Acronym nit
Name penteractitriacontiditeron,
birectified penteract,
birectified triacontiditeron,
birectified pentacross,
Gosset polytope 02,1,1
Field of sections
 ©
Circumradius sqrt(3/2) = 1.224745
Vertex figure
 ©    ©
Lace city
in approx. ASCII-art
   o3x3o x3o3x o3x3o   	-- o3x3o4o (ico)
                       
                       
                       
x3o3o x3x3o o3x3x o3o3x	-- o3o3x4o (rit)
                       
                       
                       
   o3x3o x3o3x o3x3o   	-- o3x3o4o (ico)
   
       \     \     \     \
        \     \     \     +-- o3x3o3o (rap)
         \     \     +------- x3o3x3o (srip)
          \     +------------ o3x3o3x (inv. srip)
           +----------------- o3o3x3o (inv. rap)
 ©  
x3o4o   o3x4o   x3o4o	-- o3x3o4o (ico)
                     
                     
                     
                     
o3x4o   o3o4q   o3x4o	-- o3o3x4o (rit)
                     
                     
                     
                     
x3o4o   o3x4o   x3o4o	-- o3x3o4o (ico)
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: firp firt garpop ico ohope pinnip rap rawvtip sirdop srip
raccoth 3201604000000
irohlohn 16500016001616
nat 00320000000
nit 000100032000
irl 0000016016160
& others)
Confer
related segmentotera:
rapasrip   pabdinit   coa tutcup   ica tutcup   icarit   tisdippy  
related CRFs:
mibdinit  
general polytopal classes:
partial Stott expansions   Coxeter-Elte-Gosset polytopes  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

o3o3x3o4o

. . . . . | 80   12 |  12  12 |  4  12  3 |  4  3
----------+----+-----+---------+-----------+------
. . x . . |  2 | 480 |   2   2 |  1   4  1 |  2  2
----------+----+-----+---------+-----------+------
. o3x . . |  3 |   3 | 320   * |  1   2  0 |  2  1
. . x3o . |  3 |   3 |   * 320 |  0   2  1 |  1  2
----------+----+-----+---------+-----------+------
o3o3x . .   4 |   6 |   4   0 | 80   *  * |  2  0
. o3x3o .   6 |  12 |   4   4 |  * 160  * |  1  1
. . x3o4o   6 |  12 |   0   8 |  *   * 40 |  0  2
----------+----+-----+---------+-----------+------
o3o3x3o .  10 |  30 |  20  10 |  5   5  0 | 32  *
. o3x3o4o  24 |  96 |  32  64 |  0  16  8 |  * 10

o3o3x3o4/3o

. . . .   . | 80   12 |  12  12 |  4  12  3 |  4  3
------------+----+-----+---------+-----------+------
. . x .   . |  2 | 480 |   2   2 |  1   4  1 |  2  2
------------+----+-----+---------+-----------+------
. o3x .   . |  3 |   3 | 320   * |  1   2  0 |  2  1
. . x3o   . |  3 |   3 |   * 320 |  0   2  1 |  1  2
------------+----+-----+---------+-----------+------
o3o3x .   .   4 |   6 |   4   0 | 80   *  * |  2  0
. o3x3o   .   6 |  12 |   4   4 |  * 160  * |  1  1
. . x3o4/3o   6 |  12 |   0   8 |  *   * 40 |  0  2
------------+----+-----+---------+-----------+------
o3o3x3o   .  10 |  30 |  20  10 |  5   5  0 | 32  *
. o3x3o4/3o  24 |  96 |  32  64 |  0  16  8 |  * 10

o3x3o *b3o3o

. . .    . . | 80   12 |   6   6  12 |  3  6  6  4 |  3  2  2
-------------+----+-----+-------------+-------------+---------
. x .    . . |  2 | 480 |   1   1   2 |  1  2  2  1 |  2  1  1
-------------+----+-----+-------------+-------------+---------
o3x .    . . |  3 |   3 | 160   *   * |  1  2  0  0 |  2  1  0
. x3o    . . |  3 |   3 |   * 160   * |  1  0  2  0 |  2  0  1
. x . *b3o . |  3 |   3 |   *   * 320 |  0  1  1  1 |  1  1  1
-------------+----+-----+-------------+-------------+---------
o3x3o    . .   6 |  12 |   4   4   0 | 40  *  *  * |  2  0  0
o3x . *b3o .   6 |  12 |   4   0   4 |  * 80  *  * |  1  1  0
. x3o *b3o .   6 |  12 |   0   4   4 |  *  * 80  * |  1  0  1
. x . *b3o3o   4 |   6 |   0   0   4 |  *  *  * 80 |  0  1  1
-------------+----+-----+-------------+-------------+---------
o3x3o *b3o .  24 |  96 |  32  32  32 |  8  8  8  0 | 10  *  *
o3x . *b3o3o  10 |  30 |  10   0  20 |  0  5  0  5 |  * 16  *
. x3o *b3o3o  10 |  30 |   0  10  20 |  0  0  5  5 |  *  * 16

ooo3xox3oxo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(ico || pseudo rit || ico)

o..3o..3o..4o..     & | 48  *    8   4  0 |  4   8   8   4  0 |  4  2  4   8  1  0 | 1  4 2
.o.3.o.3.o.4.o.       |  * 32    0   6  6 |  0   0   6  12  6 |  0  0  2  12  3  2 | 0  4 3
----------------------+-------+------------+-------------------+--------------------+-------
... x.. ... ...     & |  2  0 | 192   *  * |  1   2   1   0  0 |  2  1  1   2  0  0 | 1  2 1
oo.3oo.3oo.4oo.&#x  & |  1  1 |   * 192  * |  0   0   2   2  0 |  0  0  1   4  1  0 | 0  2 2
... ... .x. ...       |  0  2 |   *   * 96 |  0   0   0   2  2 |  0  0  0   4  1  1 | 0  2 2
----------------------+-------+------------+-------------------+--------------------+-------
o..3x.. ... ...     & |  3  0 |   3   0  0 | 64   *   *   *  * |  2  0  1   0  0  0 | 1  2 0
... x..3o.. ...     & |  3  0 |   3   0  0 |  * 128   *   *  * |  1  1  0   1  0  0 | 1  1 1
... xo. ... ...&#x  & |  2  1 |   1   2  0 |  *   * 192   *  * |  0  0  1   2  0  0 | 0  2 1
... ... ox. ...&#x  & |  1  2 |   0   2  1 |  *   *   * 192  * |  0  0  0   2  1  0 | 0  1 2
... .o.3.x. ...       |  0  3 |   0   0  3 |  *   *   *   * 64 |  0  0  0   2  0  1 | 0  2 1
----------------------+-------+------------+-------------------+--------------------+-------
o..3x..3o.. ...     &   6  0 |  12   0  0 |  4   4   0   0  0 | 32  *  *   *  *  * | 1  1 0
... x..3o..4o..     &   6  0 |  12   0  0 |  0   8   0   0  0 |  * 16  *   *  *  * | 1  0 1
oo.3xo. ... ...&#x  &   3  1 |   3   3  0 |  1   0   3   0  0 |  *  * 64   *  *  * | 0  2 0
... xo.3ox. ...&#x  &   3  3 |   3   6  3 |  0   1   3   3  1 |  *  *  * 128  *  * | 0  1 1
... ... oxo4ooo&#xt     2  4 |   0   8  4 |  0   0   0   8  0 |  *  *  *   * 24  * | 0  0 2
.o.3.o.3.x. ...         0  4 |   0   0  6 |  0   0   0   0  4 |  *  *  *   *  * 16 | 0  2 0
----------------------+-------+------------+-------------------+--------------------+-------
o..3x..3o..4o..     &  24  0 |  96   0  0 | 32  64   0   0  0 | 16  8  0   0  0  0 | 2  * *
oo.3xo.3ox. ...&#x  &   6  4 |  12  12  6 |  4   4  12   6  4 |  1  0  4   4  0  1 | * 32 *
... xox3oxo4ooo&#xt    12 12 |  24  48 24 |  0  16  24  48  8 |  0  2  0  16  6  0 | *  * 8

oxo3xox3oxo *b3ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(ico || pseudo rit || ico)

o..3o..3o.. *b3o..     & | 48  *    8   4  0  0 |  4  4  4  2   8  2  0  0 |  2  2  2  4  4  4  1 0 0 | 1  2  2 2
.o.3.o.3.o. *b3.o.       |  * 32    0   6  3  3 |  0  0  0  6   6  6  3  3 |  0  0  0  6  6  2  3 1 1 | 0  2  2 3
-------------------------+-------+---------------+--------------------------+--------------------------+----------
... x.. ...    ...     & |  2  0 | 192   *  *  * |  1  1  1  0   1  0  0  0 |  1  1  1  1  1  1  0 0 0 | 1  1  1 1
oo.3oo.3oo. *b3oo.&#x  & |  1  1 |   * 192  *  * |  0  0  0  1   2  1  0  0 |  0  0  0  2  2  1  1 0 0 | 0  1  1 2
.x. ... ...    ...       |  0  2 |   *   * 48  * |  0  0  0  2   0  0  2  0 |  0  0  0  4  0  0  1 1 0 | 0  2  0 2
... ... .x.    ...       |  0  2 |   *   *  * 48 |  0  0  0  0   0  2  0  2 |  0  0  0  0  4  0  1 0 1 | 0  0  2 2
-------------------------+-------+---------------+--------------------------+--------------------------+----------
o..3x.. ...    ...     & |  3  0 |   3   0  0  0 | 64  *  *  *   *  *  *  * |  1  1  0  1  0  0  0 0 0 | 1  1  0 1
... x..3o..    ...     & |  3  0 |   3   0  0  0 |  * 64  *  *   *  *  *  * |  1  0  1  0  1  0  0 0 0 | 1  0  1 1
... x.. ... *b3o..     & |  3  0 |   3   0  0  0 |  *  * 64  *   *  *  *  * |  0  1  1  0  0  1  0 0 0 | 1  1  1 0
ox. ... ...    ...&#x  & |  1  2 |   0   2  1  0 |  *  *  * 96   *  *  *  * |  0  0  0  2  0  0  1 0 0 | 0  1  0 2
... xo. ...    ...&#x  & |  2  1 |   1   2  0  0 |  *  *  *  * 192  *  *  * |  0  0  0  1  1  1  0 0 0 | 0  1  1 1
... ... ox.    ...&#x  & |  1  2 |   0   2  0  1 |  *  *  *  *   * 96  *  * |  0  0  0  0  2  0  1 0 0 | 0  0  1 2
.x.3.o. ...    ...       |  0  3 |   0   0  3  0 |  *  *  *  *   *  * 32  * |  0  0  0  2  0  0  0 1 0 | 0  2  0 1
... .o.3.x.    ...       |  0  3 |   0   0  0  3 |  *  *  *  *   *  *  * 32 |  0  0  0  0  2  0  0 0 1 | 0  0  2 1
-------------------------+-------+---------------+--------------------------+--------------------------+----------
o..3x..3o..    ...     &   6  0 |  12   0  0  0 |  4  4  0  0   0  0  0  0 | 16  *  *  *  *  *  * * * | 1  0  0 1
o..3x.. ... *b3o..     &   6  0 |  12   0  0  0 |  4  0  4  0   0  0  0  0 |  * 16  *  *  *  *  * * * | 1  1  0 0
... x..3o.. *b3o..     &   6  0 |  12   0  0  0 |  0  4  4  0   0  0  0  0 |  *  * 16  *  *  *  * * * | 1  0  1 0
ox.3xo. ...    ...&#x  &   3  3 |   3   6  3  0 |  1  0  0  3   3  0  1  0 |  *  *  * 64  *  *  * * * | 0  1  0 1
... xo.3ox.    ...&#x  &   3  3 |   3   6  0  3 |  0  1  0  0   3  3  0  1 |  *  *  *  * 64  *  * * * | 0  0  1 1
... xo. ... *b3oo.&#x  &   3  1 |   3   3  0  0 |  0  0  1  0   3  0  0  0 |  *  *  *  *  * 64  * * * | 0  1  1 0
oxo ... oxo    ...&#xt     2  4 |   0   8  2  2 |  0  0  0  4   0  4  0  0 |  *  *  *  *  *  * 24 * * | 0  0  0 2
.x.3.o. ... *b3.o.         0  4 |   0   0  6  0 |  0  0  0  0   0  0  4  0 |  *  *  *  *  *  *  * 8 * | 0  2  0 0
... .o.3.x. *b3.o.         0  4 |   0   0  0  6 |  0  0  0  0   0  0  0  4 |  *  *  *  *  *  *  * * 8 | 0  0  2 0
-------------------------+-------+---------------+--------------------------+--------------------------+----------
o..3x..3o.. *b3o..     &  24  0 |  96   0  0  0 | 32 32 32  0   0  0  0  0 |  8  8  8  0  0  0  0 0 0 | 2  *  * *
ox.3xo. ... *b3oo.&#x  &   6  4 |  12  12  6  0 |  4  0  4  6  12  0  4  0 |  0  1  0  4  0  4  0 1 0 | * 16  * *
... xo.3ox. *b3oo.&#x  &   6  4 |  12  12  0  6 |  0  4  4  0  12  6  0  4 |  0  0  1  0  4  4  0 0 1 | *  * 16 *
oxo3xox3oxo    ...        12 12 |  24  48 12 12 |  8  8  0 24  24 24  4  4 |  2  0  0  8  8  0  6 0 0 | *  *  * 8

oxoo3xoxo3oxox3ooxo&#xt   → all heights = sqrt(2/5) = 0.632456
(rap || pseudo srip || pseudo inv srip || inv rap)

o...3o...3o...3o...     & | 20  *   6   6  0   0   0 |  3  6  3  6   6  0  0  0   0   0 |  3  2  3  6  2  3  0  0  0  0 | 1  2  3  1
.o..3.o..3.o..3.o..     & |  * 60   0   2  2   4   4 |  0  0  2  1   4  1  2  2   6   6 |  0  0  1  2  2  5  1  4  2  2 | 0  1  3  3
--------------------------+-------+-------------------+----------------------------------+-------------------------------+-----------
.... x... .... ....     & |  2  0 | 60   *  *   *   * |  1  2  0  1   0  0  0  0   0   0 |  2  1  1  2  0  0  0  0  0  0 | 1  1  2  0
oo..3oo..3oo..3oo..&#x  & |  1  1 |  * 120  *   *   * |  0  0  1  1   2  0  0  0   0   0 |  0  0  1  2  1  2  0  0  0  0 | 0  1  2  1
.x.. .... .... ....     & |  0  2 |  *   * 60   *   * |  0  0  1  0   0  1  0  0   2   0 |  0  0  1  0  0  2  0  2  1  0 | 0  0  2  2
.... .... .x.. ....     & |  0  2 |  *   *  * 120   * |  0  0  0  0   1  0  1  1   0   1 |  0  0  0  1  1  1  1  1  0  1 | 0  1  2  1
.oo.3.oo.3.oo.3.oo.&#x    |  0  2 |  *   *  *   * 120 |  0  0  0  0   0  0  0  0   2   2 |  0  0  0  0  0  2  0  2  1  1 | 0  0  2  2
--------------------------+-------+-------------------+----------------------------------+-------------------------------+-----------
o...3x... .... ....     & |  3  0 |  3   0  0   0   0 | 20  *  *  *   *  *  *  *   *   * |  2  0  1  0  0  0  0  0  0  0 | 1  0  2  0
.... x...3o... ....     & |  3  0 |  3   0  0   0   0 |  * 40  *  *   *  *  *  *   *   * |  1  1  0  1  0  0  0  0  0  0 | 1  1  1  0
ox.. .... .... ....&#x  & |  1  2 |  0   2  1   0   0 |  *  * 60  *   *  *  *  *   *   * |  0  0  1  0  0  2  0  0  0  0 | 0  0  2  1
.... xo.. .... ....&#x  & |  2  1 |  1   2  0   0   0 |  *  *  * 60   *  *  *  *   *   * |  0  0  1  2  0  0  0  0  0  0 | 0  1  2  0
.... .... ox.. ....&#x  & |  1  2 |  0   2  0   1   0 |  *  *  *  * 120  *  *  *   *   * |  0  0  0  1  1  1  0  0  0  0 | 0  1  1  1
.x..3.o.. .... ....     & |  0  3 |  0   0  3   0   0 |  *  *  *  *   * 20  *  *   *   * |  0  0  1  0  0  0  0  2  0  0 | 0  0  2  1
.... .o..3.x.. ....     & |  0  3 |  0   0  0   3   0 |  *  *  *  *   *  * 40  *   *   * |  0  0  0  1  0  0  1  0  0  1 | 0  1  2  0
.... .... .x..3.o..     & |  0  3 |  0   0  0   3   0 |  *  *  *  *   *  *  * 40   *   * |  0  0  0  0  1  0  1  1  0  0 | 0  1  1  1
.xo. .... .... ....&#x  & |  0  3 |  0   0  1   0   2 |  *  *  *  *   *  *  *  * 120   * |  0  0  0  0  0  1  0  1  1  0 | 0  0  1  2
.... .ox. .... ....&#x  & |  0  3 |  0   0  0   1   2 |  *  *  *  *   *  *  *  *   * 120 |  0  0  0  0  0  1  0  1  0  1 | 0  0  2  1
--------------------------+-------+-------------------+----------------------------------+-------------------------------+-----------
o...3x...3o... ....     &   6  0 | 12   0  0   0   0 |  4  4  0  0   0  0  0  0   0   0 | 10  *  *  *  *  *  *  *  *  * | 1  0  1  0
.... x...3o...3o...     &   4  0 |  6   0  0   0   0 |  0  4  0  0   0  0  0  0   0   0 |  * 10  *  *  *  *  *  *  *  * | 1  1  0  0
ox..3xo.. .... ....&#x  &   3  3 |  3   6  3   0   0 |  1  0  3  3   0  1  0  0   0   0 |  *  * 20  *  *  *  *  *  *  * | 0  0  2  0
.... xo..3ox.. ....&#x  &   3  3 |  3   6  0   3   0 |  0  1  0  3   3  0  1  0   0   0 |  *  *  * 40  *  *  *  *  *  * | 0  1  1  0
.... .... ox..3oo..&#x  &   1  3 |  0   3  0   3   0 |  0  0  0  0   3  0  0  1   0   0 |  *  *  *  * 40  *  *  *  *  * | 0  1  0  1
oxo. .... oxo. ....&#xt &   1  5 |  0   4  2   2   4 |  0  0  2  0   2  0  0  0   2   2 |  *  *  *  *  * 60  *  *  *  * | 0  0  1  1
.... .o..3.x..3.o..     &   0  6 |  0   0  0  12   0 |  0  0  0  0   0  0  4  4   0   0 |  *  *  *  *  *  * 10  *  *  * | 0  1  1  0
.xo.3.ox. .... ....&#x  &   0  6 |  0   0  3   3   6 |  0  0  0  0   0  1  0  1   3   3 |  *  *  *  *  *  *  * 40  *  * | 0  0  1  1
.xo. .... .... .ox.&#x      0  4 |  0   0  2   0   4 |  0  0  0  0   0  0  0  0   4   0 |  *  *  *  *  *  *  *  * 30  * | 0  0  0  2
.... .ox.3.xo. ....&#x      0  6 |  0   0  0   6   6 |  0  0  0  0   0  0  2  0   0   6 |  *  *  *  *  *  *  *  *  * 20 | 0  0  2  0
--------------------------+-------+-------------------+----------------------------------+-------------------------------+-----------
o...3x...3o...3o...     &  10  0 | 30   0  0   0   0 | 10 20  0  0   0  0  0  0   0   0 |  5  5  0  0  0  0  0  0  0  0 | 2  *  *  *
.... xo..3ox..3oo..&#x  &   4  6 |  6  12  0  12   0 |  0  4  0  6  12  0  4  4   0   0 |  0  1  0  4  4  0  1  0  0  0 | * 10  *  *
oxo.3xox.3oxo. ....&#xt &   6 18 | 12  24 12  24  24 |  4  4 12 12  12  4  8  4  12  24 |  1  0  4  4  0  6  1  4  0  4 | *  * 10  *
oxo. .... oxo.3oox.&#xt &   1  9 |  0   6  6   6  12 |  0  0  3  0   6  1  0  2  12   6 |  0  0  0  0  2  3  0  2  3  0 | *  *  * 20

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