Acronym rag (old: ric)
Name rectified hexacontitetrapeton
Circumradius 1
Lace city
in approx. ASCII-art
 ©  
o   h   o	-- x3o3o3o4o (tac)
         
h   I   h	-- o3x3o3o4o (rat)
         
o   h   o	-- x3o3o3o4o (tac)

   \   \   \   \   \
     \   \   \   \   +-- o o3o3o4o (point)
       \   \   \   +---- x x3o3o4o (hexip)
         \   \   +------ compound of:
           \   \         o o3x3o4o (ico)
             \   \       u o3o3o4o (u-line)
               \   +---- x x3o3o4o (hexip)
                 +------ o o3o3o4o (point)

where:
o = o3o3o *b3o (point)
h = x3o3o *b3o (hex)
I = o3x3o *b3o (ico)
  p   P  	-- x3o3o3o4o (tac)
         
         
r   S   R	-- o3x3o3o4o (rat)
         
         
  p   P  	-- x3o3o3o4o (tac)

    \   \   \
     \   \   +- o3x3o3o3o (rix)
      \   +---- x3o3o3o3x (scad)
       +------- o3o3o3x3o (inv. rix)

where:
p = x3o3o3o (pen)
P = o3o3o3x (dual pen)
r = o3x3o3o (rap)
R = o3o3x3o (inv. rap)
S = x3o3o3x (spid)
Coordinates (1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0)   & all permutations, all changes of sign
Confer
related segmentopeta:
taccarat   rixascad   hexipaico   hexippy  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

o3x3o3o3o4o

. . . . . . | 60   16 |   8  48 |  24  64 |  32  32 | 16  2
------------+----+-----+---------+---------+---------+------
. x . . . . |  2 | 480 |   1   6 |   6  12 |  12   8 |  8  1
------------+----+-----+---------+---------+---------+------
o3x . . . . |  3 |   3 | 160   *    6   0 |  12   0 |  8  0
. x3o . . . |  3 |   3 |   * 960 |   1   4 |   4   4 |  4  1
------------+----+-----+---------+---------+---------+------
o3x3o . . .   6 |  12 |   4   4 | 240   * |   4   0 |  4  0
. x3o3o . .   4 |   6 |   0   4 |   * 960 |   1   2 |  2  1
------------+----+-----+---------+---------+---------+------
o3x3o3o . .  10 |  30 |  10  20 |   5   5 | 192   * |  2  0
. x3o3o3o .   5 |  10 |   0  10 |   0   5 |   * 384 |  1  1
------------+----+-----+---------+---------+---------+------
o3x3o3o3o .  15 |  60 |  20  60 |  15  30 |   6   6 | 64  *
. x3o3o3o4o  10 |  40 |   0  80 |   0  80 |   0  32 |  * 12

o3x3o3o3o4/3o

. . . . .   . | 60   16 |   8  48 |  24  64 |  32  32 | 16  2
--------------+----+-----+---------+---------+---------+------
. x . . .   . |  2 | 480 |   1   6 |   6  12 |  12   8 |  8  1
--------------+----+-----+---------+---------+---------+------
o3x . . .   . |  3 |   3 | 160   *    6   0 |  12   0 |  8  0
. x3o . .   . |  3 |   3 |   * 960 |   1   4 |   4   4 |  4  1
--------------+----+-----+---------+---------+---------+------
o3x3o . .   .   6 |  12 |   4   4 | 240   * |   4   0 |  4  0
. x3o3o .   .   4 |   6 |   0   4 |   * 960 |   1   2 |  2  1
--------------+----+-----+---------+---------+---------+------
o3x3o3o .   .  10 |  30 |  10  20 |   5   5 | 192   * |  2  0
. x3o3o3o   .   5 |  10 |   0  10 |   0   5 |   * 384 |  1  1
--------------+----+-----+---------+---------+---------+------
o3x3o3o3o   .  15 |  60 |  20  60 |  15  30 |   6   6 | 64  *
. x3o3o3o4/3o  10 |  40 |   0  80 |   0  80 |   0  32 |  * 12

o3o3o *b3o3x3o

. . .    . . . | 60   16 |  48   8 |  64  24 |  16  16  32 |  2  8  8
---------------+----+-----+---------+---------+-------------+---------
. . .    . x . |  2 | 480 |   6   1 |  12   6 |   4   4  12 |  1  4  4
---------------+----+-----+---------+---------+-------------+---------
. . .    o3x . |  3 |   3 | 960   * |   4   1 |   2   2   4 |  1  2  2
. . .    . x3o |  3 |   3 |   * 160    0   6 |   0   0  12 |  0  4  4
---------------+----+-----+---------+---------+-------------+---------
. o . *b3o3x .   4 |   6 |   4   0 | 960   * |   1   1   1 |  1  1  1
. . .    o3x3o   6 |  12 |   4   4 |   * 240 |   0   0   4 |  0  2  2
---------------+----+-----+---------+---------+-------------+---------
o3o . *b3o3x .   5 |  10 |  10   0 |   5   0 | 192   *   * |  1  1  0
. o3o *b3o3x .   5 |  10 |  10   0 |   5   0 |   * 192   * |  1  0  1
. o . *b3o3x3o  10 |  30 |  20  10 |   5   5 |   *   * 192 |  0  1  1
---------------+----+-----+---------+---------+-------------+---------
o3o3o *b3o3x .  10 |  40 |  80   0 |  80   0 |  16  16   0 | 12  *  *
o3o . *b3o3x3o  15 |  60 |  60  20 |  30  15 |   6   0   6 |  * 32  *
. o3o *b3o3x3o  15 |  60 |  60  20 |  30  15 |   0   6   6 |  *  * 32

xox3oxo3ooo3ooo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(tac || (pseudo) rat || tac)

o..3o..3o..3o..4o..    & | 20  *   8   8   0 |  24  8  24  0   0 |  32  24  32  0   0 | 16  32  16  0 | 1 16  1
.o.3.o.3.o.3.o.4.o.      |  * 40   0   4  12 |   0  2  24  6  24 |   0  12  48 12  16 |  0  24  32  8 | 0 16  2
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x.. ... ... ... ...    & |  2  0 | 80   *   * |   6  1   0  0   0 |  12   6   0  0   0 |  8  12   0  0 | 1  8  0
oo.3oo.3oo.3oo.4oo.&#x & |  1  1 |  * 160   * |   0  1   6  0   0 |   0   6  12  0   0 |  0  12   8  0 | 0  8  1
... .x. ... ... ...      |  0  2 |  *   * 240 |   0  0   2  1   4 |   0   2   8  4   4 |  0   8   8  4 | 0  8  1
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x..3o.. ... ... ...    & |  3  0 |  3   0   0 | 160  *   *  *   * |   4   1   0  0   0 |  4   4   0  0 | 1  4  0
xo. ... ... ... ...&#x & |  2  1 |  1   2   0 |   * 80   *  *   *    0   6   0  0   0 |  0  12   0  0 | 0  8  0
... ox. ... ... ...&#x & |  1  2 |  0   2   1 |   *  * 480  *   * |   0   1   4  0   0 |  0   4   4  0 | 0  4  1
.o.3.x. ... ... ...      |  0  3 |  0   0   3 |   *  *   * 80   *    0   2   0  4   0 |  0   8   0  4 | 0  8  0
... .x.3.o. ... ...      |  0  3 |  0   0   3 |   *  *   *  * 320 |   0   0   2  1   2 |  0   2   4  2 | 0  4  1
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x..3o..3o.. ... ...    &   4  0 |  6   0   0 |   4  0   0  0   0 | 160   *   *  *   * |  2   1   0  0 | 1  2  0
xo.3ox. ... ... ...&#x &   3  3 |  3   6   3 |   1  3   3  1   0 |   * 160   *  *   * |  0   4   0  0 | 0  4  0
... ox.3oo. ... ...&#x &   1  3 |  0   3   3 |   0  0   3  0   1 |   *   * 640  *   * |  0   1   2  0 | 0  2  1
.o.3.x.3.o. ... ...        0  6 |  0   0  12 |   0  0   0  4   4 |   *   *   * 80   * |  0   2   0  2 | 0  4  0
... .x.3.o.3.o. ...        0  4 |  0   0   6 |   0  0   0  0   4 |   *   *   *  * 160 |  0   0   2  1 | 0  2  1
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x..3o..3o..3o.. ...    &   5  0 | 10   0   0 |  10  0   0  0   0 |   5   0   0  0   0 | 64   *   *  * | 1  1  0
xo.3ox.3oo. ... ...&#x &   4  6 |  6  12  12 |   4  6  12  4   4 |   1   4   4  1   0 |  * 160   *  * | 0  2  0
... ox.3oo.3oo. ...&#x &   1  4 |  0   4   6 |   0  0   6  0   4 |   0   0   4  0   1 |  *   * 320  * | 0  1  1
.o.3.x.3.o.3.o. ...        0 10 |  0   0  30 |   0  0   0 10  20 |   0   0   0  5   5 |  *   *   * 32 | 0  2  0
-------------------------+-------+------------+-------------------+--------------------+---------------+--------
x..3o..3o..3o..4o..    &  10  0 | 40   0   0 |  80  0   0  0   0 |  80   0   0  0   0 | 32   0   0  0 | 2  *  *
xo.3ox.3oo.3oo. ...&#x &   5 10 | 10  20  30 |  10 10  30 10  20 |   5  10  20  5   5 |  1   5   5  1 | * 64  *
... oxo3ooo3ooo4ooo&#xt    2  8 |  0  16  24 |   0  0  48  0  32 |   0   0  64  0  16 |  0   0  32  0 | *  * 10

oxo3xoo3ooo3oox3oxo&#xt   → both heights = 1/sqrt(3) = 0.577350
(rix || pseudo scad || inv rix)

o..3o..3o..3o..3o..     & | 30  *    8   8   0 |  4  12   4  12  24   0 |  6  8  12  24  24   8  6  0 |  4  2 12  8  12   8  2  16  0 | 1  4  2  7  4
.o.3.o.3.o.3.o.3.o.       |  * 30    0   8   8 |  0   0   8  24  12  12 |  0  0  12   8  24  24 12  8 |  0  0  8  2   8  12  8  24  2 | 0  2  2  8  6
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
... x.. ... ... ...     & |  2  0 | 120   *   * |  1   3   0   0   3   0 |  3  3   3   6   3   0  0  0 |  3  1  6  3   3   1  0   3  0 | 1  3  1  3  1
oo.3oo.3oo.3oo.3oo.&#x  & |  1  1 |   * 240   * |  0   0   1   3   3   0 |  0  0   3   3   6   3  3  0 |  0  0  3  1   3   3  1   9  0 | 0  1  1  4  3
.x. ... ... ... ...     & |  0  2 |   *   * 120 |  0   0   1   3   0   3 |  0  0   3   0   3   6  3  3 |  0  0  3  0   1   3  3   9  1 | 0  1  1  4  3
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
o..3x.. ... ... ...     & |  3  0 |   3   0   0 | 40   *   *   *   *   *   3  0   3   0   0   0  0  0 |  3  0  6  0   0   0  0   3  0 | 1  3  0  3  1
... x..3o.. ... ...     & |  3  0 |   3   0   0 |  * 120   *   *   *   * |  1  2   0   2   0   0  0  0 |  2  1  2  2   1   0  0   0  0 | 1  2  1  1  0
ox. ... ... ... ...&#x  & |  1  2 |   0   2   1 |  *   * 120   *   *   *   0  0   3   0   0   0  3  0 |  0  0  3  0   0   0  0   9  0 | 0  1  0  4  3
... ... ... ... ox.&#x  & |  1  2 |   0   2   1 |  *   *   * 360   *   * |  0  0   0   0   2   2  1  0 |  0  0  0  0   1   2  1   4  0 | 0  0  1  2  2
... xo. ... ... ...&#x  & |  2  1 |   1   2   0 |  *   *   *   * 360   * |  0  0   1   2   2   0  0  0 |  0  0  2  1   2   1  0   2  0 | 0  1  1  2  1
.x.3.o. ... ... ...     & |  0  3 |   0   0   3 |  *   *   *   *   * 120 |  0  0   1   0   0   2  0  2 |  0  0  2  0   0   1  2   2  1 | 0  1  1  2  1
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
o..3x..3o.. ... ...     &   6  0 |  12   0   0 |  4   4   0   0   0   0 | 30  *   *   *   *   *  *  * |  2  0  2  0   0   0  0   0  0 | 1  2  0  1  0
... x..3o..3o.. ...     &   4  0 |   6   0   0 |  0   4   0   0   0   0 |  * 60   *   *   *   *  *  * |  1  1  0  1   0   0  0   0  0 | 1  1  1  0  0
ox.3xo. ... ... ...&#x  &   3  3 |   3   6   3 |  1   0   3   0   3   1 |  *  * 120   *   *   *  *  * |  0  0  2  0   0   0  0   2  0 | 0  1  0  2  1
... xo.3oo. ... ...&#x  &   3  1 |   3   3   0 |  0   1   0   0   3   0 |  *  *   * 240   *   *  *  * |  0  0  1  1   1   0  0   0  0 | 0  1  1  1  0
... xo. ... ... ox.&#x  &   2  2 |   1   4   1 |  0   0   0   2   2   0 |  *  *   *   * 360   *  *  * |  0  0  0  0   1   1  0   1  0 | 0  0  1  1  1
... ... ... oo.3ox.&#x  &   1  3 |   0   3   3 |  0   0   0   3   0   1 |  *  *   *   *   * 240  *  * |  0  0  0  0   0   1  1   1  0 | 0  0  1  1  1
oxo ... ... ... oxo&#xt     2  4 |   0   8   4 |  0   0   4   4   0   0 |  *  *   *   *   *   * 90  * |  0  0  0  0   0   0  0   4  0 | 0  0  0  2  2
.x.3.o.3.o. ... ...     &   0  4 |   0   0   6 |  0   0   0   0   0   4 |  *  *   *   *   *   *  * 60 |  0  0  1  0   0   0  1   0  1 | 0  1  1  1  0
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
o..3x..3o..3o.. ...     &  10  0 |  30   0   0 | 10  20   0   0   0   0 |  5  5   0   0   0   0  0  0 | 12  *  *  *   *   *  *   *  * | 1  1  0  0  0
... x..3o..3o..3o..     &   5  0 |  10   0   0 |  0  10   0   0   0   0 |  0  5   0   0   0   0  0  0 |  * 12  *  *   *   *  *   *  * | 1  0  1  0  0
ox.3xo.3oo. ... ...&#x  &   6  4 |  12  12   6 |  4   4   6   0  12   4 |  1  0   4   4   0   0  0  1 |  *  * 60  *   *   *  *   *  * | 0  1  0  1  0
... xo.3oo.3oo. ...&#x  &   4  1 |   6   4   0 |  0   4   0   0   6   0 |  0  1   0   4   0   0  0  0 |  *  *  * 60   *   *  *   *  * | 0  1  1  0  0
... xo.3oo. ... ox.&#x  &   3  2 |   3   6   1 |  0   1   0   3   6   0 |  0  0   0   2   3   0  0  0 |  *  *  *  * 120   *  *   *  * | 0  0  1  1  0
... xo. ... oo.3ox.&#x  &   2  3 |   1   6   3 |  0   0   0   6   3   1 |  0  0   0   0   3   2  0  0 |  *  *  *  *   * 120  *   *  * | 0  0  1  0  1
... ... oo.3oo.3ox.&#x  &   1  4 |   0   4   6 |  0   0   0   6   0   4 |  0  0   0   0   0   4  0  1 |  *  *  *  *   *   * 60   *  * | 0  0  1  1  0
oxo3xoo ... ... oxo&#xt &   4  6 |   3  18   9 |  1   0   9  12   6   2 |  0  0   2   0   3   2  3  0 |  *  *  *  *   *   *  * 120  * | 0  0  0  1  1
.x.3.o.3.o.3.o. ...     &   0  5 |   0   0  10 |  0   0   0   0   0  10 |  0  0   0   0   0   0  0  5 |  *  *  *  *   *   *  *   * 12 | 0  1  1  0  0
--------------------------+-------+-------------+------------------------+-----------------------------+-------------------------------+--------------
o..3x..3o..3o..3o..     &  15  0 |  60   0   0 | 20  60   0   0   0   0 | 15 30   0   0   0   0  0  0 |  6  6  0  0   0   0  0   0  0 | 2  *  *  *  *
ox.3xo.3oo.3oo. ...&#x  &  10  5 |  30  20  10 | 10  20  10   0  30  10 |  5  5  10  20   0   0  0  5 |  1  0  5  5   0   0  0   0  1 | * 12  *  *  *
... xo.3oo.3oo.3ox.&#x  &   5  5 |  10  20  10 |  0  10   0  30  30  10 |  0  5   0  20  30  20  0  5 |  0  1  0  5  10  10  5   0  1 | *  * 12  *  *
oxo3xoo3ooo ... oxo&#xt &   7  8 |  12  32  16 |  4   4  16  24  24   8 |  1  0   8   8  12   8  6  2 |  0  0  2  0   4   0  2   4  0 | *  *  * 30  *
oxo3xoo ... oox3oxo&#xt     6  9 |   6  36  18 |  2   0  18  36  18   6 |  0  0   6   0  18  12  9  0 |  0  0  0  0   0   6  0   6  0 | *  *  *  * 20

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