Acronym bittit
Name bitruncated triacontiditeron,
Voronoi cell of lattice D5*
Field of sections
 ©
Circumradius sqrt(9/2) = 2.121320
Vertex figure
 ©    ©
Lace city
in approx. ASCII-art
 ©  
x3o4o   u3o4o   x3x4o   u3o4o   x3o4o		-- x3x3o4o (thex)
                                     
                                     
                                     
u3o4o           o3u4o           u3o4o		-- o3u3o4o (u-ico)
                                     
                                     
                                     
x3x4o   o3u4o   o3x4q   o3u4o   x3x4o		-- o3x3x4o (tah)
                                     
                                     
                                     
u3o4o           o3u4o           u3o4o		-- o3u3o4o (u-ico)
                                     
                                     
                                     
x3o4o   u3o4o   x3x4o   u3o4o   x3o4o		-- x3x3o4o (thex)
Coordinates (sqrt(2), sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign
Dihedral angles
(at margins)
  • at tut between deca and deca:   arccos(-3/5) = 126.869898°
  • at tut between deca and thex:   arccos[-1/sqrt(5)] = 116.565051°
  • at oct between thex and thex:   90°
Confer
general polytopal classes:
lace simplices   partial Stott expansions  
External
links
hedrondude   wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

o3x3x3o4o

. . . . . | 240 |   2   4 |  1   8   4 |  4   8  1 |  4  2
----------+-----+---------+------------+-----------+------
. x . . . |   2 | 240   * |  1   4   0 |  4   4  0 |  4  1
. . x . . |   2 |   * 480 |  0   2   2 |  1   4  1 |  2  2
----------+-----+---------+------------+-----------+------
o3x . . . |   3 |   3   0 | 80   *   * |  4   0  0 |  4  0
. x3x . . |   6 |   3   3 |  * 320   * |  1   2  0 |  2  1
. . x3o . |   3 |   0   3 |  *   * 320 |  0   2  1 |  1  2
----------+-----+---------+------------+-----------+------
o3x3x . .   12 |  12   6 |  4   4   0 | 80   *  * |  2  0
. x3x3o .   12 |   6  12 |  0   4   4 |  * 160  * |  1  1
. . x3o4o    6 |   0  12 |  0   0   8 |  *   * 40 |  0  2
----------+-----+---------+------------+-----------+------
o3x3x3o .   30 |  30  30 | 10  20  10 |  5   5  0 | 32  *
. x3x3o4o   48 |  24  96 |  0  32  64 |  0  16  8 |  * 10

o3x3x3o4/3o

. . . .   . | 240 |   2   4 |  1   8   4 |  4   8  1 |  4  2
------------+-----+---------+------------+-----------+------
. x . .   . |   2 | 240   * |  1   4   0 |  4   4  0 |  4  1
. . x .   . |   2 |   * 480 |  0   2   2 |  1   4  1 |  2  2
------------+-----+---------+------------+-----------+------
o3x . .   . |   3 |   3   0 | 80   *   * |  4   0  0 |  4  0
. x3x .   . |   6 |   3   3 |  * 320   * |  1   2  0 |  2  1
. . x3o   . |   3 |   0   3 |  *   * 320 |  0   2  1 |  1  2
------------+-----+---------+------------+-----------+------
o3x3x .   .   12 |  12   6 |  4   4   0 | 80   *  * |  2  0
. x3x3o   .   12 |   6  12 |  0   4   4 |  * 160  * |  1  1
. . x3o4/3o    6 |   0  12 |  0   0   8 |  *   * 40 |  0  2
------------+-----+---------+------------+-----------+------
o3x3x3o   .   30 |  30  30 | 10  20  10 |  5   5  0 | 32  *
. x3x3o4/3o   48 |  24  96 |  0  32  64 |  0  16  8 |  * 10

o3x3o *b3x3o

. . .    . . | 240 |   4   2 |   2   2   8  1 |  1  4  4  4 |  2  2  2
-------------+-----+---------+----------------+-------------+---------
. x .    . . |   2 | 480   * |   1   1   2  0 |  1  2  2  1 |  2  1  1
. . .    x . |   2 |   * 240 |   0   0   4  1 |  0  2  2  4 |  1  2  2
-------------+-----+---------+----------------+-------------+---------
o3x .    . . |   3 |   3   0 | 160   *   *  * |  1  2  0  0 |  2  1  0
. x3o    . . |   3 |   3   0 |   * 160   *  * |  1  0  2  0 |  2  0  1
. x . *b3x . |   6 |   3   3 |   *   * 320  * |  0  1  1  1 |  1  1  1
. . .    x3o |   3 |   0   3 |   *   *   * 80 |  0  0  0  4 |  0  2  2
-------------+-----+---------+----------------+-------------+---------
o3x3o    . .    6 |  12   0 |   4   4   0  0 | 40  *  *  * |  2  0  0
o3x . *b3x .   12 |  12   6 |   4   0   4  0 |  * 80  *  * |  1  1  0
. x3o *b3x .   12 |  12   6 |   0   4   4  0 |  *  * 80  * |  1  0  1
. x . *b3x3o   12 |   6  12 |   0   0   4  4 |  *  *  * 80 |  0  1  1
-------------+-----+---------+----------------+-------------+---------
o3x3o *b3x .   48 |  96  24 |  32  32  32  0 |  8  8  8  0 | 10  *  *
o3x . *b3x3o   30 |  30  30 |  10   0  20 10 |  0  5  0  5 |  * 16  *
. x3o *b3x3o   30 |  30  30 |   0  10  20 10 |  0  0  5  5 |  *  * 16

xooox3xuxux3ooxoo4ooooo&#xt   → all heights = 1/sqrt(2) = 0.707107
(thex || u-ico || tah || u-ico || thex)

o....3o....3o....4o....     & | 96  *  * |  1   4  1   0  0  0 |  4   4  1   4   0  0  0 |  4  1  4   4  0  0 | 1  4 1
.o...3.o...3.o...4.o...     & |  * 48  * |  0   0  2   4  0  0 |  0   0  1   8   4  0  0 |  0  0  4   8  1  0 | 0  4 2
..o..3..o..3..o..4..o..       |  *  * 96 |  0   0  0   2  2  2 |  0   0  0   4   4  1  4 |  0  0  2   8  1  2 | 0  4 2
------------------------------+----------+---------------------+-------------------------+--------------------+-------
x.... ..... ..... .....     & |  2  0  0 | 48   *  *   *  *  * |  4   0  1   0   0  0  0 |  4  0  4   0  0  0 | 1  4 0
..... x.... ..... .....     & |  2  0  0 |  * 192  *   *  *  * |  1   2  0   1   0  0  0 |  2  1  1   2  0  0 | 1  2 1
oo...3oo...3oo...4oo...&#x  & |  1  1  0 |  *   * 96   *  *  * |  0   0  1   4   0  0  0 |  0  0  4   4  0  0 | 0  4 1
.oo..3.oo..3.oo..4.oo..&#x  & |  0  1  1 |  *   *  * 192  *  * |  0   0  0   2   2  0  0 |  0  0  1   4  1  0 | 0  2 2
..... ..x.. ..... .....       |  0  0  2 |  *   *  *   * 96  * |  0   0  0   2   0  1  2 |  0  0  2   4  0  2 | 0  4 1
..... ..... ..x.. .....       |  0  0  2 |  *   *  *   *  * 96 |  0   0  0   0   2  0  2 |  0  0  0   4  1  1 | 0  2 2
------------------------------+----------+---------------------+-------------------------+--------------------+-------
x....3x.... ..... .....     & |  6  0  0 |  3   3  0   0  0  0 | 64   *  *   *   *  *  * |  2  0  1   0  0  0 | 1  2 0
..... x....3o.... .....     & |  3  0  0 |  0   3  0   0  0  0 |  * 128  *   *   *  *  * |  1  1  0   1  0  0 | 1  1 1
xo... ..... ..... .....&#x  & |  2  1  0 |  1   0  2   0  0  0 |  *   * 48   *   *  *  * |  0  0  4   0  0  0 | 0  4 0
..... xux.. ..... .....&#xt & |  2  2  2 |  0   1  2   2  1  0 |  *   *  * 192   *  *  * |  0  0  1   2  0  0 | 0  2 1
..... ..... .ox.. .....&#x  & |  0  1  2 |  0   0  0   2  0  1 |  *   *  *   * 192  *  * |  0  0  0   2  1  0 | 0  1 2
..o..3..x.. ..... .....       |  0  0  3 |  0   0  0   0  3  0 |  *   *  *   *   * 32  * |  0  0  2   0  0  2 | 0  4 0
..... ..x..3..x.. .....       |  0  0  6 |  0   0  0   0  3  3 |  *   *  *   *   *  * 64 |  0  0  0   2  0  1 | 0  2 1
------------------------------+----------+---------------------+-------------------------+--------------------+-------
x....3x....3o.... .....     &  12  0  0 |  6  12  0   0  0  0 |  4   4  0   0   0  0  0 | 32  *  *   *  *  * | 1  1 0
..... x....3o....4o....     &   6  0  0 |  0  12  0   0  0  0 |  0   8  0   0   0  0  0 |  * 16  *   *  *  * | 1  0 1
xoo..3xux.. ..... .....&#xt &   6  3  3 |  3   3  6   3  3  0 |  1   0  3   3   0  1  0 |  *  * 64   *  *  * | 0  2 0
..... xux..3oox.. .....&#xt &   3  3  6 |  0   3  3   6  3  3 |  0   1  0   3   3  0  1 |  *  *  * 128  *  * | 0  1 1
..... ..... .oxo.4.ooo.&#xt     0  2  4 |  0   0  0   8  0  4 |  0   0  0   0   8  0  0 |  *  *  *   * 24  * | 0  0 2
..o..3..x..3..x.. .....         0  0 12 |  0   0  0   0 12  6 |  0   0  0   0   0  4  4 |  *  *  *   *  * 16 | 0  2 0
------------------------------+----------+---------------------+-------------------------+--------------------+-------
x....3x....3o....4o....     &  48  0  0 | 24  96  0   0  0  0 | 32  64  0   0   0  0  0 | 16  8  0   0  0  0 | 2  * *
xoo..3xux..3oox.. .....&#xt &  12  6 12 |  6  12 12  12 12  6 |  4   4  6  12   6  4  4 |  1  0  4   4  0  1 | * 32 *
..... xuxux3ooxoo4ooooo&#xt    12 12 24 |  0  24 12  48 12 24 |  0  16  0  24  48  0  8 |  0  2  0  16  6  0 | *  * 8

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