2 0 0 | * * * * * * * 36 * * * * * | 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 | 0 1 0 0 1 0 1 1 0 .....oo...3.....oo... .....oo...3.....oo...&#x | 0 0 0 2 0 0 | * * * * * * * * 36 * * * * | 0 1 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 | 0 2 0 0 0 0 2 0 0 .....o...o3.....o...o .....o...o3.....o...o&#x & | 0 0 0 1 0 1 | * * * * * * * * * 72 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 0 0 0 0 2 1 0 .......... .......x.. .......... .......... & | 0 0 0 0 2 0 | * * * * * * * * * * 18 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 | 0 0 0 0 0 0 0 1 2 .......o.o3.......o.o .......o.o3.......o.o&#x & | 0 0 0 0 1 1 | * * * * * * * * * * * 72 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 0 0 0 1 1 1 .........x .......... .......... .......... & | 0 0 0 0 0 2 | * * * * * * * * * * * * 36 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 | 0 0 0 0 0 0 1 1 2 --------------------------------------------------+------------------+----------------------------------------+--------------------------------------------------------+-------------------------- .......... .......... ox........ ..........&#x & | 1 2 0 0 0 0 | 2 0 1 0 0 0 0 0 0 0 0 0 0 | 36 * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 ooo..oo...3ooo..oo... ooo..oo...3ooo..oo...&#xr | 1 2 0 2 0 0 | 2 0 0 0 2 0 0 0 1 0 0 0 0 | * 36 * * * * * * * * * * * * * * * * * | 0 2 0 0 0 0 0 0 0 cycle: (ABFGC) .......... .x........ .x........ .......... & | 0 4 0 0 0 0 | 0 2 2 0 0 0 0 0 0 0 0 0 0 | * * 18 * * * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 .......... .......... .x........3.o........ & | 0 3 0 0 0 0 | 0 0 3 0 0 0 0 0 0 0 0 0 0 | * * * 12 * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 .......... .x..o..... .......... ..........&#x & | 0 2 1 0 0 0 | 0 1 0 2 0 0 0 0 0 0 0 0 0 | * * * * 36 * * * * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 .......... .......... .x..o..... ..........&#x & | 0 2 1 0 0 0 | 0 0 1 2 0 0 0 0 0 0 0 0 0 | * * * * * 36 * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 .......... .x...x.... .......... ..........&#x & | 0 2 0 2 0 0 | 0 1 0 0 2 0 1 0 0 0 0 0 0 | * * * * * * 36 * * * * * * * * * * * * | 0 0 0 0 1 1 0 0 0 .......... .......... .......... .o...x....&#x & | 0 1 0 2 0 0 | 0 0 0 0 2 0 0 1 0 0 0 0 0 | * * * * * * * 36 * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 .o..oo....3.o..oo.... .o..oo....3.o..oo....&#x & | 0 1 1 1 0 0 | 0 0 0 1 1 1 0 0 0 0 0 0 0 | * * * * * * * * 72 * * * * * * * * * * | 0 1 0 0 0 1 0 0 0 ...o..x... .......... .......... ..........&#x & | 0 0 1 2 0 0 | 0 0 0 0 0 2 1 0 0 0 0 0 0 | * * * * * * * * * 36 * * * * * * * * * | 0 0 0 0 0 1 1 0 0 .......... .......... ....ofx... ..........&#xt & | 0 0 1 4 0 0 | 0 0 0 0 0 2 0 1 2 0 0 0 0 | * * * * * * * * * * 36 * * * * * * * * | 0 1 0 0 0 0 1 0 0 .......... .....x.... .......... .....x.... & | 0 0 0 4 0 0 | 0 0 0 0 0 0 2 2 0 0 0 0 0 | * * * * * * * * * * * 18 * * * * * * * | 0 0 0 0 1 0 0 1 0 .......... .....x...x .......... ..........&#x & | 0 0 0 2 0 2 | 0 0 0 0 0 0 1 0 0 2 0 0 1 | * * * * * * * * * * * * 36 * * * * * * | 0 0 0 0 0 0 1 1 0 .......... .......... .......... .....x.o.f&#xt & | 0 0 0 2 1 2 | 0 0 0 0 0 0 0 1 0 2 0 2 0 | * * * * * * * * * * * * * 36 * * * * * | 0 0 0 0 0 0 1 1 0 tower: F-J-H .....oo..o3.....oo..o .....oo..o3.....oo..o&#x | 0 0 0 2 0 1 | 0 0 0 0 0 0 0 0 1 2 0 0 0 | * * * * * * * * * * * * * * 36 * * * * | 0 0 0 0 0 0 2 0 0 .......o..3.......x.. .......... .......... & | 0 0 0 0 3 0 | 0 0 0 0 0 0 0 0 0 0 3 0 0 | * * * * * * * * * * * * * * * 6 * * * | 0 0 0 0 0 0 0 0 2 .......o.x .......... .......... ..........&#x & | 0 0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * * * * 36 * * | 0 0 0 0 0 0 1 0 1 .......... .......x.x .......... ..........&#x & | 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 1 2 1 | * * * * * * * * * * * * * * * * * 36 * | 0 0 0 0 0 0 0 1 1 .........x3.........x .......... .......... | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 0 6 | * * * * * * * * * * * * * * * * * * 6 | 0 0 0 0 0 0 0 0 2 --------------------------------------------------+------------------+----------------------------------------+--------------------------------------------------------+-------------------------- .......... .......... ox........3oo........&#x & ♦ 1 3 0 0 0 0 | 3 0 3 0 0 0 0 0 0 0 0 0 0 | 3 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 12 * * * * * * * * .......... .......... oxo.ofx... ..........&#xt & ♦ 1 3 1 4 0 0 | 3 0 1 2 4 2 0 1 2 0 0 0 0 | 1 2 0 0 0 1 0 1 2 0 1 0 0 0 0 0 0 0 0 | * 36 * * * * * * * .......... .x........ .x........3.o........ & ♦ 0 6 0 0 0 0 | 0 3 6 0 0 0 0 0 0 0 0 0 0 | 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 6 * * * * * * .......... .x..o..... .x..o..... ..........&#x & ♦ 0 4 1 0 0 0 | 0 2 2 4 0 0 0 0 0 0 0 0 0 | 0 0 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 18 * * * * * .......... .x...x.... .......... .o...x....&#x & ♦ 0 2 0 4 0 0 | 0 1 0 0 4 0 2 2 0 0 0 0 0 | 0 0 0 0 0 0 2 2 0 0 0 1 0 0 0 0 0 0 0 | * * * * 18 * * * * .......... .x..ox.... .......... ..........&#x & ♦ 0 2 1 2 0 0 | 0 1 0 2 2 2 1 0 0 0 0 0 0 | 0 0 0 0 1 0 1 0 2 1 0 0 0 0 0 0 0 0 0 | * * * * * 36 * * * ...o.Fxo.x .......... .......... ...o.xfo.f&#xt & ♦ 0 0 1 8 1 4 | 0 0 0 0 0 4 2 2 4 8 0 4 2 | 0 0 0 0 0 0 0 0 0 2 2 0 2 2 4 0 2 0 0 | * * * * * * 18 * * tower: D-G-F-J-H .......... .....x.x.x .......... .....x.o.f&#xt & ♦ 0 0 0 4 2 4 | 0 0 0 0 0 0 2 2 0 4 1 4 2 | 0 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 0 2 0 | * * * * * * * 18 * tower: F-J-H .......o.x3.......x.x .......... ..........&#x & ♦ 0 0 0 0 3 6 | 0 0 0 0 0 0 0 0 0 0 3 6 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * * 12 ABCDEFGHIJ ABCDEFGHIJ ABCDEFGHIJ ABCDEFGHIJ
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