sez

Acronym

sez (old: shio)

Name

hepteractihecatonicosoctaexon,
equatorial cross-section of barz-first tark

Circumradius

sqrt(2) = 1.414214

Lace city
in approx. ASCII-art

©	r N r - o3o3x3o3o4o (brag) N R N - o3o3o3x3o4o (brox) r N r - o3o3x3o3o4o (brag) where: r - o3x3o3o4o (rat) N - o3o3x3o4o (nit) R - o3o3o3x4o (rin)

Coordinates

(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0) & all permutations, all changes of sign

Dihedral angles

at rix between bril and bril: arccos(-5/7) = 135.584691°
at dot between bril and brag: arccos[-1/sqrt(7)] = 112.207654°
at rat between brag and brag: 90°

Face vector

560, 6720, 15680, 14560, 6328, 1428, 142

Confer

related segmentoexa:: bragabrox
general polytopal classes:: Wythoffian polyexa

External
links

Incidence matrix according to Dynkin symbol

o3o3o3x3o3o4o

. . . . . . . | 560 ♦   24 |   36   48 |   24   72   32 |   6   48   48   4 |  12  32  6 |   8  4
--------------+-----+------+-----------+----------------+-------------------+------------+-------
. . . x . . . |   2 | 6720 |    3    4 |    3   12    4 |   1   12   12   1 |   4  12  3 |   4  3
--------------+-----+------+-----------+----------------+-------------------+------------+-------
. . o3x . . . |   3 |    3 | 6720    * |    2    4    0 |   1    8    4   0 |   4   8  1 |   4  2
. . . x3o . . |   3 |    3 |    * 8960 |    0    3    2 |   0    3    6   1 |   1   6  3 |   2  3
--------------+-----+------+-----------+----------------+-------------------+------------+-------
. o3o3x . . . ♦   4 |    6 |    4    0 | 3360    *    * |   1    4    0   0 |   4   4  0 |   4  1
. . o3x3o . . ♦   6 |   12 |    4    4 |    * 6720    * |   0    2    2   0 |   1   4  1 |   2  2
. . . x3o3o . ♦   4 |    6 |    0    4 |    *    * 4480 |   0    0    3   1 |   0   3  3 |   1  3
--------------+-----+------+-----------+----------------+-------------------+------------+-------
o3o3o3x . . . ♦   5 |   10 |   10    0 |    5    0    0 | 672    *    *   * |   4   0  0 |   4  0
. o3o3x3o . . ♦  10 |   30 |   20   10 |    5    5    0 |   * 2688    *   * |   1   2  0 |   2  1
. . o3x3o3o . ♦  10 |   30 |   10   20 |    0    5    5 |   *    * 2688   * |   0   2  1 |   1  2
. . . x3o3o4o ♦   8 |   24 |    0   32 |    0    0   16 |   *    *    * 280 |   0   0  3 |   0  3
--------------+-----+------+-----------+----------------+-------------------+------------+-------
o3o3o3x3o . . ♦  15 |   60 |   60   20 |   30   15    0 |   6    6    0   0 | 448   *  * |   2  0
. o3o3x3o3o . ♦  20 |   90 |   60   60 |   15   30   15 |   0    6    6   0 |   * 896  * |   1  1
. . o3x3o3o4o ♦  40 |  240 |   80  320 |    0   80  160 |   0    0   32  10 |   *   * 84 |   0  2
--------------+-----+------+-----------+----------------+-------------------+------------+-------
o3o3o3x3o3o . ♦  35 |  210 |  210  140 |  105  105   35 |  21   42   21   0 |   7   7  0 | 128  *
. o3o3x3o3o4o ♦ 160 | 1440 |  960 1920 |  240  960  960 |   0  192  384  60 |   0  64 12 |   * 14

o3o3o3x3o3o4/3o

. . . . . .   . | 560 ♦   24 |   36   48 |   24   72   32 |   6   48   48   4 |  12  32  6 |   8  4
----------------+-----+------+-----------+----------------+-------------------+------------+-------
. . . x . .   . |   2 | 6720 |    3    4 |    3   12    4 |   1   12   12   1 |   4  12  3 |   4  3
----------------+-----+------+-----------+----------------+-------------------+------------+-------
. . o3x . .   . |   3 |    3 | 6720    * |    2    4    0 |   1    8    4   0 |   4   8  1 |   4  2
. . . x3o .   . |   3 |    3 |    * 8960 |    0    3    2 |   0    3    6   1 |   1   6  3 |   2  3
----------------+-----+------+-----------+----------------+-------------------+------------+-------
. o3o3x . .   . ♦   4 |    6 |    4    0 | 3360    *    * |   1    4    0   0 |   4   4  0 |   4  1
. . o3x3o .   . ♦   6 |   12 |    4    4 |    * 6720    * |   0    2    2   0 |   1   4  1 |   2  2
. . . x3o3o   . ♦   4 |    6 |    0    4 |    *    * 4480 |   0    0    3   1 |   0   3  3 |   1  3
----------------+-----+------+-----------+----------------+-------------------+------------+-------
o3o3o3x . .   . ♦   5 |   10 |   10    0 |    5    0    0 | 672    *    *   * |   4   0  0 |   4  0
. o3o3x3o .   . ♦  10 |   30 |   20   10 |    5    5    0 |   * 2688    *   * |   1   2  0 |   2  1
. . o3x3o3o   . ♦  10 |   30 |   10   20 |    0    5    5 |   *    * 2688   * |   0   2  1 |   1  2
. . . x3o3o4/3o ♦   8 |   24 |    0   32 |    0    0   16 |   *    *    * 280 |   0   0  3 |   0  3
----------------+-----+------+-----------+----------------+-------------------+------------+-------
o3o3o3x3o .   . ♦  15 |   60 |   60   20 |   30   15    0 |   6    6    0   0 | 448   *  * |   2  0
. o3o3x3o3o   . ♦  20 |   90 |   60   60 |   15   30   15 |   0    6    6   0 |   * 896  * |   1  1
. . o3x3o3o4/3o ♦  40 |  240 |   80  320 |    0   80  160 |   0    0   32  10 |   *   * 84 |   0  2
----------------+-----+------+-----------+----------------+-------------------+------------+-------
o3o3o3x3o3o   . ♦  35 |  210 |  210  140 |  105  105   35 |  21   42   21   0 |   7   7  0 | 128  *
. o3o3x3o3o4/3o ♦ 160 | 1440 |  960 1920 |  240  960  960 |   0  192  384  60 |   0  64 12 |   * 14

o3o3o *b3x3o3o3o

. . .    . . . . | 560 ♦   24 |   48   36 |   16   16   72   24 |   4   24   24   48   6 |  6  16  16  12 |  4  4  4
-----------------+-----+------+-----------+---------------------+------------------------+----------------+---------
. . .    x . . . |   2 | 6720 |    4    3 |    2    2   12    3 |   1    6    6   12   1 |  3   6   6   4 |  3  2  2
-----------------+-----+------+-----------+---------------------+------------------------+----------------+---------
. o . *b3x . . . |   3 |    3 | 8960    * |    1    1    3    0 |   1    3    3    3   0 |  3   3   3   1 |  3  1  1
. . .    x3o . . |   3 |    3 |    * 6720 |    0    0    4    2 |   0    2    2    8   1 |  1   4   4   4 |  2  2  2
-----------------+-----+------+-----------+---------------------+------------------------+----------------+---------
o3o . *b3x . . . ♦   4 |    6 |    4    0 | 2240    *    *    * |   1    3    0    0   0 |  3   3   0   0 |  3  1  0
. o3o *b3x . . . ♦   4 |    6 |    4    0 |    * 2240    *    * |   1    0    3    0   0 |  3   0   3   0 |  3  0  1
. o . *b3x3o . . ♦   6 |   12 |    4    4 |    *    * 6720    * |   0    1    1    2   0 |  1   2   2   1 |  2  1  1
. . .    x3o3o . ♦   4 |    6 |    0    4 |    *    *    * 3360 |   0    0    0    4   1 |  0   2   2   4 |  1  2  2
-----------------+-----+------+-----------+---------------------+------------------------+----------------+---------
o3o3o *b3x . . . ♦   8 |   24 |   32    0 |    8    8    0    0 | 280    *    *    *   * |  3   0   0   0 |  3  0  0
o3o . *b3x3o . . ♦  10 |   30 |   20   10 |    5    0    5    0 |   * 1344    *    *   * |  1   2   0   0 |  2  1  0
. o3o *b3x3o . . ♦  10 |   30 |   20   10 |    0    5    5    0 |   *    * 1344    *   * |  1   0   2   0 |  2  0  1
. o . *b3x3o3o . ♦  10 |   30 |   10   20 |    0    0    5    5 |   *    *    * 2688   * |  0   1   1   1 |  1  1  1
. . .    x3o3o3o ♦   5 |   10 |    0   10 |    0    0    0    5 |   *    *    *    * 672 |  0   0   0   4 |  0  2  2
-----------------+-----+------+-----------+---------------------+------------------------+----------------+---------
o3o3o *b3x3o . . ♦  40 |  240 |  320   80 |   80   80   80    0 |  10   16   16    0   0 | 84   *   *   * |  2  0  0
o3o . *b3x3o3o . ♦  20 |   90 |   60   60 |   15    0   30   15 |   0    6    0    6   0 |  * 448   *   * |  1  1  0
. o3o *b3x3o3o . ♦  20 |   90 |   60   60 |    0   15   30   15 |   0    0    6    6   0 |  *   * 448   * |  1  0  1
. o . *b3x3o3o3o ♦  15 |   60 |   20   60 |    0    0   15   30 |   0    0    0    6   6 |  *   *   * 448 |  0  1  1
-----------------+-----+------+-----------+---------------------+------------------------+----------------+---------
o3o3o *b3x3o3o . ♦ 160 | 1440 | 1920  960 |  480  480  960  240 |  60  192  192  192   0 | 12  32  32   0 | 14  *  *
o3o . *b3x3o3o3o ♦  35 |  210 |  140  210 |   35    0  105  105 |   0   21    0   42  21 |  0   7   0   7 |  * 64  *
. o3o *b3x3o3o3o ♦  35 |  210 |  140  210 |    0   35  105  105 |   0    0   21   42  21 |  0   0   7   7 |  *  * 64

ooo3ooo3xox3oxo3ooo4ooo&#xt   → both heights =  = 1/sqrt(2) = 0.707107
(brag || pseudo brox || brag)

o..3o..3o..3o..3o..4o..     & | 320   * ♦   18    6    0 |   18   36   18   12    0    0 |   6   36   24   18   36    8   0   0 |  12  24   3   6   36   24   1   0   0 |   8  3  12  24  3  0 | 1   8  3
.o.3.o.3.o.3.o.3.o.4.o.       |   * 240 ♦    0    8   16 |    0    0   12   32   24   16 |   0    0    0    8   48   32  16  24 |   0   0   0   2   32   48   4   4  16 |   0  0   8  32  6  4 | 0   8  4
------------------------------+---------+----------------+-------------------------------+--------------------------------------+---------------------------------------+----------------------+---------
... ... x.. ... ... ...     & |   2   0 | 2880    *    * |    2    4    1    0    0    0 |   1    8    4    2    4    0   0   0 |   4   8   1   1    8    4   0   0   0 |   4  2   4   8  1  0 | 1   4  2
oo.3oo.3oo.3oo.3oo.4oo.&#x  & |   1   1 |    * 1920    * |    0    0    3    4    0    0 |   0    0    0    3   12    4   0   0 |   0   0   0   1   12   12   1   0   0 |   0  0   4  12  3  0 | 0   4  3
... ... ... .x. ... ...       |   0   2 |    *    * 1920 |    0    0    0    2    3    2 |   0    0    0    0    6    4   3   6 |   0   0   0   0    6   12   1   1   6 |   0  0   2  12  3  2 | 0   4  3
------------------------------+---------+----------------+-------------------------------+--------------------------------------+---------------------------------------+----------------------+---------
... o..3x.. ... ... ...     & |   3   0 |    3    0    0 | 1920    *    *    *    *    * |   1    4    0    1    0    0   0   0 |   4   4   0   1    4    0   0   0   0 |   4  1   4   4  0  0 | 1   4  1
... ... x..3o.. ... ...     & |   3   0 |    3    0    0 |    * 3840    *    *    *    * |   0    2    2    0    1    0   0   0 |   1   4   1   0    2    2   0   0   0 |   2  2   1   4  1  0 | 1   2  2
... ... xo. ... ... ...&#x  & |   2   1 |    1    2    0 |    *    * 2880    *    *    * |   0    0    0    2    4    0   0   0 |   0   0   0   1    8    4   0   0   0 |   0  0   4   8  1  0 | 0   4  2
... ... ... ox. ... ...&#x  & |   1   2 |    0    2    1 |    *    *    * 3840    *    * |   0    0    0    0    3    2   0   0 |   0   0   0   0    3    6   1   0   0 |   0  0   1   6  3  0 | 0   2  3
... ... .o.3.x. ... ...       |   0   3 |    0    0    3 |    *    *    *    * 1920    * |   0    0    0    0    2    0   2   2 |   0   0   0   0    4    4   0   1   4 |   0  0   2   8  1  2 | 0   4  2
... ... ... .x.3.o. ...       |   0   3 |    0    0    3 |    *    *    *    *    * 1280 |   0    0    0    0    0    2   0   3 |   0   0   0   0    0    6   1   0   3 |   0  0   0   6  3  1 | 0   2  3
------------------------------+---------+----------------+-------------------------------+--------------------------------------+---------------------------------------+----------------------+---------
o..3o..3x.. ... ... ...     & ♦   4   0 |    6    0    0 |    4    0    0    0    0    0 | 480    *    *    *    *    *   *   * |   4   0   0   1    0    0   0   0   0 |   4  0   4   0  0  0 | 1   4  0
... o..3x..3o.. ... ...     & ♦   6   0 |   12    0    0 |    4    4    0    0    0    0 |   * 1920    *    *    *    *   *   * |   1   2   0   0    1    0   0   0   0 |   2  1   1   2  0  0 | 1   2  1
... ... x..3o..3o.. ...     & ♦   4   0 |    6    0    0 |    0    4    0    0    0    0 |   *    * 1920    *    *    *   *   * |   0   2   1   0    0    1   0   0   0 |   1  2   0   2  1  0 | 1   1  2
... oo.3xo. ... ... ...&#x  & ♦   3   1 |    3    3    0 |    1    0    3    0    0    0 |   *    *    * 1920    *    *   *   * |   0   0   0   1    4    0   0   0   0 |   0  0   4   4  0  0 | 0   4  1
... ... xo.3ox. ... ...&#x  & ♦   3   3 |    3    6    3 |    0    1    3    3    1    0 |   *    *    *    * 3840    *   *   * |   0   0   0   0    2    2   0   0   0 |   0  0   1   4  1  0 | 0   2  2
... ... ... ox.3oo. ...&#x  & ♦   1   3 |    0    3    3 |    0    0    0    3    0    1 |   *    *    *    *    * 2560   *   * |   0   0   0   0    0    3   1   0   0 |   0  0   0   3  3  0 | 0   1  4
... .o.3.o.3.x. ... ...       ♦   0   4 |    0    0    6 |    0    0    0    0    4    0 |   *    *    *    *    *    * 960   * |   0   0   0   0    2    0   0   1   2 |   0  0   2   4  0  2 | 0   4  1
... ... .o.3.x.3.o. ...       ♦   0   6 |    0    0   12 |    0    0    0    0    4    4 |   *    *    *    *    *    *   * 960 |   0   0   0   0    0    2   0   0   2 |   0  0   0   4  1  1 | 0   2  2
------------------------------+---------+----------------+-------------------------------+--------------------------------------+---------------------------------------+----------------------+---------
o..3o..3x..3o.. ... ...     & ♦  10   0 |   30    0    0 |   20   10    0    0    0    0 |   5    5    0    0    0    0   0   0 | 384   *   *   *    *    *   *   *   * |   2  0   1   0  0  0 | 1   2  0
... o..3x..3o..3o.. ...     & ♦  10   0 |   30    0    0 |   10   20    0    0    0    0 |   0    5    5    0    0    0   0   0 |   * 768   *   *    *    *   *   *   * |   1  1   0   1  0  0 | 1   1  1
... ... x..3o..3o..4o..     & ♦   8   0 |   24    0    0 |    0   32    0    0    0    0 |   0    0   16    0    0    0   0   0 |   *   * 120   *    *    *   *   *   * |   0  2   0   0  1  0 | 1   0  2
oo.3oo.3xo. ... ... ...&#x  & ♦   4   1 |    6    4    0 |    4    0    6    0    0    0 |   1    0    0    4    0    0   0   0 |   *   *   * 480    *    *   *   *   * |   0  0   4   0  0  0 | 0   4  0
... oo.3xo.3ox. ... ...&#x  & ♦   6   4 |   12   12    6 |    4    4   12    6    4    0 |   0    1    0    4    4    0   1   0 |   *   *   *   * 1920    *   *   *   * |   0  0   1   2  0  0 | 0   2  1
... ... xo.3ox.3oo. ...&#x  & ♦   4   6 |    6   12   12 |    0    4    6   12    4    4 |   0    0    1    0    4    4   0   1 |   *   *   *   *    * 1920   *   *   * |   0  0   0   2  1  0 | 0   1  2
... ... ... oxo3ooo4ooo&#xt   ♦   2   6 |    0   12   12 |    0    0    0   24    0    8 |   0    0    0    0    0   16   0   0 |   *   *   *   *    *    * 160   *   * |   0  0   0   0  3  0 | 0   0  3
.o.3.o.3.o.3.x. ... ...       ♦   0   5 |    0    0   10 |    0    0    0    0   10    0 |   0    0    0    0    0    0   5   0 |   *   *   *   *    *    *   * 192   * |   0  0   2   0  0  2 | 0   4  0
... .o.3.o.3.x.3.o. ...       ♦   0  10 |    0    0   30 |    0    0    0    0   20   10 |   0    0    0    0    0    0   5   5 |   *   *   *   *    *    *   *   * 384 |   0  0   0   2  0  1 | 0   2  1
------------------------------+---------+----------------+-------------------------------+--------------------------------------+---------------------------------------+----------------------+---------
o..3o..3x..3o..3o.. ...     & ♦  20   0 |   90    0    0 |   60   60    0    0    0    0 |  15   30   15    0    0    0   0   0 |   6   6   0   0    0    0   0   0   0 | 128  *   *   *  *  * | 1   1  0
... o..3x..3o..3o..4o..     & ♦  40   0 |  240    0    0 |   80  320    0    0    0    0 |   0   80  160    0    0    0   0   0 |   0  32  10   0    0    0   0   0   0 |   * 24   *   *  *  * | 1   0  1
oo.3oo.3xo.3ox. ... ...&#x  & ♦  10   5 |   30   20   10 |   20   10   30   10   10    0 |   5    5    0   20   10    0   5   0 |   1   0   0   5    5    0   0   1   0 |   *  * 384   *  *  * | 0   2  0
... oo.3xo.3ox.3oo. ...&#x  & ♦  10  10 |   30   30   30 |   10   20   30   30   20   10 |   0    5    5   10   20   10   5   5 |   0   1   0   0    5    5   0   0   1 |   *  *   * 768  *  * | 0   1  1
... ... xox3oxo3ooo4ooo&#xt   ♦  16  24 |   48   96   96 |    0   64   48  192   32   64 |   0    0   32    0   64  128   0  16 |   0   0   2   0    0   32   8   0   0 |   *  *   *   * 60  * | 0   0  2
.o.3.o.3.o.3.x.3.o. ...       ♦   0  15 |    0    0   60 |    0    0    0    0   60   20 |   0    0    0    0    0    0  30  15 |   0   0   0   0    0    0   0   6   6 |   *  *   *   *  * 64 | 0   2  0
------------------------------+---------+----------------+-------------------------------+--------------------------------------+---------------------------------------+----------------------+---------
o..3o..3x..3o..3o..4o..     & ♦ 160   0 | 1440    0    0 |  960 1920    0    0    0    0 | 240  960  960    0    0    0   0   0 | 192 384  60   0    0    0   0   0   0 |  64 12   0   0  0  0 | 2   *  *
oo.3oo.3xo.3ox.3oo. ...&#x  & ♦  20  15 |   90   60   60 |   60   60   90   60   60   20 |  15   30   15   60   60   20  30  15 |   6   6   0  15   30   15   0   6   6 |   1  0   6   6  0  1 | * 128  *
... ooo3xox3oxo3ooo4ooo&#xt   ♦  80  80 |  480  480  480 |  160  640  480  960  320  320 |   0  160  320  160  640  640  80 160 |   0  64  20   0  160  320  40   0  32 |   0  2   0  64 10  0 | *   * 12

oxooo3ooxoo3xooxo3oxoox3ooxoo3oooxo&#xt   → all heights = sqrt(2/7) = 0.534522
(bril || pseudo spil || pseudo sibpof || pseudo inv. spil || inv. bril)

...

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