Acronym ... Name pentacontitetrapeton dual,convex hull of madek Circumradius sqrt(2/3) = 0.816497 Lace cityin approx. ASCII-art ``` p p E O p X X p O E p p | | | | | +-- o3o3o *b3o3o (point) | | | | +------- o3o3o *b3o3x (tac) | | | +---------- x3o3o *b3o3o (hin) | | +-------------- o3o3x *b3o3o (alt. hin) | +----------------- o3o3o *b3o3x (tac) +---------------------- o3o3o *b3o3o (point) where: p = o3o3o *b3o (point) X = x3o3o *b3o ("normal" hex) E = o3o3x *b3o ("even" hex) O = o3o3o *b3x ("odd" hex) ``` Dual mo

This polyteron can be obtained as the convex hull of the 2 jak compound (madek). Here all the edges of the former remain as long ones, while the short ones come in as interconnections of the 2 vertex set members. In the compound the hixes all did form (subdimensional) compounds (stade) in turn. Thus here the hull of those (o3o3m3o3o) is to be used for facets. Note that this fattening to (subdimensional) hulls already fills out everything, i.e. no further facets have to be added here.

Incidence matrix according to Dynkin symbol

```xo3oo3oo3oo3ox *c3oo&#zy   → height = 1
y = R = sqrt(2/3) = sqrt(6)/3 = 0.816497
(tegum sum of 2 inverted jaks)

o.3o.3o.3o.3o. *c3o.     & | 54 |  16  10 |  120 |  160 |  80 | 16
---------------------------+----+---------+------+------+-----+---
x. .. .. .. ..    ..     & |  2 | 432   * ♦    5 |   10 |  10 |  5  x
oo3oo3oo3oo3oo *c3oo&#y    |  2 |   * 270 ♦   16 |   32 |  24 |  8  y
---------------------------+----+---------+------+------+-----+---
xo .. .. .. ..    ..&#y  & |  3 |   1   2 | 2160 ♦    4 |   6 |  4
---------------------------+----+---------+------+------+-----+---
xo .. .. .. ox    ..&#y    ♦  4 |   2   4 |    4 | 2160 |   3 |  3
---------------------------+----+---------+------+------+-----+---
xo3oo .. oo3ox    ..&#zy   ♦  6 |   6   9 |   18 |    9 | 720 |  2
---------------------------+----+---------+------+------+-----+---
xo3oo3oo3oo3ox    ..&#zy   ♦ 12 |  30  30 |  120 |   90 |  20 | 72
```

```ooxooo3oooooo3oooxoo *b3oooooo3oxooxo&#yt   → height(1,2) = height(3,4) = height(5,6) = 1/sqrt(6) = 2/sqrt(24) = 0.408248
height(2,3) = height(4,5) = 1/sqrt(24) = 0.204124
y = R = sqrt(2/3) = 4/sqrt(24) = 0.816497
(pt || pseudo tac || pseudo hin || pseudo alt. hin || pseudo tac || pt)

o.....3o.....3o..... *b3o.....3o.....        & | 2  *  * | 10 16  0   0   0  0   0  0 | 40  80   0   0   0   0   0 | 160   0   0   0  0 |  80   0   0 | 16  0
.o....3.o....3.o.... *b3.o....3.o....        & | * 20  * |  1  0  8   8   8  1   0  0 |  8   8  24  32  32  16   0 |  32  48  48  32  0 |  24  32  24 |  8  8
..o...3..o...3..o... *b3..o...3..o...        & | *  * 32 |  0  1  0   5   5  0  10  5 |  0   5  30  10  40   5  30 |  10  30  90  20 10 |  10  40  30 |  6 10
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
oo....3oo....3oo.... *b3oo....3oo....&#y     & | 1  1  0 | 20  *  *   *   *  *   *  * ♦  8   8   0   0   0   0   0 |  32   0   0   0  0 |  24   0   0 |  8  0  y
o.o...3o.o...3o.o... *b3o.o...3o.o...&#x     & | 1  0  1 |  * 32  *   *   *  *   *  * ♦  0   5   0   0   0   0   0 |  10   0   0   0  0 |  10   0   0 |  5  0  x
...... ...... ......    ...... .x....        & | 0  2  0 |  *  * 80   *   *  *   *  * ♦  1   0   0   4   0   0   0 |   4   6   0   0  0 |   6   4   0 |  4  1  x
.oo...3.oo...3.oo... *b3.oo...3.oo...&#y     & | 0  1  1 |  *  *  * 160   *  *   *  * ♦  0   1   6   4   4   1   0 |   4  12  12   4  0 |   6  12   6 |  4  4  y
.o.o..3.o.o..3.o.o.. *b3.o.o..3.o.o..&#x     & | 0  1  1 |  *  *  *   * 160  *   *  * ♦  0   0   0   0   4   1   0 |   0   0   6   4  0 |   0   4   6 |  1  4  x
.o..o.3.o..o.3.o..o. *b3.o..o.3.o..o.&#y       | 0  2  0 |  *  *  *   *   * 10   *  * ♦  0   0   0   0   0  16   0 |   0   0   0  32  0 |   0   0  24 |  0  8  y
..x... ...... ......    ...... ......        & | 0  0  2 |  *  *  *   *   *  * 160  * ♦  0   0   3   0   0   0   2 |   0   3   6   0  1 |   1   6   3 |  2  3  x
..oo..3..oo..3..oo.. *b3..oo..3..oo..&#y       | 0  0  2 |  *  *  *   *   *  *   * 80 ♦  0   0   0   0   8   0   8 |   0   0  24   4  4 |   0  12  12 |  2  6  y
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
...... ...... ......    ...... ox....&#y     & | 1  2  0 |  2  0  1   0   0  0   0  0 | 80   *   *   *   *   *   * ♦   4   0   0   0  0 |   6   0   0 |  4  0
ooo...3ooo...3ooo... *b3ooo...3ooo...&#(xyy) & | 1  1  1 |  1  1  0   1   0  0   0  0 |  * 160   *   *   *   *   * ♦   4   0   0   0  0 |   6   0   0 |  4  0
.ox... ...... ......    ...... ......        & | 0  1  2 |  0  0  0   2   0  0   1  0 |  *   * 480   *   *   *   * ♦   0   2   2   0  0 |   1   4   1 |  2  2
...... ...... ......    ...... .xo...&#y     & | 0  2  1 |  0  0  1   2   0  0   0  0 |  *   *   * 320   *   *   * ♦   1   3   0   0  0 |   3   3   0 |  3  1
.ooo..3.ooo..3.ooo.. *b3.ooo..3.ooo..&#(xyy) & | 0  1  2 |  0  0  0   1   1  0   0  1 |  *   *   *   * 640   *   * ♦   0   0   3   1  0 |   0   3   3 |  1  3
.oo.o.3.oo.o.3.oo.o. *b3.oo.o.3.oo.o.&#(xyy) & | 0  2  1 |  0  0  0   1   1  1   0  0 |  *   *   *   *   * 160   * ♦   0   0   0   4  0 |   0   0   6 |  0  4
..xo.. ...... ......    ...... ......        & | 0  0  3 |  0  0  0   0   0  0   1  2 |  *   *   *   *   *   * 320 ♦   0   0   3   0  1 |   0   3   3 |  1  3
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
...... ...... ......    ...... oxo...&#(xy)  & ♦ 1  2  1 |  2  1  1   2   0  0   0  0 |  1   2   0   1   0   0   0 | 320   *   *   *  * |   3   0   0 |  3  0
.ox... ...... ......    ...... .xo...&#y     & ♦ 0  2  2 |  0  0  1   4   0  0   1  0 |  0   0   2   2   0   0   0 |   * 480   *   *  * |   1   2   0 |  2  1
.oxo.. ...... ......    ...... ......&#(xy)  & ♦ 0  1  3 |  0  0  0   2   1  0   1  2 |  0   0   1   0   2   0   1 |   *   * 960   *  * |   0   2   1 |  1  2
.oooo.3.oooo.3.oooo. *b3.oooo.3.oooo.&#(xy)    ♦ 0  2  2 |  0  0  0   2   2  1   0  1 |  0   0   0   0   2   2   0 |   *   *   * 320  * |   0   0   3 |  0  3
..xo.. ...... ..ox..    ...... ......&#y       ♦ 0  0  4 |  0  0  0   0   0  0   2  4 |  0   0   0   0   0   0   4 |   *   *   *   * 80 |   0   0   3 |  0  3
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
oox... ...... ......    ooo...3oxo...&#yt    & ♦ 1  3  2 |  3  2  3   6   0  0   1  0 |  3   6   3   6   0   0   0 |   6   3   0   0  0 | 160   *   * |  2  0
.oxo..3.ooo.. ......    ...... .xoo..&#yt    & ♦ 0  2  4 |  0  0  1   6   2  0   3  3 |  0   0   6   3   6   0   3 |   0   3   6   0  0 |   * 320   * |  1  1
.oxoo. ...... .ooxo.    ...... ......&#(xy)    ♦ 0  2  4 |  0  0  0   4   4  1   2  4 |  0   0   2   0   8   4   4 |   0   0   4   4  1 |   *   * 240 |  0  2
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
ooxo..3oooo.. ...... *b3oooo..3oxoo..&#yt    & ♦ 1  5  6 |  5  5 10  20   5  0  10  5 | 10  20  30  30  20   0  10 |  30  30  30   0  0 |  10  10   0 | 32  *
.oxoo.3.oooo.3.ooxo.    ...... .xoox.&#yt      ♦ 0  4  8 |  0  0  2  16  16  2  12 12 |  0   0  24   8  48  16  24 |   0  12  48  24  6 |   0   8  12 |  * 40
```