Acronym tich
Name truncated cubic honeycomb
 
 © ©    ©
Vertex figure
 ©
Confer
general polytopal classes:
partial Stott expansions  
unit-edged relatives:
atich
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x4x3o4o   (N → ∞)

. . . . | 6N |  1   4 |  4  4 | 4 1
--------+----+--------+-------+----
x . . . |  2 | 3N   * |  4  0 | 4 0
. x . . |  2 |  * 12N |  1  2 | 2 1
--------+----+--------+-------+----
x4x . . |  8 |  4   4 | 3N  * | 2 0
. x3o . |  3 |  0   3 |  * 8N | 1 1
--------+----+--------+-------+----
x4x3o .  24 | 12  24 |  6  8 | N *
. x3o4o   6 |  0  12 |  0  8 | * N

snubbed forms: s4x3o4o

x4x3o4/3o   (N → ∞)

. . .   . | 6N |  1   4 |  4  4 | 4 1
----------+----+--------+-------+----
x . .   . |  2 | 3N   * |  4  0 | 4 0
. x .   . |  2 |  * 12N |  1  2 | 2 1
----------+----+--------+-------+----
x4x .   . |  8 |  4   4 | 3N  * | 2 0
. x3o   . |  3 |  0   3 |  * 8N | 1 1
----------+----+--------+-------+----
x4x3o   .  24 | 12  24 |  6  8 | N *
. x3o4/3o   6 |  0  12 |  0  8 | * N

o3x3o *b4x   (N → ∞)

. . .    . | 12N |   4  1 |  2  2  4 |  1 2 2
-----------+-----+--------+----------+-------
. x .    . |   2 | 24N  * |  1  1  1 |  1 1 1
. . .    x |   2 |   * 6N |  0  0  4 |  0 2 2
-----------+-----+--------+----------+-------
o3x .    . |   3 |   3  0 | 8N  *  * |  1 1 0
. x3o    . |   3 |   3  0 |  * 8N  * |  1 0 1
. x . *b4x |   8 |   4  4 |  *  * 6N |  0 1 1
-----------+-----+--------+----------+-------
o3x3o    .    6 |  12  0 |  4  4  0 | 2N * *
o3x . *b4x   24 |  24 12 |  8  0  6 |  * N *
. x3o *b4x   24 |  24 12 |  0  8  6 |  * * N

snubbed forms: o3x3o *b4s

:wxw:4:oxo:4:ooo:&##x   (N → ∞)   → height(1,2) = height(2,3) = 1/sqrt(2) = 0.707107
                                    height(3,1') = 1

 o.. 4 o.. 4 o..      | N  * * |  4 1  0  0  0 |  4  4 0  0 | 1 4
 .o. 4 .o. 4 .o.      | * 4N * |  1 0  1  2  1 |  2  2 2  2 | 1 4
 ..o 4 ..o 4 ..o      | *  * N |  0 1  0  0  4 |  0  4 0  4 | 1 4
----------------------+--------+---------------+------------+----
 oo. 4 oo. 4 oo. &#x  | 1  1 0 | 4N *  *  *  * |  2  1 0  0 | 1 2
:o.o:4:o.o:4:o.o:&#x  | 1  0 1 |  * N  *  *  * |  0  4 0  0 | 0 4
 .x.   ...   ...      | 0  2 0 |  * * 2N  *  * |  0  2 2  0 | 0 4
 ...   .x.   ...      | 0  2 0 |  * *  * 4N  * |  1  0 1  1 | 1 2
 .oo 4 .oo 4 .oo &#x  | 0  1 1 |  * *  *  * 4N |  0  1 0  2 | 1 2
----------------------+--------+---------------+------------+----
 ...   ox.   ... &#x  | 1  2 0 |  2 0  0  1  0 | 4N  * *  * | 1 1
:wxw:  ...   ... &#xt | 2  4 2 |  2 2  2  0  2 |  * 2N *  * | 0 2
 .x. 4 .x.   ...      | 0  8 0 |  0 0  4  4  0 |  *  * N  * | 0 2
 ...   .xo   ... &#x  | 0  2 1 |  0 0  0  1  2 |  *  * * 4N | 1 1
----------------------+--------+---------------+------------+----
 ...   oxo 4 ooo &#xt  1  4 1 |  4 0  0  4  4 |  4  0 0  4 | N *
:wxw:4:oxo:  ... &#xt  4 16 4 |  8 4  8  8  8 |  4  4 2  4 | * N

:ooxwwx:3:xwwxoo:3:wxooxw:3*a&##x   (N → ∞)   → height(1,2) = height(3,4) = height(5,6) = 1/sqrt(3) = 0.577350
                                                 height(2,3) = height(4,5) = height(6,1') = sqrt(2/3) = 0.816497

 o..... 3 o..... 3 o..... 3*a     | 3N  *  *  *  *  * |  2  1  0  0  0  0  0  0  0  0  0  2 | 1  2 0  0  0 0  0 0  0  0 0  2 0  1  2 | 1 1 2 0 0 1
 .o.... 3 .o.... 3 .o.... 3*a     |  * 3N  *  *  *  * |  0  1  2  2  0  0  0  0  0  0  0  0 | 0  2 1  1  2 0  0 0  0  0 0  2 0  0  0 | 1 1 2 1 0 0
 ..o... 3 ..o... 3 ..o... 3*a     |  *  * 3N  *  *  * |  0  0  0  2  2  1  0  0  0  0  0  0 | 0  2 0  2  1 1  2 0  0  0 0  0 0  0  0 | 2 1 1 1 0 0
 ...o.. 3 ...o.. 3 ...o.. 3*a     |  *  *  * 3N  *  * |  0  0  0  0  0  1  2  2  0  0  0  0 | 0  2 0  0  0 0  2 1  2  1 0  0 0  0  0 | 2 1 1 0 1 0
 ....o. 3 ....o. 3 ....o. 3*a     |  *  *  *  * 3N  * |  0  0  0  0  0  0  0  2  2  1  0  0 | 0  0 0  0  0 0  2 0  1  2 1  2 0  0  0 | 1 2 1 0 1 0
 .....o 3 .....o 3 .....o 3*a     |  *  *  *  *  * 3N |  0  0  0  0  0  0  0  0  0  1  2  2 | 0  0 0  0  0 0  2 0  0  0 0  2 1  2  1 | 1 2 1 0 0 1
----------------------------------+-------------------+-------------------------------------+----------------------------------------+------------
 ......   x.....   ......         |  2  0  0  0  0  0 | 3N  *  *  *  *  *  *  *  *  *  *  * | 1  1 0  0  0 0  0 0  0  0 0  0 0  0  1 | 1 0 1 0 0 1
 oo.... 3 oo.... 3 oo.... 3*a&#x  |  1  1  0  0  0  0 |  * 3N  *  *  *  *  *  *  *  *  *  * | 0  2 0  0  0 0  0 0  0  0 0  2 0  0  0 | 1 1 2 0 0 0
 ......   ......   .x....         |  0  2  0  0  0  0 |  *  * 3N  *  *  *  *  *  *  *  *  * | 0  0 1  0  1 0  0 0  0  0 0  1 0  0  0 | 0 1 1 1 0 0
 .oo... 3 .oo... 3 .oo... 3*a&#x  |  0  1  1  0  0  0 |  *  *  * 6N  *  *  *  *  *  *  *  * | 0  1 0  1  1 0  0 0  0  0 0  0 0  0  0 | 1 0 1 1 0 0
 ..x...   ......   ......         |  0  0  2  0  0  0 |  *  *  *  * 3N  *  *  *  *  *  *  * | 0  0 0  1  0 1  1 0  0  0 0  0 0  0  0 | 1 1 0 1 0 0
 ..oo.. 3 ..oo.. 3 ..oo.. 3*a&#x  |  0  0  1  1  0  0 |  *  *  *  *  * 3N  *  *  *  *  *  * | 0  2 0  0  0 0  2 0  0  0 0  0 0  0  0 | 2 1 1 0 0 0
 ......   ...x..   ......         |  0  0  0  2  0  0 |  *  *  *  *  *  * 3N  *  *  *  *  * | 0  1 0  0  0 0  0 1  1  0 0  0 0  0  0 | 1 0 1 0 1 0
 ...oo. 3 ...oo. 3 ...oo. 3*a&#x  |  0  0  0  1  1  0 |  *  *  *  *  *  *  * 6N  *  *  *  * | 0  0 0  0  0 0  1 0  1  1 0  0 0  0  0 | 1 1 0 0 1 0
 ......   ......   ....x.         |  0  0  0  0  2  0 |  *  *  *  *  *  *  *  * 3N  *  *  * | 0  0 0  0  0 0  0 0  0  1 1  1 0  0  0 | 0 1 1 0 1 0
 ....oo 3 ....oo 3 ....oo 3*a&#x  |  0  0  0  0  1  1 |  *  *  *  *  *  *  *  *  * 3N  *  * | 0  0 0  0  0 0  2 0  0  0 0  2 0  0  0 | 1 2 1 0 0 0
 .....x   ......   ......         |  0  0  0  0  0  2 |  *  *  *  *  *  *  *  *  *  * 3N  * | 0  0 0  0  0 0  1 0  0  0 0  0 1  1  0 | 1 1 0 0 0 1
:o....o:3:o....o:3:o....o:3*a&#x  |  1  0  0  0  0  1 |  *  *  *  *  *  *  *  *  *  *  * 6N | 0  0 0  0  0 0  0 0  0  0 0  1 0  1  1 | 0 1 1 0 0 1
----------------------------------+-------------------+-------------------------------------+----------------------------------------+------------
 o..... 3 x.....   ......         |  3  0  0  0  0  0 |  3  0  0  0  0  0  0  0  0  0  0  0 | N  * *  *  * *  * *  *  * *  * *  *  * | 1 0 0 0 0 1
 ......   xwwx..   ......    &#xt |  2  2  2  2  0  0 |  1  2  0  2  0  2  1  0  0  0  0  0 | * 3N *  *  * *  * *  *  * *  * *  *  * | 1 0 1 0 0 0
 .o....   ......   .x.... 3*a     |  0  3  0  0  0  0 |  0  0  3  0  0  0  0  0  0  0  0  0 | *  * N  *  * *  * *  *  * *  * *  *  * | 0 1 0 1 0 0
 .ox...   ......   ......    &#x  |  0  1  2  0  0  0 |  0  0  0  2  1  0  0  0  0  0  0  0 | *  * * 3N  * *  * *  *  * *  * *  *  * | 1 0 0 1 0 0
 ......   ......   .xo...    &#x  |  0  2  1  0  0  0 |  0  0  1  2  0  0  0  0  0  0  0  0 | *  * *  * 3N *  * *  *  * *  * *  *  * | 0 0 1 1 0 0
 ..x...   ......   ..o... 3*a     |  0  0  3  0  0  0 |  0  0  0  0  3  0  0  0  0  0  0  0 | *  * *  *  * N  * *  *  * *  * *  *  * | 0 1 0 1 0 0
 ..xwwx   ......   ......    &#xt |  0  0  2  2  2  2 |  0  0  0  0  1  2  0  2  0  2  1  0 | *  * *  *  * * 3N *  *  * *  * *  *  * | 1 1 0 0 0 0
 ......   ...x.. 3 ...o..         |  0  0  0  3  0  0 |  0  0  0  0  0  0  3  0  0  0  0  0 | *  * *  *  * *  * N  *  * *  * *  *  * | 0 0 1 0 1 0
 ......   ...xo.   ......    &#x  |  0  0  0  2  1  0 |  0  0  0  0  0  0  1  2  0  0  0  0 | *  * *  *  * *  * * 3N  * *  * *  *  * | 1 0 0 0 1 0
 ......   ......   ...ox.    &#x  |  0  0  0  1  2  0 |  0  0  0  0  0  0  0  2  1  0  0  0 | *  * *  *  * *  * *  * 3N *  * *  *  * | 0 1 0 0 1 0
 ......   ....o. 3 ....x.         |  0  0  0  0  3  0 |  0  0  0  0  0  0  0  0  3  0  0  0 | *  * *  *  * *  * *  *  * N  * *  *  * | 0 0 1 0 1 0
 ......   ......  :wx..xw:   &#xt |  2  2  0  0  2  2 |  0  2  1  0  0  0  0  0  1  2  0  2 | *  * *  *  * *  * *  *  * * 3N *  *  * | 0 1 1 0 0 0
 .....x 3 .....o   ......         |  0  0  0  0  0  3 |  0  0  0  0  0  0  0  0  0  0  3  0 | *  * *  *  * *  * *  *  * *  * N  *  * | 1 0 0 0 0 1
:o....x:  ......   ......    &#x  |  1  0  0  0  0  2 |  0  0  0  0  0  0  0  0  0  0  1  2 | *  * *  *  * *  * *  *  * *  * * 3N  * | 0 1 0 0 0 1
 ......  :x....o:  ......    &#x  |  2  0  0  0  0  1 |  1  0  0  0  0  0  0  0  0  0  0  2 | *  * *  *  * *  * *  *  * *  * *  * 3N | 0 0 1 0 0 1
----------------------------------+-------------------+-------------------------------------+----------------------------------------+------------
 ooxwwx 3 xwwxoo   ......    &#xt   3  3  6  6  3  3 |  3  3  0  6  3  6  3  6  0  3  3  0 | 1  3 0  3  0 0  3 0  3  0 0  0 1  0  0 | N * * * * *
:ooxwwx:  ......  :wxooxw:3*a&#xt   3  3  3  3  6  6 |  0  3  3  0  3  3  0  6  3  6  3  6 | 0  0 1  0  0 1  3 0  0  3 0  3 0  3  0 | * N * * * *
 ......  :xwwxoo:3:wxooxw:   &#xt   6  6  3  3  3  3 |  3  6  3  6  0  3  3  0  3  3  0  6 | 0  3 0  0  3 0  0 1  0  0 1  3 0  0  3 | * * N * * *
 .ox...   ......   .xo... 3*a&#x    0  3  3  0  0  0 |  0  0  3  6  3  0  0  0  0  0  0  0 | 0  0 1  3  3 1  0 0  0  0 0  0 0  0  0 | * * * N * *
 ......   ...xo. 3 ...ox.    &#x    0  0  0  3  3  0 |  0  0  0  0  0  0  3  6  3  0  0  0 | 0  0 0  0  0 0  0 1  3  3 1  0 0  0  0 | * * * * N *
:o....x:3:x....o:  ......    &#x    3  0  0  0  0  3 |  3  0  0  0  0  0  0  0  0  0  3  6 | 1  0 0  0  0 0  0 0  0  0 0  0 1  3  3 | * * * * * N

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