Acronym captid (old: hiptid)
Name celliprismatotruncated dodecateron,
hedratoprismatotruncated dodecateron,
steriruncitruncated hexateron
Field of sections
` ©`
Vertex figure
` ©    ©`
Lace city
in approx. ASCII-art
```               x3x3o     x3x3o

x3x3x               x3x3x

u3o3x     x3x3u     x3x3u     u3o3x

x3o3x     u3o3u     x3u3x     u3o3u     x3o3x

x3o3u     u3x3x     u3x3x     x3o3u

x3x3x               x3x3x

o3x3x     o3x3x

\_       \_       \_       \_       \_
\_       \_       \_       \_       +--  x3x3o3x (prip)
\_       \_       \_       +---------  x3x3o3u ((x,x,u)-prip)
\_       \_       +----------------  x3x3x3x (gippid)
\_       +-----------------------  u3o3x3x (inv. (x,x,u)-prip)
+------------------------------  x3o3x3x (inv. prip)
```
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
 by cells: gippid hiddip pittip prip tuttip recaptid 6 0 12 0 30 captid 0 20 0 12 30
& others)
Confer pripro
Confer
general polytopal classes:
lace simplices
External

Incidence matrix according to Dynkin symbol

```x3x3o3x3x

. . . . . | 360 |   1   2   2   1 |   2   2  1   1   2   2   1   2 |  1  2  2  1  2  1  1  2  1 | 1  1  2  1 1
----------+-----+-----------------+--------------------------------+----------------------------+-------------
x . . . . |   2 | 180   *   *   * |   2   2  1   0   0   0   0   0 |  1  2  2  1  2  0  0  0  0 | 1  1  2  1 0
. x . . . |   2 |   * 360   *   * |   1   0  0   1   1   1   0   0 |  1  1  1  0  0  1  1  1  0 | 1  1  1  0 1
. . . x . |   2 |   *   * 360   * |   0   1  0   0   1   0   1   1 |  0  1  0  1  1  1  0  1  1 | 1  0  1  1 1
. . . . x |   2 |   *   *   * 180 |   0   0  1   0   0   2   0   2 |  0  0  2  0  2  0  1  2  1 | 0  1  2  1 1
----------+-----+-----------------+--------------------------------+----------------------------+-------------
x3x . . . |   6 |   3   3   0   0 | 120   *  *   *   *   *   *   * |  1  1  1  0  0  0  0  0  0 | 1  1  1  0 0
x . . x . |   4 |   2   0   2   0 |   * 180  *   *   *   *   *   * |  0  1  0  1  1  0  0  0  0 | 1  0  1  1 0
x . . . x |   4 |   2   0   0   2 |   *   * 90   *   *   *   *   * |  0  0  2  0  2  0  0  0  0 | 0  1  2  1 0
. x3o . . |   3 |   0   3   0   0 |   *   *  * 120   *   *   *   * |  1  0  0  0  0  1  1  0  0 | 1  1  0  0 1
. x . x . |   4 |   0   2   2   0 |   *   *  *   * 180   *   *   * |  0  1  0  0  0  1  0  1  0 | 1  0  1  0 1
. x . . x |   4 |   0   2   0   2 |   *   *  *   *   * 180   *   * |  0  0  1  0  0  0  1  1  0 | 0  1  1  0 1
. . o3x . |   3 |   0   0   3   0 |   *   *  *   *   *   * 120   * |  0  0  0  1  0  1  0  0  1 | 1  0  0  1 1
. . . x3x |   6 |   0   0   3   3 |   *   *  *   *   *   *   * 120 |  0  0  0  0  1  0  0  1  1 | 0  0  1  1 1
----------+-----+-----------------+--------------------------------+----------------------------+-------------
x3x3o . . ♦  12 |   6  12   0   0 |   4   0  0   4   0   0   0   0 | 30  *  *  *  *  *  *  *  * | 1  1  0  0 0
x3x . x . ♦  12 |   6   6   6   0 |   2   3  0   0   3   0   0   0 |  * 60  *  *  *  *  *  *  * | 1  0  1  0 0
x3x . . x ♦  12 |   6   6   0   6 |   2   0  3   0   0   3   0   0 |  *  * 60  *  *  *  *  *  * | 0  1  1  0 0
x . o3x . ♦   6 |   3   0   6   0 |   0   3  0   0   0   0   2   0 |  *  *  * 60  *  *  *  *  * | 1  0  0  1 0
x . . x3x ♦  12 |   6   0   6   6 |   0   3  3   0   0   0   0   2 |  *  *  *  * 60  *  *  *  * | 0  0  1  1 0
. x3o3x . ♦  12 |   0  12  12   0 |   0   0  0   4   6   0   4   0 |  *  *  *  *  * 30  *  *  * | 1  0  0  0 1
. x3o . x ♦   6 |   0   6   0   3 |   0   0  0   2   0   3   0   0 |  *  *  *  *  *  * 60  *  * | 0  1  0  0 1
. x . x3x ♦  12 |   0   6   6   6 |   0   0  0   0   3   3   0   2 |  *  *  *  *  *  *  * 60  * | 0  0  1  0 1
. . o3x3x ♦  12 |   0   0  12   6 |   0   0  0   0   0   0   4   4 |  *  *  *  *  *  *  *  * 30 | 0  0  0  1 1
----------+-----+-----------------+--------------------------------+----------------------------+-------------
x3x3o3x . ♦  60 |  30  60  60   0 |  20  30  0  20  30   0  20   0 |  5 10  0 10  0  5  0  0  0 | 6  *  *  * *
x3x3o . x ♦  24 |  12  24   0  12 |   8   0  6   8   0  12   0   0 |  2  0  4  0  0  0  4  0  0 | * 15  *  * *
x3x . x3x ♦  36 |  18  18  18  18 |   6   9  9   0   9   9   0   6 |  0  3  3  0  3  0  0  3  0 | *  * 20  * *
x . o3x3x ♦  24 |  12   0  24  12 |   0  12  6   0   0   0   8   8 |  0  0  0  4  4  0  0  0  2 | *  *  * 15 *
. x3o3x3x ♦  60 |   0  60  60  30 |   0   0  0  20  30  30  20  20 |  0  0  0  0  0  5 10 10  5 | *  *  *  * 6
```
```or
. . . . .    | 360 |   2   4 |   4   4  1   2   2 |  2   4   4   2  1 |  2  2  2
-------------+-----+---------+--------------------+-------------------+---------
x . . . .  & |   2 | 360   * |   2   2  1   0   0 |  1   2   4   1  0 |  1  2  2
. x . . .  & |   2 |   * 720 |   1   1  0   1   1 |  1   2   1   1  1 |  2  1  1
-------------+-----+---------+--------------------+-------------------+---------
x3x . . .  & |   6 |   3   3 | 240   *  *   *   * |  1   1   1   0  0 |  1  1  1
x . . x .  & |   4 |   2   2 |   * 360  *   *   * |  0   1   1   1  0 |  1  1  1
x . . . x    |   4 |   4   0 |   *   * 90   *   * |  0   0   4   0  0 |  0  2  2
. x3o . .  & |   3 |   0   3 |   *   *  * 240   * |  1   0   0   1  1 |  2  1  0
. x . x .    |   4 |   0   4 |   *   *  *   * 180 |  0   2   0   0  1 |  2  0  1
-------------+-----+---------+--------------------+-------------------+---------
x3x3o . .  & ♦  12 |   6  12 |   4   0  0   4   0 | 60   *   *   *  * |  1  1  0
x3x . x .  & ♦  12 |   6  12 |   2   3  0   0   3 |  * 120   *   *  * |  1  0  1
x3x . . x  & ♦  12 |  12   6 |   2   3  3   0   0 |  *   * 120   *  * |  0  1  1
x . o3x .  & ♦   6 |   3   6 |   0   3  0   2   0 |  *   *   * 120  * |  1  1  0
. x3o3x .    ♦  12 |   0  24 |   0   0  0   8   6 |  *   *   *   * 30 |  2  0  0
-------------+-----+---------+--------------------+-------------------+---------
x3x3o3x .  & ♦  60 |  30 120 |  20  30  0  40  30 |  5  10   0  10  5 | 12  *  *
x3x3o . x  & ♦  24 |  24  24 |   8  12  6   8   0 |  2   0   4   4  0 |  * 30  *
x3x . x3x    ♦  36 |  36  36 |  12  18  9   0   9 |  0   6   6   0  0 |  *  * 20
```

```xxxux3xxxoo3ooxxx3xuxxx&#xt   → all heights = sqrt(4/5) = 0.774597
(prip || pseudo (x,x,u)-prip || pseudo gippid || pseudo inv. (x,x,u)-prip || inv. prip)

o....3o....3o....3o....     & | 120   *   * |  1   2   2   1  0   0   0   0   0 |  2  2  1  2  1  1   2   2  0  0   0   0   0  0  0  0 |  1  2  1  1  2  2  1  2  1  0  0  0  0  0 | 1  1  2  1  1
.o...3.o...3.o...3.o...     & |   * 120   * |  0   0   0   1  1   2   2   0   0 |  0  0  0  0  0  1   2   2  2  1   2   2   1  0  0  0 |  0  0  0  0  2  2  1  2  1  1  2  2  1  0 | 0  1  2  1  2
..o..3..o..3..o..3..o..       |   *   * 120 |  0   0   0   0  0   0   2   2   2 |  0  0  0  0  0  0   0   2  0  0   2   2   2  2  2  1 |  0  0  0  0  0  2  0  2  2  0  2  2  1  2 | 0  0  2  2  2
------------------------------+-------------+-----------------------------------+------------------------------------------------------+-------------------------------------------+--------------
x.... ..... ..... .....     & |   2   0   0 | 60   *   *   *  *   *   *   *   * |  2  2  0  0  0  1   0   0  0  0   0   0   0  0  0  0 |  1  2  1  0  2  2  0  0  0  0  0  0  0  0 | 1  1  2  1  0
..... x.... ..... .....     & |   2   0   0 |  * 120   *   *  *   *   *   *   * |  1  0  1  1  0  0   1   0  0  0   0   0   0  0  0  0 |  1  1  0  1  1  0  1  1  0  0  0  0  0  0 | 1  1  1  0  1
..... ..... ..... x....     & |   2   0   0 |  *   * 120   *  *   *   *   *   * |  0  1  0  1  1  0   0   1  0  0   0   0   0  0  0  0 |  0  1  1  1  0  1  0  1  1  0  0  0  0  0 | 1  0  1  1  1
oo...3oo...3oo...3oo...&#x  & |   1   1   0 |  *   *   * 120  *   *   *   *   * |  0  0  0  0  0  1   2   2  0  0   0   0   0  0  0  0 |  0  0  0  0  2  2  1  2  1  0  0  0  0  0 | 0  1  2  1  1
.x... ..... ..... .....     & |   0   2   0 |  *   *   *   * 60   *   *   *   * |  0  0  0  0  0  1   0   0  2  0   2   0   0  0  0  0 |  0  0  0  0  2  2  0  0  0  1  2  1  0  0 | 0  1  2  1  1
..... .x... ..... .....     & |   0   2   0 |  *   *   *   *  * 120   *   *   * |  0  0  0  0  0  0   1   0  1  1   0   1   0  0  0  0 |  0  0  0  0  1  0  1  1  0  1  1  0  1  0 | 0  1  1  0  2
.oo..3.oo..3.oo..3.oo..&#x  & |   0   1   1 |  *   *   *   *  *   * 240   *   * |  0  0  0  0  0  0   0   1  0  0   1   1   1  0  0  0 |  0  0  0  0  0  1  0  1  1  0  1  1  1  0 | 0  0  1  1  2
..x.. ..... ..... .....     & |   0   0   2 |  *   *   *   *  *   *   * 120   * |  0  0  0  0  0  0   0   1  0  0   1   0   0  1  1  1 |  0  0  0  0  0  2  0  1  1  0  1  1  0  2 | 0  0  2  2  1
..... ..x.. ..... .....     & |   0   0   2 |  *   *   *   *  *   *   *   * 120 |  0  0  0  0  0  0   0   0  0  0   0   1   1  1  1  0 |  0  0  0  0  0  0  0  1  1  0  1  1  1  1 | 0  0  1  1  2
------------------------------+-------------+-----------------------------------+------------------------------------------------------+-------------------------------------------+--------------
x....3x.... ..... .....     & |   6   0   0 |  3   3   0   0  0   0   0   0   0 | 40  *  *  *  *  *   *   *  *  *   *   *   *  *  *  * |  1  1  0  0  1  0  0  0  0  0  0  0  0  0 | 1  1  1  0  0
x.... ..... ..... x....     & |   4   0   0 |  2   0   2   0  0   0   0   0   0 |  * 60  *  *  *  *   *   *  *  *   *   *   *  *  *  * |  0  1  1  0  0  1  0  0  0  0  0  0  0  0 | 1  0  1  1  0
..... x....3o.... .....     & |   3   0   0 |  0   3   0   0  0   0   0   0   0 |  *  * 40  *  *  *   *   *  *  *   *   *   *  *  *  * |  1  0  0  1  0  0  1  0  0  0  0  0  0  0 | 1  1  0  0  1
..... x.... ..... x....     & |   4   0   0 |  0   2   2   0  0   0   0   0   0 |  *  *  * 60  *  *   *   *  *  *   *   *   *  *  *  * |  0  1  0  1  0  0  0  1  0  0  0  0  0  0 | 1  0  1  0  1
..... ..... o....3x....     & |   3   0   0 |  0   0   3   0  0   0   0   0   0 |  *  *  *  * 40  *   *   *  *  *   *   *   *  *  *  * |  0  0  1  1  0  0  0  0  1  0  0  0  0  0 | 1  0  0  1  1
xx... ..... ..... .....&#x  & |   2   2   0 |  1   0   0   2  1   0   0   0   0 |  *  *  *  *  * 60   *   *  *  *   *   *   *  *  *  * |  0  0  0  0  2  2  0  0  0  0  0  0  0  0 | 0  1  2  1  0
..... xx... ..... .....&#x  & |   2   2   0 |  0   1   0   2  0   1   0   0   0 |  *  *  *  *  *  * 120   *  *  *   *   *   *  *  *  * |  0  0  0  0  1  0  1  1  0  0  0  0  0  0 | 0  1  1  0  1
..... ..... ..... xux..&#x  & |   2   2   2 |  0   0   1   2  0   0   2   1   0 |  *  *  *  *  *  *   * 120  *  *   *   *   *  *  *  * |  0  0  0  0  0  1  0  1  1  0  0  0  0  0 | 0  0  1  1  1
.x...3.x... ..... .....     & |   0   6   0 |  0   0   0   0  3   3   0   0   0 |  *  *  *  *  *  *   *   * 40  *   *   *   *  *  *  * |  0  0  0  0  1  0  0  0  0  1  1  0  0  0 | 0  1  1  0  1
..... .x...3.o... .....     & |   0   3   0 |  0   0   0   0  0   3   0   0   0 |  *  *  *  *  *  *   *   *  * 40   *   *   *  *  *  * |  0  0  0  0  0  0  1  0  0  1  0  0  1  0 | 0  1  0  0  2
.xx.. ..... ..... .....&#x  & |   0   2   2 |  0   0   0   0  1   0   2   1   0 |  *  *  *  *  *  *   *   *  *  * 120   *   *  *  *  * |  0  0  0  0  0  1  0  0  0  0  1  1  0  0 | 0  0  1  1  1
..... .xx.. ..... .....&#x  & |   0   2   2 |  0   0   0   0  0   1   2   0   1 |  *  *  *  *  *  *   *   *  *  *   * 120   *  *  *  * |  0  0  0  0  0  0  0  1  0  0  1  0  1  0 | 0  0  1  0  2
..... ..... .ox.. .....&#x  & |   0   1   2 |  0   0   0   0  0   0   2   0   1 |  *  *  *  *  *  *   *   *  *  *   *   * 120  *  *  * |  0  0  0  0  0  0  0  0  1  0  0  1  1  0 | 0  0  0  1  2
..x..3..x.. ..... .....     & |   0   0   6 |  0   0   0   0  0   0   0   3   3 |  *  *  *  *  *  *   *   *  *  *   *   *   * 40  *  * |  0  0  0  0  0  0  0  0  1  0  1  0  0  1 | 0  0  1  1  1
..x.. ..... ..x.. .....     & |   0   0   4 |  0   0   0   0  0   0   0   2   2 |  *  *  *  *  *  *   *   *  *  *   *   *   *  * 60  * |  0  0  0  0  0  0  0  1  0  0  0  1  0  1 | 0  0  1  1  1
..x.. ..... ..... ..x..       |   0   0   4 |  0   0   0   0  0   0   0   4   0 |  *  *  *  *  *  *   *   *  *  *   *   *   *  *  * 30 |  0  0  0  0  0  2  0  0  0  0  0  0  0  2 | 0  0  2  2  0
------------------------------+-------------+-----------------------------------+------------------------------------------------------+-------------------------------------------+--------------
x....3x....3o.... .....     & ♦  12   0   0 |  6  12   0   0  0   0   0   0   0 |  4  0  4  0  0  0   0   0  0  0   0   0   0  0  0  0 | 10  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  1  0  0  0
x....3x.... ..... x....     & ♦  12   0   0 |  6   6   6   0  0   0   0   0   0 |  2  3  0  3  0  0   0   0  0  0   0   0   0  0  0  0 |  * 20  *  *  *  *  *  *  *  *  *  *  *  * | 1  0  1  0  0
x.... ..... o....3x....     & ♦   6   0   0 |  3   0   6   0  0   0   0   0   0 |  0  3  0  0  2  0   0   0  0  0   0   0   0  0  0  0 |  *  * 20  *  *  *  *  *  *  *  *  *  *  * | 1  0  0  1  0
..... x....3o....3x....     & ♦  12   0   0 |  0  12  12   0  0   0   0   0   0 |  0  0  4  6  4  0   0   0  0  0   0   0   0  0  0  0 |  *  *  * 10  *  *  *  *  *  *  *  *  *  * | 1  0  0  0  1
xx...3xx... ..... .....&#x  & ♦   6   6   0 |  3   3   0   6  3   3   0   0   0 |  1  0  0  0  0  3   3   0  1  0   0   0   0  0  0  0 |  *  *  *  * 40  *  *  *  *  *  *  *  *  * | 0  1  1  0  0
xxx.. ..... ..... xux..&#xt & ♦   4   4   4 |  2   0   2   4  2   0   4   4   0 |  0  1  0  0  0  2   0   2  0  0   2   0   0  0  0  1 |  *  *  *  *  * 60  *  *  *  *  *  *  *  * | 0  0  1  1  0
..... xx...3oo... .....&#x  & ♦   3   3   0 |  0   3   0   3  0   3   0   0   0 |  0  0  1  0  0  0   3   0  0  1   0   0   0  0  0  0 |  *  *  *  *  *  * 40  *  *  *  *  *  *  * | 0  1  0  0  1
..... xxx.. ..... xux..&#xt & ♦   4   4   4 |  0   2   2   4  0   2   4   2   2 |  0  0  0  1  0  0   2   2  0  0   0   2   0  0  1  0 |  *  *  *  *  *  *  * 60  *  *  *  *  *  * | 0  0  1  0  1
..... ..... oox..3xux..&#xt & ♦   3   3   6 |  0   0   3   3  0   0   6   3   3 |  0  0  0  0  1  0   0   3  0  0   0   0   3  1  0  0 |  *  *  *  *  *  *  *  * 40  *  *  *  *  * | 0  0  0  1  1
.x...3.x...3.o... .....     & ♦   0  12   0 |  0   0   0   0  6  12   0   0   0 |  0  0  0  0  0  0   0   0  4  4   0   0   0  0  0  0 |  *  *  *  *  *  *  *  *  * 10  *  *  *  * | 0  1  0  0  1
.xx..3.xx.. ..... .....&#x  & ♦   0   6   6 |  0   0   0   0  3   3   6   3   3 |  0  0  0  0  0  0   0   0  1  0   3   3   0  1  0  0 |  *  *  *  *  *  *  *  *  *  * 40  *  *  * | 0  0  1  0  1
.xx.. ..... .ox.. .....&#x  & ♦   0   2   4 |  0   0   0   0  1   0   4   2   2 |  0  0  0  0  0  0   0   0  0  0   2   0   2  0  1  0 |  *  *  *  *  *  *  *  *  *  *  * 60  *  * | 0  0  0  1  1
..... .xxo.3.oxx. .....&#xt   ♦   0   6   6 |  0   0   0   0  0   6  12   0   6 |  0  0  0  0  0  0   0   0  0  2   0   6   6  0  0  0 |  *  *  *  *  *  *  *  *  *  *  *  * 20  * | 0  0  0  0  2
..x..3..x.. ..... ..x..     & ♦   0   0  12 |  0   0   0   0  0   0   0  12   6 |  0  0  0  0  0  0   0   0  0  0   0   0   0  2  3  3 |  *  *  *  *  *  *  *  *  *  *  *  *  * 20 | 0  0  1  1  0
------------------------------+-------------+-----------------------------------+------------------------------------------------------+-------------------------------------------+--------------
x....3x....3o....3x....     & ♦  60   0   0 | 30  60  60   0  0   0   0   0   0 | 20 30 20 30 20  0   0   0  0  0   0   0   0  0  0  0 |  5 10 10  5  0  0  0  0  0  0  0  0  0  0 | 2  *  *  *  *
xx...3xx...3oo... .....&#x  & ♦  12  12   0 |  6  12   0  12  6  12   0   0   0 |  4  0  4  0  0  6  12   0  4  4   0   0   0  0  0  0 |  1  0  0  0  4  0  4  0  0  1  0  0  0  0 | * 10  *  *  *
xxx..3xxx.. ..... xux..&#xt & ♦  12  12  12 |  6   6   6  12  6   6  12  12   6 |  2  3  0  3  0  6   6   6  2  0   6   6   0  2  3  3 |  0  1  0  0  2  3  0  3  0  0  2  0  0  1 | *  * 20  *  *
xxx.. ..... oox..3xux..&#xt & ♦   6   6  12 |  3   0   6   6  3   0  12  12   6 |  0  3  0  0  2  3   0   6  0  0   6   0   6  2  3  3 |  0  0  1  0  0  3  0  0  2  0  0  3  0  1 | *  *  * 20  *
..... xxxo.3ooxx.3xuxx.&#xt & ♦  12  24  24 |  0  12  12  12  6  24  48  12  24 |  0  0  4  6  4  0  12  12  4  8  12  24  24  4  6  0 |  0  0  0  1  0  0  4  6  4  1  4  6  4  0 | *  *  *  * 10
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