Acronym sarx
Name small rhombated hexateron,
cantellated hexateron
Circumradius sqrt(5/3) = 1.290994
Vertex figure
 ©
Lace city
in approx. ASCII-art
      x3o3o  o3x3o  		-- o3x3o3o (rap)
                    
                    
                    
x3o3o  u3o3o  x3x3o 		-- x3x3o3o (tip)
                    
                    
                    
 o3x3o  x3x3o  x3o3x		-- x3o3x3o (srip)
Lace hyper city
in approx. ASCII-art
     .    .   
              
 .   o3o  x3o 
              
  .   x3o  o3x
(rap layer)
    o3o  x3o  
              
o3o   .   u3o 
              
 x3o  u3o  x3x
(tip layer)
    x3o  o3x  
              
x3o  u3o  x3x 
              
 o3x  x3x  x3o
(srip layer)
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: rap rawvtip sirdop srip tepe thiddip tip tuttip
rawcax 66001520015
rawx 66000060
sarx 600615000
lawx 006015060
& others)
Confer
related segmentotera:
rapatip   trathiddip  
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x3o3x3o3o

. . . . . | 60 |  2   6 |  1  6  3   6 |  3  6  3  2 | 3  2 1
----------+----+--------+--------------+-------------+-------
x . . . . |  2 | 60   * |  1  3  0   0 |  3  3  0  0 | 3  1 0
. . x . . |  2 |  * 180 |  0  1  1   2 |  1  2  2  1 | 2  1 1
----------+----+--------+--------------+-------------+-------
x3o . . . |  3 |  3   0 | 20  *  *   * |  3  0  0  0 | 3  0 0
x . x . . |  4 |  2   2 |  * 90  *   * |  1  2  0  0 | 2  1 0
. o3x . . |  3 |  0   3 |  *  * 60   * |  1  0  2  0 | 2  0 1
. . x3o . |  3 |  0   3 |  *  *  * 120 |  0  1  1  1 | 1  1 1
----------+----+--------+--------------+-------------+-------
x3o3x . .  12 | 12  12 |  4  6  4   0 | 15  *  *  * | 2  0 0
x . x3o .   6 |  3   6 |  0  3  0   2 |  * 60  *  * | 1  1 0
. o3x3o .   6 |  0  12 |  0  0  4   4 |  *  * 30  * | 1  0 1
. . x3o3o   4 |  0   6 |  0  0  0   4 |  *  *  * 30 | 0  1 1
----------+----+--------+--------------+-------------+-------
x3o3x3o .  30 | 30  60 | 10 30 20  20 |  5 10  5  0 | 6  * *
x . x3o3o   8 |  4  12 |  0  6  0   8 |  0  4  0  2 | * 15 *
. o3x3o3o  10 |  0  30 |  0  0 10  20 |  0  0  5  5 | *  * 6

x3o3x3o3/2o

. . . .   . | 60 |  2   6 |  1  6  3   6 |  3  6  3  2 | 3  2 1
------------+----+--------+--------------+-------------+-------
x . . .   . |  2 | 60   * |  1  3  0   0 |  3  3  0  0 | 3  1 0
. . x .   . |  2 |  * 180 |  0  1  1   2 |  1  2  2  1 | 2  1 1
------------+----+--------+--------------+-------------+-------
x3o . .   . |  3 |  3   0 | 20  *  *   * |  3  0  0  0 | 3  0 0
x . x .   . |  4 |  2   2 |  * 90  *   * |  1  2  0  0 | 2  1 0
. o3x .   . |  3 |  0   3 |  *  * 60   * |  1  0  2  0 | 2  0 1
. . x3o   . |  3 |  0   3 |  *  *  * 120 |  0  1  1  1 | 1  1 1
------------+----+--------+--------------+-------------+-------
x3o3x .   .  12 | 12  12 |  4  6  4   0 | 15  *  *  * | 2  0 0
x . x3o   .   6 |  3   6 |  0  3  0   2 |  * 60  *  * | 1  1 0
. o3x3o   .   6 |  0  12 |  0  0  4   4 |  *  * 30  * | 1  0 1
. . x3o3/2o   4 |  0   6 |  0  0  0   4 |  *  *  * 30 | 0  1 1
------------+----+--------+--------------+-------------+-------
x3o3x3o   .  30 | 30  60 | 10 30 20  20 |  5 10  5  0 | 6  * *
x . x3o3/2o   8 |  4  12 |  0  6  0   8 |  0  4  0  2 | * 15 *
. o3x3o3/2o  10 |  0  30 |  0  0 10  20 |  0  0  5  5 | *  * 6

oxx3xxo3oox3ooo&#xt   → both heights = sqrt(3/5) = 0.774597
(rap || pseudo tip || srip)

o..3o..3o..3o..     | 10  *  * |  6  2  0  0  0  0  0 |  3  6  1  6  0  0  0  0  0  0  0  0 | 3 2  6  3 0  0  0  0 0  0 0 | 1 2 3  0 0 0
.o.3.o.3.o.3.o.     |  * 20  * |  0  1  1  3  3  0  0 |  0  0  1  3  3  3  3  3  0  0  0  0 | 0 0  3  3 1  3  3  1 0  0 0 | 0 1 3  1 1 0
..o3..o3..o3..o     |  *  * 30 |  0  0  0  0  2  2  4 |  0  0  0  0  0  2  1  4  1  4  2  2 | 0 0  0  1 0  4  2  2 2  2 1 | 0 0 2  2 1 1
--------------------+----------+----------------------+-------------------------------------+-----------------------------+-------------
... x.. ... ...     |  2  0  0 | 30  *  *  *  *  *  * |  1  2  0  1  0  0  0  0  0  0  0  0 | 2 1  2  1 0  0  0  0 0  0 0 | 1 1 2  0 0 0
oo.3oo.3oo.3oo.&#x  |  1  1  0 |  * 20  *  *  *  *  * |  0  0  1  3  0  0  0  0  0  0  0  0 | 0 0  3  3 0  0  0  0 0  0 0 | 0 1 3  0 0 0
.x. ... ... ...     |  0  2  0 |  *  * 10  *  *  *  * |  0  0  1  0  0  3  0  0  0  0  0  0 | 0 0  0  3 0  3  0  0 0  0 0 | 0 0 3  1 0 0
... .x. ... ...     |  0  2  0 |  *  *  * 30  *  *  * |  0  0  0  1  2  0  1  0  0  0  0  0 | 0 0  2  1 1  0  2  0 0  0 0 | 0 1 2  0 1 0
.oo3.oo3.oo3.oo&#x  |  0  1  1 |  *  *  *  * 60  *  * |  0  0  0  0  0  1  1  2  0  0  0  0 | 0 0  0  1 0  2  2  1 0  0 0 | 0 0 2  1 1 0
..x ... ... ...     |  0  0  2 |  *  *  *  *  * 30  * |  0  0  0  0  0  1  0  0  1  2  0  0 | 0 0  0  1 0  2  0  0 2  1 0 | 0 0 2  1 0 1
... ... ..x ...     |  0  0  2 |  *  *  *  *  *  * 60 |  0  0  0  0  0  0  0  1  0  1  1  1 | 0 0  0  0 0  1  1  1 1  1 1 | 0 0 1  1 1 1
--------------------+----------+----------------------+-------------------------------------+-----------------------------+-------------
o..3x.. ... ...     |  3  0  0 |  3  0  0  0  0  0  0 | 10  *  *  *  *  *  *  *  *  *  *  * | 2 0  0  1 0  0  0  0 0  0 0 | 1 0 2  0 0 0
... x..3o.. ...     |  3  0  0 |  3  0  0  0  0  0  0 |  * 20  *  *  *  *  *  *  *  *  *  * | 1 1  1  0 0  0  0  0 0  0 0 | 1 1 1  0 0 0
ox. ... ... ...&#x  |  1  2  0 |  0  2  1  0  0  0  0 |  *  * 10  *  *  *  *  *  *  *  *  * | 0 0  0  3 0  0  0  0 0  0 0 | 0 0 3  0 0 0
... xx. ... ...&#x  |  2  2  0 |  1  2  0  1  0  0  0 |  *  *  * 30  *  *  *  *  *  *  *  * | 0 0  2  1 0  0  0  0 0  0 0 | 0 1 2  0 0 0
... .x.3.o. ...     |  0  3  0 |  0  0  0  3  0  0  0 |  *  *  *  * 20  *  *  *  *  *  *  * | 0 0  1  0 1  0  1  0 0  0 0 | 0 1 1  0 1 0
.xx ... ... ...&#x  |  0  2  2 |  0  0  1  0  2  1  0 |  *  *  *  *  * 30  *  *  *  *  *  * | 0 0  0  1 0  2  0  0 0  0 0 | 0 0 2  1 0 0
... .xo ... ...&#x  |  0  2  1 |  0  0  0  1  2  0  0 |  *  *  *  *  *  * 30  *  *  *  *  * | 0 0  0  1 0  0  2  0 0  0 0 | 0 0 2  0 1 0
... ... .ox ...&#x  |  0  1  2 |  0  0  0  0  2  0  1 |  *  *  *  *  *  *  * 60  *  *  *  * | 0 0  0  0 0  1  1  1 0  0 0 | 0 0 1  1 1 0
..x3..o ... ...     |  0  0  3 |  0  0  0  0  0  3  0 |  *  *  *  *  *  *  *  * 10  *  *  * | 0 0  0  1 0  0  0  0 2  0 0 | 0 0 2  0 0 1
..x ... ..x ...     |  0  0  4 |  0  0  0  0  0  2  2 |  *  *  *  *  *  *  *  *  * 30  *  * | 0 0  0  0 0  1  0  0 1  1 0 | 0 0 1  1 0 1
... ..o3..x ...     |  0  0  3 |  0  0  0  0  0  0  3 |  *  *  *  *  *  *  *  *  *  * 20  * | 0 0  0  0 0  0  1  0 1  0 1 | 0 0 1  0 1 1
... ... ..x3..o     |  0  0  3 |  0  0  0  0  0  0  3 |  *  *  *  *  *  *  *  *  *  *  * 20 | 0 0  0  0 0  0  0  1 0  1 1 | 0 0 0  1 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 | 5 *  *  * *  *  *  * *  * * | 1 0 1  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 | * 5  *  * *  *  *  * *  * * | 1 1 0  0 0 0
... xx.3oo. ...&#x    3  3  0 |  3  3  0  3  0  0  0 |  0  1  0  3  1  0  0  0  0  0  0  0 | * * 20  * *  *  *  * *  * * | 0 1 1  0 0 0
oxx3xxo ... ...&#xt   3  6  3 |  3  6  3  3  6  3  0 |  1  0  3  3  0  3  3  0  1  0  0  0 | * *  * 10 *  *  *  * *  * * | 0 0 2  0 0 0
... .x.3.o.3.o.       0  4  0 |  0  0  0  6  0  0  0 |  0  0  0  0  4  0  0  0  0  0  0  0 | * *  *  * 5  *  *  * *  * * | 0 1 0  0 1 0
.xx ... .ox ...&#x    0  2  4 |  0  0  1  0  4  2  2 |  0  0  0  0  0  2  0  2  0  1  0  0 | * *  *  * * 30  *  * *  * * | 0 0 1  1 0 0
... .xo3.ox ...&#x    0  3  3 |  0  0  0  3  6  0  3 |  0  0  0  0  1  0  3  3  0  0  1  0 | * *  *  * *  * 20  * *  * * | 0 0 1  0 1 0
... ... .ox3.oo&#x    0  1  3 |  0  0  0  0  3  0  3 |  0  0  0  0  0  0  0  3  0  0  0  1 | * *  *  * *  *  * 20 *  * * | 0 0 0  1 1 0
..x3..o3..x ...       0  0 12 |  0  0  0  0  0 12 12 |  0  0  0  0  0  0  0  0  4  6  4  0 | * *  *  * *  *  *  * 5  * * | 0 0 1  0 0 1
..x ... ..x3..o       0  0  6 |  0  0  0  0  0  3  6 |  0  0  0  0  0  0  0  0  0  3  0  2 | * *  *  * *  *  *  * * 10 * | 0 0 0  1 0 1
... ..o3..x3..o       0  0  6 |  0  0  0  0  0  0 12 |  0  0  0  0  0  0  0  0  0  0  4  4 | * *  *  * *  *  *  * *  * 5 | 0 0 0  0 1 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 | 5 5  0  0 0  0  0  0 0  0 0 | 1 * *  * * *
... xx.3oo.3oo.&#x    4  4  0 |  6  4  0  6  0  0  0 |  0  4  0  6  4  0  0  0  0  0  0  0 | 0 1  4  0 1  0  0  0 0  0 0 | * 5 *  * * *
oxx3xxo3oox ...&#xt   6 12 12 | 12 12  6 12 24 12 12 |  4  4  6 12  4 12 12 12  4  6  4  0 | 1 0  4  4 0  6  4  0 1  0 0 | * * 5  * * *
.xx ... .ox3.oo&#x    0  2  6 |  0  0  1  0  6  3  6 |  0  0  0  0  0  3  0  6  0  3  0  2 | 0 0  0  0 0  3  0  2 0  1 0 | * * * 10 * *
... .xo3.ox3.oo&#x    0  4  6 |  0  0  0  6 12  0 12 |  0  0  0  0  4  0  6 12  0  0  4  4 | 0 0  0  0 1  0  4  4 0  0 1 | * * *  * 5 *
..x3..o3..x3..o       0  0 30 |  0  0  0  0  0 30 60 |  0  0  0  0  0  0  0  0 10 30 20 20 | 0 0  0  0 0  0  0  0 5 10 5 | * * *  * * 1

ox(ou)xx3oo(xo)xo xx(uo)xo3ox(ox)oo&#xt   → all heights = 1/sqrt(3) = 0.577350
({3} || pseudo thiddip || pseudo tegum sum of 2 alternate (x,u)-triddips || pseudo alternate thiddip || ortho {3})

o.(..)..3o.(..).. o.(..)..3o.(..)..     & | 6  *  * | 2  6  0  0  0  0  0  0 | 1  6  6  3  0  0  0  0  0  0  0  0 0 |  2  6  3 3 0  0  0 0  0 | 2 1 3 0
.o(..)..3.o(..).. .o(..)..3.o(..)..     & | * 36  * | 0  1  2  1  1  2  1  0 | 0  2  1  1  1  2  2  1  2  2  1  1 0 |  1  2  2 1 1  1  1 2  3 | 1 1 3 1
..(o.)..3..(o.).. ..(o.)..3..(o.)..     & | *  * 18 | 0  0  0  0  0  4  2  2 | 0  0  0  0  0  0  2  4  2  4  1  2 1 |  0  0  1 1 0  2  2 2  6 | 0 1 3 2
------------------------------------------+---------+------------------------+--------------------------------------+-------------------------+--------
..(..).. ..(..).. x.(..).. ..(..)..     & | 2  0  0 | 6  *  *  *  *  *  *  * | 1  0  3  0  0  0  0  0  0  0  0  0 0 |  0  3  0 3 0  0  0 0  0 | 1 0 3 0
oo(..)..3oo(..).. oo(..)..3oo(..)..&#x  & | 1  1  0 | * 36  *  *  *  *  *  * | 0  2  1  1  0  0  0  0  0  0  0  0 0 |  1  2  2 1 0  0  0 0  0 | 1 1 2 0
.x(..).. ..(..).. ..(..).. ..(..)..     & | 0  2  0 | *  * 36  *  *  *  *  * | 0  1  0  0  1  1  1  0  0  0  0  0 0 |  1  1  1 0 1  1  0 1  0 | 1 1 2 0
..(..).. ..(..).. .x(..).. ..(..)..     & | 0  2  0 | *  *  * 18  *  *  *  * | 0  0  1  0  0  2  0  0  0  0  1  0 0 |  0  2  0 1 1  0  0 2  0 | 1 0 3 0
..(..).. ..(..).. ..(..).. .x(..)..     & | 0  2  0 | *  *  *  * 18  *  *  * | 0  0  0  1  0  0  0  0  2  0  0  1 0 |  0  0  2 1 0  0  1 0  2 | 0 1 2 1
.o(o.)..3.o(o.).. .o(o.)..3.o(o.)..&#x  & | 0  1  1 | *  *  *  *  * 72  *  * | 0  0  0  0  0  0  1  1  1  1  0  0 0 |  0  0  1 0 0  1  1 1  2 | 0 1 2 1
.o(.o)..3.o(.o).. .o(.o)..3.o(.o)..&#x  & | 0  1  1 | *  *  *  *  *  * 36  * | 0  0  0  0  0  0  0  0  0  2  1  1 0 |  0  0  0 1 0  0  0 2  3 | 0 0 3 1
..(..).. ..(x.).. ..(..).. ..(..)..     & | 0  0  2 | *  *  *  *  *  *  * 18 | 0  0  0  0  0  0  0  2  0  0  0  1 1 |  0  0  0 1 0  2  1 0  2 | 0 1 2 1
------------------------------------------+---------+------------------------+--------------------------------------+-------------------------+--------
..(..).. ..(..).. x.(..)..3..(o.)..     & | 3  0  0 | 3  0  0  0  0  0  0  0 | 2  *  *  *  *  *  *  *  *  *  *  * * |  0  0  0 3 0  0  0 0  0 | 0 0 3 0
ox(..).. ..(..).. ..(..).. ..(..)..&#x  & | 1  2  0 | 0  2  1  0  0  0  0  0 | * 36  *  *  *  *  *  *  *  *  *  * * |  1  1  1 0 0  0  0 0  0 | 1 1 1 0
..(..).. ..(..).. xx(..).. ..(..)..&#x  & | 2  2  0 | 1  2  0  1  0  0  0  0 | *  * 18  *  *  *  *  *  *  *  *  * * |  0  2  0 1 0  0  0 0  0 | 1 0 2 0
..(..).. ..(..).. ..(..).. ox(..)..&#x  & | 1  2  0 | 0  2  0  0  1  0  0  0 | *  *  * 18  *  *  *  *  *  *  *  * * |  0  0  2 1 0  0  0 0  0 | 0 1 2 0
.x(..)..3.o(..).. ..(..).. ..(..)..     & | 0  3  0 | 0  0  3  0  0  0  0  0 | *  *  *  * 12  *  *  *  *  *  *  * * |  1  0  0 0 1  1  0 0  0 | 1 1 1 0
.x(..).. ..(..).. .x(..).. ..(..)..     & | 0  4  0 | 0  0  2  2  0  0  0  0 | *  *  *  *  * 18  *  *  *  *  *  * * |  0  1  0 0 1  0  0 1  0 | 1 0 2 0
.x(o.).. ..(..).. ..(..).. ..(..)..&#x  & | 0  2  1 | 0  0  1  0  0  2  0  0 | *  *  *  *  *  * 36  *  *  *  *  * * |  0  0  1 0 0  1  0 1  0 | 0 1 2 0
..(..).. .o(x.).. ..(..).. ..(..)..&#x  & | 0  1  2 | 0  0  0  0  0  2  0  1 | *  *  *  *  *  *  * 36  *  *  *  * * |  0  0  0 0 0  1  1 0  1 | 0 1 1 1
..(..).. ..(..).. ..(..).. .x(o.)..&#x  & | 0  2  1 | 0  0  0  0  1  2  0  0 | *  *  *  *  *  *  *  * 36  *  *  * * |  0  0  1 0 0  0  1 0  1 | 0 1 1 1
.o(oo)o.3.o(oo)o. .o(oo)o.3.o(oo)o.&#xr   | 0  2  2 | 0  0  0  0  0  2  2  0 | *  *  *  *  *  *  *  *  * 36  *  * * |  0  0  0 0 0  0  0 1  2 | 0 0 2 1  cycle (BCED)
..(..).. ..(..).. .x(.o).. ..(..)..&#x  & | 0  2  1 | 0  0  0  1  0  0  2  0 | *  *  *  *  *  *  *  *  *  * 18  * * |  0  0  0 1 0  0  0 2  0 | 0 0 3 0
..(..).. ..(..).. ..(..).. .x(.x)..&#x  & | 0  2  2 | 0  0  0  0  1  0  2  1 | *  *  *  *  *  *  *  *  *  *  * 18 * |  0  0  0 1 0  0  0 0  2 | 0 0 2 1
..(o.)..3..(x.).. ..(..).. ..(..)..     & | 0  0  3 | 0  0  0  0  0  0  0  3 | *  *  *  *  *  *  *  *  *  *  *  * 6 |  0  0  0 1 0  2  0 0  0 | 0 1 2 0
------------------------------------------+---------+------------------------+--------------------------------------+-------------------------+--------
ox(..)..3oo(..).. ..(..).. ..(..)..&#x  &  1  3  0 | 0  3  3  0  0  0  0  0 | 0  3  0  0  1  0  0  0  0  0  0  0 0 | 12  *  * * *  *  * *  * | 1 1 0 0
ox(..).. ..(..).. xx(..).. ..(..)..&#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 |  * 18  * * *  *  * *  * | 1 0 1 0
ox(o.).. ..(..).. ..(..).. ox(o.)..&#xt &  1  4  1 | 0  4  2  0  2  4  0  0 | 0  2  0  2  0  0  2  0  2  0  0  0 0 |  *  * 18 * *  *  * *  * | 0 1 1 0
..(..).. ..(..).. xx(.o)..3ox(.x)..&#xt &  3  6  3 | 3  6  0  3  3  0  6  3 | 1  0  3  3  0  0  0  0  0  0  3  3 1 |  *  *  * 6 *  *  * *  * | 0 0 2 0
.x(..)..3.o(..).. .x(..).. ..(..)..     &  0  6  0 | 0  0  6  3  0  0  0  0 | 0  0  0  0  2  3  0  0  0  0  0  0 0 |  *  *  * * 6  *  * *  * | 1 0 1 0
.x(o.)..3.o(x.).. ..(..).. ..(..)..&#x  &  0  3  3 | 0  0  3  0  0  6  0  3 | 0  0  0  0  1  0  3  3  0  0  0  0 1 |  *  *  * * * 12  * *  * | 0 1 1 0
..(..).. .o(x.).. ..(..).. .x(o.)..&#xt &  0  2  2 | 0  0  0  0  1  4  0  1 | 0  0  0  0  0  0  0  2  2  0  0  0 0 |  *  *  * * *  * 18 *  * | 0 1 0 1
.x(ou)x. ..(..).. .x(ou)x. ..(..)..&#xt    0  8  4 | 0  0  4  4  0  8  8  0 | 0  0  0  0  0  2  4  0  0  4  4  0 0 |  *  *  * * *  *  * 9  * | 0 0 2 0
..(..).. ..(..).. ..(..).. .x(ox)o.&#xr    0  3  3 | 0  0  0  0  1  4  3  1 | 0  0  0  0  0  0  0  1  1  2  0  1 0 |  *  *  * * *  *  * * 36 | 0 0 1 1  cycle (BCED)
------------------------------------------+---------+------------------------+--------------------------------------+-------------------------+--------
ox(..)..3oo(..).. xx(..).. ..(..)..&#x  &  2  6  0 | 1  6  6  3  0  0  0  0 | 0  6  3  0  2  3  0  0  0  0  0  0 0 |  2  3  0 0 1  0  0 0  0 | 6 * * *
ox(o.)..3oo(x.).. ..(..).. ox(o.)..&#xt &  1  6  3 | 0  6  6  0  3 12  0  3 | 0  6  0  3  2  0  6  6  6  0  0  0 1 |  2  0  3 0 0  2  3 0  0 | * 6 * *
ox(ou)x. ..(..).. xx(uo)x.3ox(ox)o.&#xt &  3 18  9 | 3 12 12  9  6 24 18  6 | 1  6  6  6  2  6 12  6  6 12  9  6 2 |  0  3  3 2 1  2  0 3  6 | * * 6 *
..(..).. .o(xo)x. ..(..).. .x(ox)o.&#xr    0  4  4 | 0  0  0  0  2  8  4  2 | 0  0  0  0  0  0  0  4  4  4  0  2 0 |  0  0  0 0 0  0  2 0  4 | * * * 9

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