Acronym spix
Name small prismated hexateron,
runcinated hexateron
Field of sections
 ©
Circumradius sqrt(17/12) = 1.190238
Lace city
in approx. ASCII-art
                _+---------------- x o3x3o (ope)
              _/              _+-- x x3o3x (cope)
            _/              _/

       o3x3o   o3o3x  		-- o3x3o3o (rap)
                      
                      
                      
o3x3o   x3x3o   x3o3x 		-- o3x3o3x (inv. srip)
                      
                      
                      
 o3o3x   x3o3x   x3o3o		-- x3o3o3x (spid)
Vertex figure
 ©    ©
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: chope duhd garpop ope rap rawvtip spid triddip
topax 150600000
rippix 06006600
spix 0001560620
& others)
Confer
segmentochora:
tetacope  
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x3o3o3x3o

. . . . . | 60   3   6 |  3  12   6  3 |  1  6  6  6  2  3 | 2  3  3 1
----------+----+--------+---------------+-------------------+----------
x . . . . |  2 | 90   * |  2   4   0  0 |  1  4  2  2  0  0 | 2  2  1 0
. . . x . |  2 |  * 180 |  0   2   2  1 |  0  1  2  2  1  2 | 1  1  2 1
----------+----+--------+---------------+-------------------+----------
x3o . . . |  3 |  3   0 | 60   *   *  * |  1  2  0  0  0  0 | 2  1  0 0
x . . x . |  4 |  2   2 |  * 180   *  * |  0  1  1  1  0  0 | 1  1  1 0
. . o3x . |  3 |  0   3 |  *   * 120  * |  0  0  1  0  1  1 | 1  0  1 1
. . . x3o |  3 |  0   3 |  *   *   * 60 |  0  0  0  2  0  2 | 0  1  2 1
----------+----+--------+---------------+-------------------+----------
x3o3o . .   4 |  6   0 |  4   0   0  0 | 15  *  *  *  *  * | 2  0  0 0
x3o . x .   6 |  6   3 |  2   3   0  0 |  * 60  *  *  *  * | 1  1  0 0
x . o3x .   6 |  3   6 |  0   3   2  0 |  *  * 60  *  *  * | 1  0  1 0
x . . x3o   6 |  3   6 |  0   3   0  2 |  *  *  * 60  *  * | 0  1  1 0
. o3o3x .   4 |  0   6 |  0   0   4  0 |  *  *  *  * 30  * | 1  0  0 1
. . o3x3o   6 |  0  12 |  0   0   4  4 |  *  *  *  *  * 30 | 0  0  1 1
----------+----+--------+---------------+-------------------+----------
x3o3o3x .  20 | 30  30 | 20  30  20  0 |  5 10 10  0  5  0 | 6  *  * *
x3o . x3o   9 |  9   9 |  3   9   0  3 |  0  3  0  3  0  0 | * 20  * *
x . o3x3o  12 |  6  24 |  0  12   8  8 |  0  0  4  4  0  2 | *  * 15 *
. o3o3x3o  10 |  0  30 |  0   0  20 10 |  0  0  0  0  5  5 | *  *  * 6

x3o3o3x3/2o

. . . .   . | 60   3   6 |  3  12   6  3 |  1  6  6  6  2  3 | 2  3  3 1
------------+----+--------+---------------+-------------------+----------
x . . .   . |  2 | 90   * |  2   4   0  0 |  1  4  2  2  0  0 | 2  2  1 0
. . . x   . |  2 |  * 180 |  0   2   2  1 |  0  1  2  2  1  2 | 1  1  2 1
------------+----+--------+---------------+-------------------+----------
x3o . .   . |  3 |  3   0 | 60   *   *  * |  1  2  0  0  0  0 | 2  1  0 0
x . . x   . |  4 |  2   2 |  * 180   *  * |  0  1  1  1  0  0 | 1  1  1 0
. . o3x   . |  3 |  0   3 |  *   * 120  * |  0  0  1  0  1  1 | 1  0  1 1
. . . x3/2o |  3 |  0   3 |  *   *   * 60 |  0  0  0  2  0  2 | 0  1  2 1
------------+----+--------+---------------+-------------------+----------
x3o3o .   .   4 |  6   0 |  4   0   0  0 | 15  *  *  *  *  * | 2  0  0 0
x3o . x   .   6 |  6   3 |  2   3   0  0 |  * 60  *  *  *  * | 1  1  0 0
x . o3x   .   6 |  3   6 |  0   3   2  0 |  *  * 60  *  *  * | 1  0  1 0
x . . x3/2o   6 |  3   6 |  0   3   0  2 |  *  *  * 60  *  * | 0  1  1 0
. o3o3x   .   4 |  0   6 |  0   0   4  0 |  *  *  *  * 30  * | 1  0  0 1
. . o3x3/2o   6 |  0  12 |  0   0   4  4 |  *  *  *  *  * 30 | 0  0  1 1
------------+----+--------+---------------+-------------------+----------
x3o3o3x   .  20 | 30  30 | 20  30  20  0 |  5 10 10  0  5  0 | 6  *  * *
x3o . x3/2o   9 |  9   9 |  3   9   0  3 |  0  3  0  3  0  0 | * 20  * *
x . o3x3/2o  12 |  6  24 |  0  12   8  8 |  0  0  4  4  0  2 | *  * 15 *
. o3o3x3/2o  10 |  0  30 |  0   0  20 10 |  0  0  0  0  5  5 | *  *  * 6

oox3xxo3ooo3oxx&#xt   → both heights = sqrt(3/5) = 0.774597
(rap || inv pseudo srip || spid)

o..3o..3o..3o..     | 10  *  * |  6  3  0  0  0  0  0 |  3  6 12  3  0  0  0  0  0  0  0  0  0  0 | 3 2  6  6  6  1 0  0  0  0  0  0  0 0  0  0 0 | 1 3  3 2 0  0  0 0
.o.3.o.3.o.3.o.     |  * 30  * |  0  1  4  2  2  0  0 |  0  0  4  2  2  2  4  1  1  4  4  0  0  0 | 0 0  2  2  4  1 1  2  2  2  2  4  2 0  0  0 0 | 0 1  2 2 1  2  1 0
..o3..o3..o3..o     |  *  * 20 |  0  0  0  0  3  3  3 |  0  0  0  0  0  0  0  0  3  3  6  3  6  3 | 0 0  0  0  0  0 0  0  3  6  1  3  3 1  3  3 1 | 0 0  0 1 1  3  3 1
--------------------+----------+----------------------+-------------------------------------------+-----------------------------------------------+-------------------
... x.. ... ...     |  2  0  0 | 30  *  *  *  *  *  * |  1  2  2  0  0  0  0  0  0  0  0  0  0  0 | 2 1  2  2  1  0 0  0  0  0  0  0  0 0  0  0 0 | 1 2  1 1 0  0  0 0
oo.3oo.3oo.3oo.&#x  |  1  1  0 |  * 30  *  *  *  *  * |  0  0  4  2  0  0  0  0  0  0  0  0  0  0 | 0 0  2  2  4  1 0  0  0  0  0  0  0 0  0  0 0 | 0 1  2 2 0  0  0 0
... .x. ... ...     |  0  2  0 |  *  * 60  *  *  *  * |  0  0  1  0  1  1  1  0  0  2  0  0  0  0 | 0 0  1  1  1  0 1  1  1  0  1  1  0 0  0  0 0 | 0 1  1 1 1  1  0 0
... ... ... .x.     |  0  2  0 |  *  *  * 30  *  *  * |  0  0  0  1  0  0  2  1  0  0  2  0  0  0 | 0 0  0  0  2  1 0  1  0  1  0  2  2 0  0  0 0 | 0 0  1 2 0  1  1 0
.oo3.oo3.oo3.oo&#x  |  0  1  1 |  *  *  *  * 60  *  * |  0  0  0  0  0  0  0  0  1  2  2  0  0  0 | 0 0  0  0  0  0 0  0  2  2  1  2  1 0  0  0 0 | 0 0  0 1 1  2  1 0
..x ... ... ...     |  0  0  2 |  *  *  *  *  * 30  * |  0  0  0  0  0  0  0  0  1  0  0  2  2  0 | 0 0  0  0  0  0 0  0  2  2  0  0  0 1  2  1 0 | 0 0  0 0 1  2  1 1
... ... ... ..x     |  0  0  2 |  *  *  *  *  *  * 30 |  0  0  0  0  0  0  0  0  0  0  2  0  2  2 | 0 0  0  0  0  0 0  0  0  2  0  1  2 0  1  2 1 | 0 0  0 1 0  1  2 1
--------------------+----------+----------------------+-------------------------------------------+-----------------------------------------------+-------------------
o..3x.. ... ...     |  3  0  0 |  3  0  0  0  0  0  0 | 10  *  *  *  *  *  *  *  *  *  *  *  *  * | 2 0  2  0  0  0 0  0  0  0  0  0  0 0  0  0 0 | 1 2  1 0 0  0  0 0
... x..3o.. ...     |  3  0  0 |  3  0  0  0  0  0  0 |  * 20  *  *  *  *  *  *  *  *  *  *  *  * | 1 1  0  1  0  0 0  0  0  0  0  0  0 0  0  0 0 | 1 1  0 1 0  0  0 0
... xx. ... ...&#x  |  2  2  0 |  1  2  1  0  0  0  0 |  *  * 60  *  *  *  *  *  *  *  *  *  *  * | 0 0  1  1  1  0 0  0  0  0  0  0  0 0  0  0 0 | 0 1  1 1 0  0  0 0
... ... ... ox.&#x  |  1  2  0 |  0  2  0  1  0  0  0 |  *  *  * 30  *  *  *  *  *  *  *  *  *  * | 0 0  0  0  2  1 0  0  0  0  0  0  0 0  0  0 0 | 0 0  1 2 0  0  0 0
.o.3.x. ... ...     |  0  3  0 |  0  0  3  0  0  0  0 |  *  *  *  * 20  *  *  *  *  *  *  *  *  * | 0 0  1  0  0  0 1  1  1  0  0  0  0 0  0  0 0 | 0 1  1 0 1  0  0 0
... .x.3.o. ...     |  0  3  0 |  0  0  3  0  0  0  0 |  *  *  *  *  * 20  *  *  *  *  *  *  *  * | 0 0  0  1  0  0 1  0  0  0  1  0  0 0  0  0 0 | 0 1  0 1 1  0  0 0
... .x. ... .x.     |  0  4  0 |  0  0  2  2  0  0  0 |  *  *  *  *  *  * 30  *  *  *  *  *  *  * | 0 0  0  0  1  0 0  1  0  0  0  1  0 0  0  0 0 | 0 0  1 1 0  1  0 0
... ... .o.3.x.     |  0  3  0 |  0  0  0  3  0  0  0 |  *  *  *  *  *  *  * 10  *  *  *  *  *  * | 0 0  0  0  0  1 0  0  0  0  0  0  2 0  0  0 0 | 0 0  0 2 0  0  1 0
.ox ... ... ...&#x  |  0  1  2 |  0  0  0  0  2  1  0 |  *  *  *  *  *  *  *  * 30  *  *  *  *  * | 0 0  0  0  0  0 0  0  2  2  0  0  0 0  0  0 0 | 0 0  0 0 1  2  1 0
... .xo ... ...&#x  |  0  2  1 |  0  0  1  0  2  0  0 |  *  *  *  *  *  *  *  *  * 60  *  *  *  * | 0 0  0  0  0  0 0  0  1  0  1  1  0 0  0  0 0 | 0 0  0 1 1  1  0 0
... ... ... .xx&#x  |  0  2  2 |  0  0  0  1  2  0  1 |  *  *  *  *  *  *  *  *  *  * 60  *  *  * | 0 0  0  0  0  0 0  0  0  1  0  1  1 0  0  0 0 | 0 0  0 1 0  1  1 0
..x3..o ... ...     |  0  0  3 |  0  0  0  0  0  3  0 |  *  *  *  *  *  *  *  *  *  *  * 20  *  * | 0 0  0  0  0  0 0  0  1  0  0  0  0 1  1  0 0 | 0 0  0 0 1  1  0 1
..x ... ... ..x     |  0  0  4 |  0  0  0  0  0  2  2 |  *  *  *  *  *  *  *  *  *  *  *  * 30  * | 0 0  0  0  0  0 0  0  0  1  0  0  0 0  1  1 0 | 0 0  0 0 0  1  1 1
... ... ..o3..x     |  0  0  3 |  0  0  0  0  0  0  3 |  *  *  *  *  *  *  *  *  *  *  *  *  * 20 | 0 0  0  0  0  0 0  0  0  0  0  0  1 0  0  1 1 | 0 0  0 1 0  0  1 1
--------------------+----------+----------------------+-------------------------------------------+-----------------------------------------------+-------------------
o..3x..3o.. ...       6  0  0 | 12  0  0  0  0  0  0 |  4  4  0  0  0  0  0  0  0  0  0  0  0  0 | 5 *  *  *  *  * *  *  *  *  *  *  * *  *  * * | 1 1  0 0 0  0  0 0
... x..3o..3o..       4  0  0 |  6  0  0  0  0  0  0 |  0  4  0  0  0  0  0  0  0  0  0  0  0  0 | * 5  *  *  *  * *  *  *  *  *  *  * *  *  * * | 1 0  0 1 0  0  0 0
oo.3xx. ... ...&#x    3  3  0 |  3  3  3  0  0  0  0 |  1  0  3  0  1  0  0  0  0  0  0  0  0  0 | * * 20  *  *  * *  *  *  *  *  *  * *  *  * * | 0 1  1 0 0  0  0 0
... xx.3oo. ...&#x    3  3  0 |  3  3  3  0  0  0  0 |  0  1  3  0  0  1  0  0  0  0  0  0  0  0 | * *  * 20  *  * *  *  *  *  *  *  * *  *  * * | 0 1  0 1 0  0  0 0
... xx. ... ox.&#x    2  4  0 |  1  4  2  2  0  0  0 |  0  0  2  2  0  0  1  0  0  0  0  0  0  0 | * *  *  * 30  * *  *  *  *  *  *  * *  *  * * | 0 0  1 1 0  0  0 0
... ... oo.3ox.&#x    1  3  0 |  0  3  0  3  0  0  0 |  0  0  0  3  0  0  0  1  0  0  0  0  0  0 | * *  *  *  * 10 *  *  *  *  *  *  * *  *  * * | 0 0  0 2 0  0  0 0
.o.3.x.3.o. ...       0  6  0 |  0  0 12  0  0  0  0 |  0  0  0  0  4  4  0  0  0  0  0  0  0  0 | * *  *  *  *  * 5  *  *  *  *  *  * *  *  * * | 0 1  0 0 1  0  0 0
.o.3.x. ... .x.       0  6  0 |  0  0  6  3  0  0  0 |  0  0  0  0  2  0  3  0  0  0  0  0  0  0 | * *  *  *  *  * * 10  *  *  *  *  * *  *  * * | 0 0  1 0 0  1  0 0
.ox3.xo ... ...&#x    0  3  3 |  0  0  3  0  6  3  0 |  0  0  0  0  1  0  0  0  3  3  0  1  0  0 | * *  *  *  *  * *  * 20  *  *  *  * *  *  * * | 0 0  0 0 1  1  0 0
.ox ... ... .xx&#x    0  2  4 |  0  0  0  1  4  2  2 |  0  0  0  0  0  0  0  0  2  0  2  0  1  0 | * *  *  *  *  * *  *  * 30  *  *  * *  *  * * | 0 0  0 0 0  1  1 0
... .xo3.oo ...&#x    0  3  1 |  0  0  3  0  3  0  0 |  0  0  0  0  0  1  0  0  0  3  0  0  0  0 | * *  *  *  *  * *  *  *  * 20  *  * *  *  * * | 0 0  0 1 1  0  0 0
... .xo ... .xx&#x    0  4  2 |  0  0  2  2  4  0  1 |  0  0  0  0  0  0  1  0  0  2  2  0  0  0 | * *  *  *  *  * *  *  *  *  * 30  * *  *  * * | 0 0  0 1 0  1  0 0
... ... .oo3.xx&#x    0  3  3 |  0  0  0  3  3  0  3 |  0  0  0  0  0  0  0  1  0  0  3  0  0  1 | * *  *  *  *  * *  *  *  *  *  * 20 *  *  * * | 0 0  0 1 0  0  1 0
..x3..o3..o ...       0  0  4 |  0  0  0  0  0  6  0 |  0  0  0  0  0  0  0  0  0  0  0  4  0  0 | * *  *  *  *  * *  *  *  *  *  *  * 5  *  * * | 0 0  0 0 1  0  0 1
..x3..o ... ..x       0  0  6 |  0  0  0  0  0  6  3 |  0  0  0  0  0  0  0  0  0  0  0  2  3  0 | * *  *  *  *  * *  *  *  *  *  *  * * 10  * * | 0 0  0 0 0  1  0 1
..x ... ..o3..x       0  0  6 |  0  0  0  0  0  3  6 |  0  0  0  0  0  0  0  0  0  0  0  0  3  2 | * *  *  *  *  * *  *  *  *  *  *  * *  * 10 * | 0 0  0 0 0  0  1 1
... ..o3..o3..x       0  0  4 |  0  0  0  0  0  0  6 |  0  0  0  0  0  0  0  0  0  0  0  0  0  4 | * *  *  *  *  * *  *  *  *  *  *  * *  *  * 5 | 0 0  0 1 0  0  0 1
--------------------+----------+----------------------+-------------------------------------------+-----------------------------------------------+-------------------
o..3x..3o..3o..      10  0  0 | 30  0  0  0  0  0  0 | 10 20  0  0  0  0  0  0  0  0  0  0  0  0 | 5 5  0  0  0  0 0  0  0  0  0  0  0 0  0  0 0 | 1 *  * * *  *  * *
oo.3xx.3oo. ...&#x    6  6  0 | 12  6 12  0  0  0  0 |  4  4 12  0  4  4  0  0  0  0  0  0  0  0 | 1 0  4  4  0  0 1  0  0  0  0  0  0 0  0  0 0 | * 5  * * *  *  * *
oo.3xx. ... ox.&#x    3  6  0 |  3  6  6  3  0  0  0 |  1  0  6  3  2  0  3  0  0  0  0  0  0  0 | 0 0  2  0  3  0 0  1  0  0  0  0  0 0  0  0 0 | * * 10 * *  *  * *
... xxo3ooo3oxx&#xt   4 12  4 |  6 12 12 12 12  0  6 |  0  4 12 12  0  4  6  4  0 12 12  0  0  4 | 0 1  0  4  6  4 0  0  0  0  4  6  4 0  0  0 1 | * *  * 5 *  *  * *
.ox3.xo3.oo ...&#x    0  6  4 |  0  0 12  0 12  6  0 |  0  0  0  0  4  4  0  0  6 12  0  4  0  0 | 0 0  0  0  0  0 1  0  4  0  4  0  0 1  0  0 0 | * *  * * 5  *  * *
.ox3.xo ... .xx&#x    0  6  6 |  0  0  6  3 12  6  3 |  0  0  0  0  2  0  3  0  6  6  6  2  3  0 | 0 0  0  0  0  0 0  1  2  3  0  3  0 0  1  0 0 | * *  * * * 10  * *
.ox ... .oo3.xx&#x    0  3  6 |  0  0  0  3  6  3  6 |  0  0  0  0  0  0  0  1  3  0  6  0  3  2 | 0 0  0  0  0  0 0  0  0  3  0  0  2 0  0  1 0 | * *  * * *  * 10 *
..x3..o3..o3..x       0  0 20 |  0  0  0  0  0 30 30 |  0  0  0  0  0  0  0  0  0  0  0 20 30 20 | 0 0  0  0  0  0 0  0  0  0  0  0  0 5 10 10 5 | * *  * * *  *  * 1

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