Acronym hi, pD
Name hecatonicosachoron,
120-cell,
dodecacontachoron,
twelftychoron,
cosmochoron,
dodecaplex,
polydodecahedron

 © ` ©`showing its relationto swirl symmetry
Cross sections
` ©`
Edge radius sqrt[27+12 sqrt(5)]/2 = 3.668542
Face radius sqrt[(65+29 sqrt(5))/10] = 3.603415
Density 1
Vertex figure
` ©`
Vertex layers
 Layer Symmetry Subsymmetries o3o3o5o o3o3o . o3o . o o . o5o . o3o5o 1 o3o3o5x o3o3o .vertex first o3o . xedge first o . o5x{5} first . o3o5xdoe first 2 o3o3f .vertex figure o3f . f f . o5f . o3o5f 3 o3f3x . o3F . o F . f5o . o3f5o 4a f3x3f . f3x . F x . o5F . f3x5o 4b B . x5o 5 F3f3o . f3F . o F . F5o . x3f5o 6 B3o3o . F3f . f f . f5f . f3o5f 7a x3f3F . B3o . x o . F5x . o3o5F 7b x3f . B C . f5o 8a f3o3B . x3B . o B . F5o . F3o5x 8b F3F3o . f3o . C 9a C3o3o . F3F . F F . x5F . o3o5F 9b o3o3C . o3o . D D . o5f 9c f3F3f . 10a o3B3x . f3F . B B . f5f . f3o5f 10b B3f3o . 11a F3o3B . f3B . f C . o5F . x3f5o 11b C3o . f o . f5F 12a F3f3F . o3B . B f . f5F . f3x5o 12b T . o5x 13a o3o3D . B3f . F o . B5o . o3f5o 13b B3x3f . o3C . F 13c F3o . D 14a f3o3C . D3o . o x . o5B . o3o5f 14b o3B3f . F3f . C B . F5x 15a f3F3F . o3o . T F . F5f . o3o5xopposite doe 15b D . o5F 16a o3C3o . F3B . x f . B5o 16b x3f3B . B3x . B T . o5f 16c B3f3x . 17a F3F3f . B3F . f C . f5f 17b f3o . T 18a C3o3f . C3f . o f . o5B 18b f3B3o . o3B . C T . f5o 19a D3o3o . o3D . F F . f5F 19b f3x3B . f3F . D D . F5o 20a F3f3F . f3C . f x . B5o 20b x3f . T B . x5F 21a B3o3F . B3f . B o . o5B 21b o3C . B 22a x3B3o . B3F . F f . F5f 22b o3f3B . T . x5o 23a o3o3C . x3D . o C . F5o 23b C3o3o . D3x . o o . F5f 23c f3F3f . F3F . C 24a B3o3f . F3B . F B . f5f 24b o3F3F . 25a F3f3x . f3B . B F . F5x 25b C3o . B D . f5o 26a o3o3B . C3f . f B . o5F 26b f3x . T 27a o3f3F . D3o . F o . x5F 27b F3f . D C . o5f 28a f3x3f . f3C . o f . f5f 28b B3o . C 29a x3f3o . F3B . f F . o5F 29b o3f . T 30a f3o3o . B3F . x x . F5o 30b x3B . B B . o5x 31 o3o3o .opposite vertex o3o . T F . o5f 32a o3D . o f . f5o 32b f3F . C 33a f3B . F o . x5oopposite {5} 33b C3o . F 33c o3F . D 34 B3o . B 35a B3f . f 35b o3C . f 36 F3f . B 37a F3F . F 37b o3o . D 38a B3x . o 38b o3f . C 39a o3B . x 39b f3x . B 40 f3F . f 41 F3f . o 42 x3f . F 43 F3o . o 44 f3o . f 45 o3o . xopposite edge
(F=ff=f+x=2x+v, B=fff=F+f=2f+x=3x+2v, C=B+x=2F=2f+2x=4x+2v, D=C+v=3f+x=4x+3v, T=FF=3f+2x=5x+3v)
Lace city
in approx. ASCII-art
 ``` ©   ``` ``` o5x o5f o5f f5o f5o x5o o5F o5F x5o F5o F5o f5f f5f f5o F5x f5o F5o F5o o5f x5F x5F o5f f5f f5f o5F F5f o5F o5x f5F f5F o5x B5o F5x o5B o5B F5x o5F F5f F5f o5F o5f B5o B5o o5f f5f f5f f5o o5B o5B f5o F5o f5F f5F F5o x5F B5o B5o x5F o5B x5o F5f F5f x5o F5o f5F F5o f5f f5f f5o F5x F5x f5o o5F o5F o5f x5F o5f f5f f5f o5F o5F o5x F5o F5o o5x o5f o5f f5o f5o x5o ```
 ``` _ +--------------------------------------------- o3o3o _ - _ +--------------------------------------------- f3o3o _ - _ - _ +------------------------------------------- x3f3o _ - _ - _ - _ +-------------------------------------- f3x3f _ - _ - _ - _ - _ +------------------------------------ o3f3F _ - _ - _ - _ - _ - _ +------------------------------------ o3o3B _ - _ - _ - _ - _ - _ - _ +---------------------------------- F3f3x _ - _ - _ - _ - _ - _ - _ - _ +---------------------------- B3o3f + o3F3F _ - _ - _ - _ - _ - _ - _ - _ - _ +-------------------------- o3o3C + C3o3o + f3F3f _ - _ - _ - _ - _ - _ - _ - _ - _ - _ +-------------------- x3B3o + o3f3B _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ +------------------ B3o3F _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ +------------------ F3f3F _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ +---------------- D3o3o + f3x3B _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ +---------- C3o3f + f3B3o _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ +-------- F3F3f _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ +-- o3C3o + x3f3B + B3f3o _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - _ - ``` ``` o3o o3f f3x x3f f3o o3o -- o3o5x o3o o3F F3f f3F F3o o3o -- o3o5f o3f f3F B3o F3F o3B F3f f3o -- o3f5o f3x F3f B3o x3B fC3Bo Bo3fC B3x o3B f3F x3f -- f3x5o x3f F3F fC3Bo D3o F3B B3F o3D Bo3fC F3F f3x -- x3f5o f3o f3F Bo3fC F3B C3f f3C B3F fC3Bo F3f o3f -- f3o5f o3o o3B B3F F3B B3o o3o -- o3o5F F3o F3f B3x o3D f3C xD3Dx C3f D3o x3B f3F o3F -- F3o5x o3o o3B B3F F3B B3o o3o -- o3o5F f3o f3F Bo3fC F3B C3f f3C B3F fC3Bo F3f o3f -- f3o5f x3f F3F fC3Bo D3o F3B B3F o3D Bo3fC F3F f3x -- x3f5o f3x F3f B3o x3B fC3Bo Bo3fC B3x o3B f3F x3f -- f3x5o o3f f3F B3o F3F o3B F3f f3o -- o3f5o o3o o3F F3f f3F F3o o3o -- o3o5f o3o o3f f3x x3f f3o o3o -- o3o5x ``` ``` ©   ```
 ``` ©   ``` ``` o2x f2f F2o x2F F2o f2f o2x -- o3o5x o2f F2F B2o f2B B2o F2F o2f -- o3o5f o2o f2F B2f F2B oC2Co F2B B2f f2F o2o -- o3f5o f2o F2f Bx2xB f2C Co2FD B2B D2f B2B Co2FD f2C Bx2xB F2f f2o -- f3x5o x2o F2F f2B C2f FD2DF B2C o2T T2x o2T B2C FD2DF C2f f2B F2F x2o -- x3f5o f2f o2B B2F FD2Co C2B fT2Tf B2D fT2Tf C2B FD2Co B2F o2B f2f -- f3o5f o2F B2B T2o F2T T2o B2B o2F -- o3o5F F2x B2f oC2Co f2D x2T D2B T2F C2C T2F D2B x2T f2D oC2Co B2f F2x -- F3o5x o2F B2B T2o F2T T2o B2B o2F -- o3o5F f2f o2B B2F FD2Co C2B fT2Tf B2D fT2Tf C2B FD2Co B2F o2B f2f -- f3o5f x2o F2F f2B C2f FD2DF B2C o2T T2x o2T B2C FD2DF C2f f2B F2F x2o -- x3f5o f2o F2f Bx2xB f2C Co2FD B2B D2f B2B Co2FD f2C Bx2xB F2f f2o -- f3x5o o2o f2F B2f F2B oC2Co F2B B2f f2F o2o -- o3f5o o2f F2F B2o f2B B2o F2F o2f -- o3o5f o2x f2f F2o x2F F2o f2f o2x -- o3o5x ```
Coordinates
1. 2, τ2, 0, 0)                           all permutations, all changes of sign
2. (sqrt(5) τ2/2, τ2/2, τ2/2, τ2/2) all permutations, all changes of sign
3. 3/2, τ3/2, τ3/2, 1/2)              all permutations, all changes of sign
4. 4/2, τ/2, τ/2, τ/2)                  all permutations, all changes of sign
5. 4/2, τ2/2, 1/2, 0)                  all even permutations, all changes of sign
6. 3/2, sqrt(5) τ2/2, 0, τ/2)      all even permutations, all changes of sign
7. 3/2, τ2/2, τ2, τ/2)                  all even permutations, all changes of sign
where τ = (1+sqrt(5))/2
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
 by cells: doe hi 120
)
Dual ex
Dihedral angles
• at {5} between doe and doe:   144°
Confer
Grünbaumian relatives:
2hi
decompositions:
rox || hi   hi - 120 ikadoes
isogonal relatives:
hidhi
general polytopal classes:
regular   noble polytopes
External

As abstract polytope hi is isomorphic to gogishi, thereby replacing pentagons by pentagrams resp. replacing doe by gissid.

The 120 does could be divided into 12 cycles of 10, thus describing its swirl subsymmetry. Any 2 of those stacked does in such a ring are connected by special pentagons with a-type edges only. All non-polar pentagons of each doe belong to a second class. But there will be a chiral subset of 5 tropal edges of each doe, which is of that type too. And the other ones will belong to the former class, then. I.e. at that tropal edge there will be incident, as third pentagon, one such cycle dividing one again. That is, the non-polar pentagons would have the edge sequence a-b-a-b-b. Further it will turn out that those cycle dividing pentagons are completely separated from each other, i.e. there is incident just one such pentagon at any vertex of hi only.

Note that hi can be thought of as the external blend of 1 rox + 600 octpies + 1200 pens + 120 ikadoees. This decomposition is described as the degenerate segmentoteron oo3xo3oo5ox&#x.

The number of ways to color the hecatonicosachoron with different colors per cell is 120!/7200 = 9.290976 · 10194. – This is because the color group is the permutation group of 120 elements and has size 120!, while the order of the pure rotational hecatonicosachoral group is 7 200. (The reflectional hecatonicosachoral group would have twice as many, i.e. 14 400 elements.)

Incidence matrix according to Dynkin symbol

```o3o3o5x

. . . . | 600 ♦    4 |   6 |   4
--------+-----+------+-----+----
. . . x |   2 | 1200 |   3 |   3
--------+-----+------+-----+----
. . o5x |   5 |    5 | 720 |   2
--------+-----+------+-----+----
. o3o5x ♦  20 |   30 |  12 | 120

snubbed forms: o3o3o5β
```

```o3o3o5/4x

. . .   . | 600 ♦    4 |   6 |   4
----------+-----+------+-----+----
. . .   x |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
. . o5/4x |   5 |    5 | 720 |   2
----------+-----+------+-----+----
. o3o5/4x ♦  20 |   30 |  12 | 120
```

```o3o3/2o5x

. .   . . | 600 ♦    4 |   6 |   4
----------+-----+------+-----+----
. .   . x |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
. .   o5x |   5 |    5 | 720 |   2
----------+-----+------+-----+----
. o3/2o5x ♦  20 |   30 |  12 | 120
```

```o3o3/2o5/4x

. .   .   . | 600 ♦    4 |   6 |   4
------------+-----+------+-----+----
. .   .   x |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
. .   o5/4x |   5 |    5 | 720 |   2
------------+-----+------+-----+----
. o3/2o5/4x ♦  20 |   30 |  12 | 120
```

```o3/2o3o5x

.   . . . | 600 ♦    4 |   6 |   4
----------+-----+------+-----+----
.   . . x |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
.   . o5x |   5 |    5 | 720 |   2
----------+-----+------+-----+----
.   o3o5x ♦  20 |   30 |  12 | 120
```

```o3/2o3o5/4x

.   . .   . | 600 ♦    4 |   6 |   4
------------+-----+------+-----+----
.   . .   x |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
.   . o5/4x |   5 |    5 | 720 |   2
------------+-----+------+-----+----
.   o3o5/4x ♦  20 |   30 |  12 | 120
```

```o3/2o3/2o5x

.   .   . . | 600 ♦    4 |   6 |   4
------------+-----+------+-----+----
.   .   . x |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
.   .   o5x |   5 |    5 | 720 |   2
------------+-----+------+-----+----
.   o3/2o5x ♦  20 |   30 |  12 | 120
```

```o3/2o3/2o5/4x

.   .   .   . | 600 ♦    4 |   6 |   4
--------------+-----+------+-----+----
.   .   .   x |   2 | 1200 |   3 |   3
--------------+-----+------+-----+----
.   .   o5/4x |   5 |    5 | 720 |   2
--------------+-----+------+-----+----
.   o3/2o5/4x ♦  20 |   30 |  12 | 120
```

```acc. to swirl subsymmetry:

600 ♦   2   2 |   1   5 |   4
-----+---------+---------+----
2 | 600   * |   1   2 |   3  a
2 |   * 600 |   0   3 |   3  b
-----+---------+---------+----
5 |   5   0 | 120   * |   2  aaaaa
5 |   2   3 |   * 600 |   2  ababb
-----+---------+---------+----
♦ 20 |  15  15 |   2  10 | 120
```

```xofoFo|f|FxFfBo-5-oxofoF|f|xFfFoB-2-BoFfFx|f|oFofox-5-oBfFxF|f|Fofoxo-&#zx   → existing heights = 0
B = 2f+x = 4.236068
F = f+x = 2.618034

o..... . ...... 5 o..... . ...... 2 o..... . ...... 5 o..... . ......      & | 100   *   *   * ♦   2   2   0   0   0   0 |  1   4   1   0   0 |  2   2
..o... . ...... 5 ..o... . ...... 2 ..o... . ...... 5 ..o... . ......      & |   * 200   *   * ♦   0   1   2   1   0   0 |  0   3   1   2   0 |  1   3
....o. . ...... 5 ....o. . ...... 2 ....o. . ...... 5 ....o. . ......      & |   *   * 200   * ♦   0   0   0   1   1   2 |  0   0   1   2   3 |  0   4
...... o ...... 5 ...... o ...... 2 ...... o ...... 5 ...... o ......        |   *   *   * 100 ♦   0   0   0   0   0   4 |  0   0   0   2   4 |  0   4
-----------------------------------------------------------------------------+-----------------+-------------------------+--------------------+-------
x..... . ......   ...... . ......   ...... . ......   ...... . ......      & |   2   0   0   0 | 100   *   *   *   *   * |  1   2   0   0   0 |  2   1
o.o... . ...... 5 o.o... . ...... 2 o.o... . ...... 5 o.o... . ......&#x   & |   1   1   0   0 |   * 200   *   *   *   * |  0   2   1   0   0 |  1   2
..oo.. . ...... 5 ..oo.. . ...... 2 ..oo.. . ...... 5 ..oo.. . ......&#x   & |   0   2   0   0 |   *   * 200   *   *   * |  0   2   0   1   0 |  1   2
..o.o. . ...... 5 ..o.o. . ...... 2 ..o.o. . ...... 5 ..o.o. . ......&#x   & |   0   1   1   0 |   *   *   * 200   *   * |  0   0   1   2   0 |  0   3
...... . ......   ...... . ......   ...... . ......   ....x. . ......      & |   0   0   2   0 |   *   *   *   * 100   * |  0   0   1   0   2 |  0   3
....o. o ...... 5 ....o. o ...... 2 ....o. o ...... 5 ....o. o ......&#x   & |   0   0   1   1 |   *   *   *   *   * 400 |  0   0   0   1   2 |  0   3
-----------------------------------------------------------------------------+-----------------+-------------------------+--------------------+-------
x..... . ...... 5 o..... . ......   ...... . ......   ...... . ......      & |   5   0   0   0 |   5   0   0   0   0   0 | 20   *   *   *   * |  2   0
x.fo.. . ......   ...... . ......   ...... . ......   ...... . ......&#xt  & |   2   3   0   0 |   1   2   2   0   0   0 |  * 200   *   *   * |  1   1
...... . ......   ...... . ......   ...... . ......   o.f.x. . ......&#xt  & |   1   2   2   0 |   0   2   0   2   1   0 |  *   * 100   *   * |  0   2
..oooo o ...... 5 ..oooo o ...... 2 ..oooo o ...... 5 ..oooo o ......&#xr  & |   0   2   2   1 |   0   0   1   2   0   2 |  *   *   * 200   * |  0   2
...... . ......   ...... . ......   ...... . ......   ....x. f .o....&#xt  & |   0   0   3   2 |   0   0   0   0   1   4 |  *   *   *   * 200 |  0   2
-----------------------------------------------------------------------------+-----------------+-------------------------+--------------------+-------
xofo.. . ...... 5 oxof.. . ......   ...... . ......   ...... . ......&#xt  & ♦  10  10   0   0 |  10  10  10   0   0   0 |  2  10   0   0   0 | 20   *  tower: a-c-d-b
x.foFo f .x....   ...... . ......   ...... . ......   o.fFxF f .o....&#xt  & ♦   2   6   8   4 |   1   4   4   6   3  12 |  0   2   2   4   4 |  * 100
```

```ooC|foB|xoF|f-3-ooo|ooo|fff|x-3-Coo|Bfo|Fxo|f *b3-oCo|oBf|oFx|f-&#zx   → existing heights = 0
C = 2f+2x = 5.236068
B = 2f+x = 4.236068
F = f+x = 2.618034
(tegum sum of 3 C-hexes, 3 (f,B)-rits, 3 (x,f,F)-tahs, and 1 (f,x)-tico)

o.. ... ... .-3-o.. ... ... .-3-o.. ... ... . *b3-o.. ... ... .       | 8 * *  *  *  *  *  *  *   * ♦  4  0  0  0  0  0  0   0  0   0  0   0  0 |  6  0  0  0  0  0  0  0  0 |  4  0  0  0
.o. ... ... .-3-.o. ... ... .-3-.o. ... ... . *b3-.o. ... ... .       | * 8 *  *  *  *  *  *  *   * ♦  0  4  0  0  0  0  0   0  0   0  0   0  0 |  0  6  0  0  0  0  0  0  0 |  0  4  0  0
..o ... ... .-3-..o ... ... .-3-..o ... ... . *b3-..o ... ... .       | * * 8  *  *  *  *  *  *   * ♦  0  0  4  0  0  0  0   0  0   0  0   0  0 |  0  0  6  0  0  0  0  0  0 |  0  0  4  0
... o.. ... .-3-... o.. ... .-3-... o.. ... . *b3-... o.. ... .       | * * * 32  *  *  *  *  *   * ♦  1  0  0  3  0  0  0   0  0   0  0   0  0 |  3  0  0  3  0  0  0  0  0 |  3  0  1  0
... .o. ... .-3-... .o. ... .-3-... .o. ... . *b3-... .o. ... .       | * * *  * 32  *  *  *  *   * ♦  0  1  0  0  3  0  0   0  0   0  0   0  0 |  0  3  0  0  3  0  0  0  0 |  1  3  0  0
... ..o ... .-3-... ..o ... .-3-... ..o ... . *b3-... ..o ... .       | * * *  *  * 32  *  *  *   * ♦  0  0  1  0  0  3  0   0  0   0  0   0  0 |  0  0  3  0  0  3  0  0  0 |  0  1  3  0
... ... o.. .-3-... ... o.. .-3-... ... o.. . *b3-... ... o.. .       | * * *  *  *  * 96  *  *   * ♦  0  0  0  1  0  0  1   2  0   0  0   0  0 |  1  0  0  2  0  0  2  1  0 |  2  0  1  1
... ... .o. .-3-... ... .o. .-3-... ... .o. . *b3-... ... .o. .       | * * *  *  *  *  * 96  *   * ♦  0  0  0  0  1  0  0   0  1   2  0   0  0 |  0  1  0  0  2  0  1  0  2 |  1  2  0  1
... ... ..o .-3-... ... ..o .-3-... ... ..o . *b3-... ... ..o .       | * * *  *  *  *  *  * 96   * ♦  0  0  0  0  0  1  0   0  0   0  1   2  0 |  0  0  1  0  0  2  0  2  1 |  0  1  2  1
... ... ... o-3-... ... ... o-3-... ... ... o *b3-... ... ... o       | * * *  *  *  *  *  *  * 192 ♦  0  0  0  0  0  0  0   1  0   1  0   1  1 |  0  0  0  1  1  1  1  1  1 |  1  1  1  1
----------------------------------------------------------------------+-----------------------------+-------------------------------------------+----------------------------+------------
o.. o.. ... .-3-o.. o.. ... .-3-o.. o.. ... . *b3-o.. o.. ... .-&#x   | 1 0 0  1  0  0  0  0  0   0 | 32  *  *  *  *  *  *   *  *   *  *   *  * |  3  0  0  0  0  0  0  0  0 |  3  0  0  0
.o. .o. ... .-3-.o. .o. ... .-3-.o. .o. ... . *b3-.o. .o. ... .-&#x   | 0 1 0  0  1  0  0  0  0   0 |  * 32  *  *  *  *  *   *  *   *  *   *  * |  0  3  0  0  0  0  0  0  0 |  0  3  0  0
..o ..o ... .-3-..o ..o ... .-3-..o ..o ... . *b3-..o ..o ... .-&#x   | 0 0 1  0  0  1  0  0  0   0 |  *  * 32  *  *  *  *   *  *   *  *   *  * |  0  0  3  0  0  0  0  0  0 |  0  0  3  0
... o.. o.. .-3-... o.. o.. .-3-... o.. o.. . *b3-... o.. o.. .-&#x   | 0 0 0  1  0  0  1  0  0   0 |  *  *  * 96  *  *  *   *  *   *  *   *  * |  1  0  0  2  0  0  0  0  0 |  2  0  1  0
... .o. .o. .-3-... .o. .o. .-3-... .o. .o. . *b3-... .o. .o. .-&#x   | 0 0 0  0  1  0  0  1  0   0 |  *  *  *  * 96  *  *   *  *   *  *   *  * |  0  1  0  0  2  0  0  0  0 |  1  2  0  0
... ..o ..o .-3-... ..o ..o .-3-... ..o ..o . *b3-... ..o ..o .-&#x   | 0 0 0  0  0  1  0  0  1   0 |  *  *  *  *  * 96  *   *  *   *  *   *  * |  0  0  1  0  0  2  0  0  0 |  0  1  2  0
... ... x.. .   ... ... ... .   ... ... ... .     ... ... ... .       | 0 0 0  0  0  0  2  0  0   0 |  *  *  *  *  *  * 48   *  *   *  *   *  * |  1  0  0  0  0  0  2  0  0 |  2  0  0  1
... ... o.. o-3-... ... o.. o-3-... ... o.. o *b3-... ... o.. o-&#x   | 0 0 0  0  0  0  1  0  0   1 |  *  *  *  *  *  *  * 192  *   *  *   *  * |  0  0  0  1  0  0  1  1  0 |  1  0  1  1
... ... ... .   ... ... ... .   ... ... .x. .     ... ... ... .       | 0 0 0  0  0  0  0  2  0   0 |  *  *  *  *  *  *  *   * 48   *  *   *  * |  0  1  0  0  0  0  0  0  2 |  0  2  0  1
... ... .o. o-3-... ... .o. o-3-... ... .o. o *b3-... ... .o. o-&#x   | 0 0 0  0  0  0  0  1  0   1 |  *  *  *  *  *  *  *   *  * 192  *   *  * |  0  0  0  0  1  0  1  0  1 |  1  1  0  1
... ... ... .   ... ... ... .   ... ... ... .     ... ... ..x .       | 0 0 0  0  0  0  0  0  2   0 |  *  *  *  *  *  *  *   *  *   * 48   *  * |  0  0  1  0  0  0  0  2  0 |  0  0  2  1
... ... ..o o-3-... ... ..o o-3-... ... ..o o *b3-... ... ..o o-&#x   | 0 0 0  0  0  0  0  0  1   1 |  *  *  *  *  *  *  *   *  *   *  * 192  * |  0  0  0  0  0  1  0  1  1 |  0  1  1  1
... ... ... .   ... ... ... x   ... ... ... .     ... ... ... .       | 0 0 0  0  0  0  0  0  0   2 |  *  *  *  *  *  *  *   *  *   *  *   * 96 |  0  0  0  1  1  1  0  0  0 |  1  1  1  0
----------------------------------------------------------------------+-----------------------------+-------------------------------------------+----------------------------+------------
o.. f.. x.. .   ... ... ... .   ... ... ... .     ... ... ... .-&#xt  | 1 0 0  2  0  0  2  0  0   0 |  2  0  0  2  0  0  1   0  0   0  0   0  0 | 48  *  *  *  *  *  *  *  * |  2  0  0  0
... ... ... .   ... ... ... .   .o. .f. .x. .     ... ... ... .-&#xt  | 0 1 0  0  2  0  0  2  0   0 |  0  2  0  0  2  0  0   0  1   0  0   0  0 |  * 48  *  *  *  *  *  *  * |  0  2  0  0
... ... ... .   ... ... ... .   ... ... ... .     ..o ..f ..x .-&#xt  | 0 0 1  0  0  2  0  0  2   0 |  0  0  2  0  0  2  0   0  0   0  1   0  0 |  *  * 48  *  *  *  *  *  * |  0  0  2  0
... ... ... .   ... o.. f.. x   ... ... ... .     ... ... ... .-&#xt  | 0 0 0  1  0  0  2  0  0   2 |  0  0  0  2  0  0  0   2  0   0  0   0  1 |  *  *  * 96  *  *  *  *  * |  1  0  1  0
... ... ... .   ... .o. .f. x   ... ... ... .     ... ... ... .-&#xt  | 0 0 0  0  1  0  0  2  0   2 |  0  0  0  0  2  0  0   0  0   2  0   0  1 |  *  *  *  * 96  *  *  *  * |  1  1  0  0
... ... ... .   ... ..o ..f x   ... ... ... .     ... ... ... .-&#xt  | 0 0 0  0  0  1  0  0  2   2 |  0  0  0  0  0  2  0   0  0   0  0   2  1 |  *  *  *  *  * 96  *  *  * |  0  1  1  0
... ... xo. f   ... ... ... .   ... ... ... .     ... ... ... .-&#xt  | 0 0 0  0  0  0  2  1  0   2 |  0  0  0  0  0  0  1   2  0   2  0   0  0 |  *  *  *  *  *  * 96  *  * |  1  0  0  1  tower g-j-h
... ... ... .   ... ... ... .   ... ... ... .     ... ... o.x f-&#xt  | 0 0 0  0  0  0  1  0  2   2 |  0  0  0  0  0  0  0   2  0   0  1   2  0 |  *  *  *  *  *  *  * 96  * |  0  0  1  1  tower g-j-i
... ... ... .   ... ... ... .   ... ... .xo f     ... ... ... .-&#xt  | 0 0 0  0  0  0  0  2  1   2 |  0  0  0  0  0  0  0   0  1   2  0   2  0 |  *  *  *  *  *  *  *  * 96 |  0  1  0  1  tower h-j-i
----------------------------------------------------------------------+-----------------------------+-------------------------------------------+----------------------------+------------
o.. fo. xo. f-3-o.. oo. ff. x   ... ... ... .     ... ... ... .-&#xt  ♦ 1 0 0  3  1  0  6  3  0   6 |  3  0  0  6  3  0  3   6  0   6  0   0  3 |  3  0  0  3  3  0  3  0  0 | 32  *  *  *  tower a-d-g-j-h-e
... ... ... .   .o. .oo .ff x-3-.o. .fo .xo f     ... ... ... .-&#xt  ♦ 0 1 0  0  3  1  0  6  3   6 |  0  3  0  0  6  3  0   0  3   6  0   6  3 |  0  3  0  0  3  3  0  0  3 |  * 32  *  *  tower b-e-h-j-i-f
... ... ... .   ..o o.o f.f x   ... ... ... . *b3-..o o.f o.x f-&#xt  ♦ 0 0 1  1  0  3  3  0  6   6 |  0  0  3  3  0  6  0   6  0   0  3   6  3 |  0  0  3  3  0  3  0  3  0 |  *  * 32  *  tower c-f-i-j-g-d
... ... xoF f   ... ... ... .   ... ... Fxo f     ... ... oFx f-&#zx  ♦ 0 0 0  0  0  0  4  4  4   8 |  0  0  0  0  0  0  2   8  2   8  2   8  0 |  0  0  0  0  0  0  4  4  4 |  *  *  * 24
```