Acronym bittin
Name bitruncated penteract
Field of sections
` ©`
Lace city
in approx. ASCII-art
 ``` © ``` ```x3x4o o3u4o o3x4q o3u4o x3x4o -- o3x3x4o (tah) o3u4o o3o4Q o3u4o -- o3o3u4o (u-rit) o3x4q o3o4Q o3o4Q o3x4q -- o3o3x4q ((x,q)-tat), where: Q=2q o3u4o o3o4Q o3u4o -- o3o3u4o (u-rit) x3x4o o3u4o o3x4q o3u4o x3x4o -- o3x3x4o (tah) ```
Vertex figure
` ©    ©`
Coordinates (sqrt(2), sqrt(2), sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
Dihedral angles
(at margins)
• at tet between tip and tip:   arccos(-3/5) = 126.869898°
• at tut between tah and tip:   arccos[-1/sqrt(5)] = 116.565051°
• at toe between tah and tah:   90°
Confer
general polytopal classes:
lace simplices   partial Stott expansions
External

Incidence matrix according to Dynkin symbol

```o3o3x3x4o

. . . . . | 320 |   3   2 |   3   6  1 |  1   6  3 |  2  3
----------+-----+---------+------------+-----------+------
. . x . . |   2 | 480   * |   2   2  0 |  1   4  1 |  2  2
. . . x . |   2 |   * 320 |   0   3  1 |  0   3  3 |  1  3
----------+-----+---------+------------+-----------+------
. o3x . . |   3 |   3   0 | 320   *  * |  1   2  0 |  2  1
. . x3x . |   6 |   3   3 |   * 320  * |  0   2  1 |  1  2
. . . x4o |   4 |   0   4 |   *   * 80 |  0   0  3 |  0  3
----------+-----+---------+------------+-----------+------
o3o3x . . ♦   4 |   6   0 |   4   0  0 | 80   *  * |  2  0
. o3x3x . ♦  12 |  12   6 |   4   4  0 |  * 160  * |  1  1
. . x3x4o ♦  24 |  12  24 |   0   8  6 |  *   * 40 |  0  2
----------+-----+---------+------------+-----------+------
o3o3x3x . ♦  20 |  30  10 |  20  10  0 |  5   5  0 | 32  *
. o3x3x4o ♦  96 |  96  96 |  32  64 24 |  0  16  8 |  * 10
```

```o3o3x3x4/3o

. . . .   . | 320 |   3   2 |   3   6  1 |  1   6  3 |  2  3
------------+-----+---------+------------+-----------+------
. . x .   . |   2 | 480   * |   2   2  0 |  1   4  1 |  2  2
. . . x   . |   2 |   * 320 |   0   3  1 |  0   3  3 |  1  3
------------+-----+---------+------------+-----------+------
. o3x .   . |   3 |   3   0 | 320   *  * |  1   2  0 |  2  1
. . x3x   . |   6 |   3   3 |   * 320  * |  0   2  1 |  1  2
. . . x4/3o |   4 |   0   4 |   *   * 80 |  0   0  3 |  0  3
------------+-----+---------+------------+-----------+------
o3o3x .   . ♦   4 |   6   0 |   4   0  0 | 80   *  * |  2  0
. o3x3x   . ♦  12 |  12   6 |   4   4  0 |  * 160  * |  1  1
. . x3x4/3o ♦  24 |  12  24 |   0   8  6 |  *   * 40 |  0  2
------------+-----+---------+------------+-----------+------
o3o3x3x   . ♦  20 |  30  10 |  20  10  0 |  5   5  0 | 32  *
. o3x3x4/3o ♦  96 |  96  96 |  32  64 24 |  0  16  8 |  * 10
```

```x3x3x *b3o3o

. . .    . . | 320 |   1   3   1 |   3  1   3   3 |  3  3  3  1 |  3  1  1
-------------+-----+-------------+----------------+-------------+---------
x . .    . . |   2 | 160   *   * |   3  1   0   0 |  3  3  0  0 |  3  1  0
. x .    . . |   2 |   * 480   * |   1  0   1   2 |  1  2  2  1 |  2  1  1
. . x    . . |   2 |   *   * 160 |   0  1   3   0 |  3  0  3  0 |  3  0  1
-------------+-----+-------------+----------------+-------------+---------
x3x .    . . |   6 |   3   3   0 | 160  *   *   * |  1  2  0  0 |  2  1  0
x . x    . . |   4 |   2   0   2 |   * 80   *   * |  3  0  0  0 |  3  0  0
. x3x    . . |   6 |   0   3   3 |   *  * 160   * |  1  0  2  0 |  2  0  1
. x . *b3o . |   3 |   0   3   0 |   *  *   * 320 |  0  1  1  1 |  1  1  1
-------------+-----+-------------+----------------+-------------+---------
x3x3x    . . ♦  24 |  12  12  12 |   4  6   4   0 | 40  *  *  * |  2  0  0
x3x . *b3o . ♦  12 |   6  12   0 |   4  0   0   4 |  * 80  *  * |  1  1  0
. x3x *b3o . ♦  12 |   0  12   6 |   0  0   4   4 |  *  * 80  * |  1  0  1
. x . *b3o3o ♦   4 |   0   6   0 |   0  0   0   4 |  *  *  * 80 |  0  1  1
-------------+-----+-------------+----------------+-------------+---------
x3x3x *b3o . ♦  96 |  48  96  48 |  32 24  32  32 |  8  8  8  0 | 10  *  *
x3x . *b3o3o ♦  20 |  10  30   0 |  10  0   0  20 |  0  5  0  5 |  * 16  *
. x3x *b3o3o ♦  20 |   0  30  10 |   0  0  10  20 |  0  0  5  5 |  *  * 16
```

```o3o3x3x4s

demi( . . . . . ) | 320 |   3   1   1 |   3   3  1   3 |  1  3  3  3 |  1  3  1
------------------+-----+-------------+----------------+-------------+---------
demi( . . x . . ) |   2 | 480   *   * |   2   1  0   1 |  1  2  1  2 |  1  2  1
demi( . . . x . ) |   2 |   * 160   * |   0   3  1   0 |  0  3  3  0 |  1  3  0
sefa( . . . x4s ) |   2 |   *   * 160 |   0   0  1   3 |  0  0  3  3 |  0  3  1
------------------+-----+-------------+----------------+-------------+---------
demi( . o3x . . ) |   3 |   3   0   0 | 320   *  *   * |  1  1  0  1 |  1  1  1
demi( . . x3x . ) |   6 |   3   3   0 |   * 160  *   * |  0  2  1  0 |  1  2  0
. . . x4s   |   4 |   0   2   2 |   *   * 80   * |  0  0  3  0 |  0  3  0
sefa( . . x3x4s ) |   6 |   3   0   3 |   *   *  * 160 |  0  0  1  2 |  0  2  1
------------------+-----+-------------+----------------+-------------+---------
demi( o3o3x . . ) ♦   4 |   6   0   0 |   4   0  0   0 | 80  *  *  * |  1  0  1
demi( . o3x3x . ) ♦  12 |  12   6   0 |   4   4  0   0 |  * 80  *  * |  1  1  0
. . x3x4s   ♦  24 |  12  12  12 |   0   4  6   4 |  *  * 40  * |  0  2  0
sefa( . o3x3x4s ) ♦  12 |  12   0   6 |   4   0  0   4 |  *  *  * 80 |  0  1  1
------------------+-----+-------------+----------------+-------------+---------
demi( o3o3x3x . ) ♦  20 |  30  10   0 |  20  10  0   0 |  5  5  0  0 | 16  *  *
. o3x3x4s   ♦  96 |  96  48  48 |  32  32 24  32 |  0  8  8  8 |  * 10  *
sefa( o3o3x3x4s ) ♦  20 |  30   0  10 |  20   0  0  10 |  5  0  0  5 |  *  * 16

starting figure: o3o3x3x4x
```

```ooooo3xooox3xuxux4ooqoo&#xt   → all heights = 1/sqrt(2) = 0.707107
(tah || u-rit || (x,q)-tat || u-rit || tah)

o....3o....3o....4o....     & | 192  *  * |   2   2   1   0  0 |  1   4  1   2   2  0  0 |  2  2  1   4  1  0 | 1  2 2
.o...3.o...3.o...4.o...     & |   * 64  * |   0   0   3   2  0 |  0   0  0   3   6  1  0 |  0  0  1   6  3  0 | 0  2 3
..o..3..o..3..o..4..o..       |   *  * 64 |   0   0   0   2  3 |  0   0  0   0   6  1  3 |  0  0  0   6  3  1 | 0  2 3
------------------------------+-----------+--------------------+-------------------------+--------------------+-------
..... x.... ..... .....     & |   2  0  0 | 192   *   *   *  * |  1   2  0   1   0  0  0 |  2  1  1   2  0  0 | 1  2 1
..... ..... x.... .....     & |   2  0  0 |   * 192   *   *  * |  0   2  1   0   1  0  0 |  1  2  0   2  1  0 | 1  1 2
oo...3oo...3oo...4oo...&#x  & |   1  1  0 |   *   * 192   *  * |  0   0  0   2   2  0  0 |  0  0  1   4  1  0 | 0  2 2
.oo..3.oo..3.oo..4.oo..&#x  & |   0  1  1 |   *   *   * 128  * |  0   0  0   0   3  1  0 |  0  0  0   3  3  0 | 0  1 3
..... ..... ..x.. .....       |   0  0  2 |   *   *   *   * 96 |  0   0  0   0   2  0  2 |  0  0  0   4  1  1 | 0  2 2
------------------------------+-----------+--------------------+-------------------------+--------------------+-------
o....3x.... ..... .....     & |   3  0  0 |   3   0   0   0  0 | 64   *  *   *   *  *  * |  2  0  1   0  0  0 | 1  2 0
..... x....3x.... .....     & |   6  0  0 |   3   3   0   0  0 |  * 128  *   *   *  *  * |  1  1  0   1  0  0 | 1  1 1
..... ..... x....4o....     & |   4  0  0 |   0   4   0   0  0 |  *   * 48   *   *  *  * |  0  2  0   0  1  0 | 1  0 2
..... xo... ..... .....&#x  & |   2  1  0 |   1   0   2   0  0 |  *   *  * 192   *  *  * |  0  0  1   2  0  0 | 0  2 1
..... ..... xux.. .....&#xt & |   2  2  2 |   0   1   2   2  1 |  *   *  *   * 192  *  * |  0  0  0   2  1  0 | 0  1 2
..... ..... ..... .oqo.&#xt   |   0  2  2 |   0   0   0   4  0 |  *   *  *   *   * 32  * |  0  0  0   0  3  0 | 0  0 3
..... ..o..3..x.. .....       |   0  0  3 |   0   0   0   0  3 |  *   *  *   *   *  * 64 |  0  0  0   2  0  1 | 0  2 1
------------------------------+-----------+--------------------+-------------------------+--------------------+-------
o....3x....3x.... .....     & ♦  12  0  0 |  12   6   0   0  0 |  4   4  0   0   0  0  0 | 32  *  *   *  *  * | 1  1 0
..... x....3x....4o....     & ♦  24  0  0 |  12  24   0   0  0 |  0   8  6   0   0  0  0 |  * 16  *   *  *  * | 1  0 1
oo...3xo... ..... .....&#x  & ♦   3  1  0 |   3   0   3   0  0 |  1   0  0   3   0  0  0 |  *  * 64   *  *  * | 0  2 0
..... xoo..3xux.. .....&#xt & ♦   6  3  3 |   3   3   6   3  3 |  0   1  0   3   3  0  1 |  *  *  * 128  *  * | 0  1 1
..... ..... xuxux4ooqoo&#xt   ♦   8  8  8 |   0   8   8  16  4 |  0   0  2   0   8  4  0 |  *  *  *   * 24  * | 0  0 2
..o..3..o..3..x.. .....       ♦   0  0  4 |   0   0   0   0  6 |  0   0  0   0   0  0  4 |  *  *  *   *  * 16 | 0  2 0
------------------------------+-----------+--------------------+-------------------------+--------------------+-------
o....3x....3x....4o....     & ♦  96  0  0 |  96  96   0   0  0 | 32  64 24   0   0  0  0 | 16  8  0   0  0  0 | 2  * *
ooo..3xoo..3xux.. .....&#xt & ♦  12  4  4 |  12   6  12   4  6 |  4   4  0  12   6  0  4 |  1  0  4   4  0  1 | * 32 *
..... xooox3xuxux4ooqoo&#xt   ♦  48 24 24 |  24  48  48  48 24 |  0  16 12  24  48 12  8 |  0  2  0  16  6  0 | *  * 8
```