© ©
©
©
- general polytopal classes:
- partial Stott expansions
- unit-edged relatives:
- atich
links
| Acronym | tich |
| Name | truncated cubic honeycomb |
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| Vertex figure |
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| Confer |
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External links |
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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
wx4ox3xo4xw&#zx (N → ∞) → height = 0 (tegum sum of 2 inverted (w,x,x)-prichs) o.4o.3o.4o. & | 24N | 2 1 2 | 1 2 2 3 | 1 3 1 ------------------+-----+-------------+--------------+-------- .. .. x. .. & | 2 | 24N * * | 1 1 0 1 | 1 1 1 .. .. .. x. & | 2 | * 12N * | 0 2 2 0 | 1 3 0 oo4oo3oo4oo&#x | 2 | * * 24N | 0 0 1 2 | 0 2 1 ------------------+-----+-------------+--------------+-------- .. o.3x. .. & | 3 | 3 0 0 | 8N * * * | 1 0 1 .. .. x.4x. & | 8 | 4 4 0 | * 6N * * | 1 1 0 wx .. .. xw&#zx | 8 | 0 4 4 | * * 6N * | 0 2 0 .. ox .. ..&#x & | 3 | 1 0 2 | * * * 24N | 0 1 1 ------------------+-----+-------------+--------------+-------- .. o.3x.4x. & ♦ 24 | 24 12 0 | 8 6 0 0 | N * * wx4ox .. xw&#zx & ♦ 24 | 8 12 16 | 0 2 4 8 | * 3N * .. ox3xo ..&#x ♦ 6 | 6 0 6 | 2 0 0 6 | * * 4N
: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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