Acronym tot
Name truncated triacontiditeron,
truncated pentacross
Field of sections
` ©`
Circumradius sqrt(5/2) = 1.581139
wrt. hex
sqrt(2) = 1.414214
wrt. tip
3/sqrt(10) = 0.948683
Vertex figure
` ©    ©`
Lace city
in approx. ASCII-art
 ``` ©   ``` ``` o3o4o x3o4o o3o4o -- x3o3o4o (hex) o3o4o u3o4o o3o4o -- u3o3o4o (u-hex) x3o4o u3o4o x3x4o u3o4o x3o4o -- x3x3o4o (thex) o3o4o u3o4o o3o4o -- u3o3o4o (u-hex) o3o4o x3o4o o3o4o -- x3o3o4o (hex) ```
Coordinates (sqrt(2), 1/sqrt(2), 0, 0, 0)   & all permutations, all changes of sign
Volume 119 sqrt(2)/15 = 11.219428
Surface (5+76 sqrt(5))/3 = 58.313722
Dihedral angles
(at margins)
• at tut between tip and tip:   arccos(-3/5) = 126.869898°
• at tet between hex and tip:   arccos[-1/sqrt(5)] = 116.565051°
Confer
related CRFs:
hextum
general polytopal classes:
lace simplices   partial Stott expansions
analogs:
truncated orthoplex tOn   truncated Gossetic t(2n,1)
External

Incidence matrix according to Dynkin symbol

```x3x3o3o4o

. . . . . | 80 |  1   6 |  6  12 | 12   8 |  8  1
----------+----+--------+--------+--------+------
x . . . . |  2 | 40   * ♦  6   0 | 12   0 |  8  0
. x . . . |  2 |  * 240 |  1   4 |  4   4 |  4  1
----------+----+--------+--------+--------+------
x3x . . . |  6 |  3   3 | 80   * |  4   0 |  4  0
. x3o . . |  3 |  0   3 |  * 320 |  1   2 |  2  1
----------+----+--------+--------+--------+------
x3x3o . . ♦ 12 |  6  12 |  4   4 | 80   * |  2  0
. x3o3o . ♦  4 |  0   6 |  0   4 |  * 160 |  1  1
----------+----+--------+--------+--------+------
x3x3o3o . ♦ 20 | 10  30 | 10  20 |  5   5 | 32  *
. x3o3o4o ♦  8 |  0  24 |  0  32 |  0  16 |  * 10
```

```x3x3o3o4/3o

. . . .   . | 80 |  1   6 |  6  12 | 12   8 |  8  1
------------+----+--------+--------+--------+------
x . . .   . |  2 | 40   * ♦  6   0 | 12   0 |  8  0
. x . .   . |  2 |  * 240 |  1   4 |  4   4 |  4  1
------------+----+--------+--------+--------+------
x3x . .   . |  6 |  3   3 | 80   * |  4   0 |  4  0
. x3o .   . |  3 |  0   3 |  * 320 |  1   2 |  2  1
------------+----+--------+--------+--------+------
x3x3o .   . ♦ 12 |  6  12 |  4   4 | 80   * |  2  0
. x3o3o   . ♦  4 |  0   6 |  0   4 |  * 160 |  1  1
------------+----+--------+--------+--------+------
x3x3o3o   . ♦ 20 | 10  30 | 10  20 |  5   5 | 32  *
. x3o3o4/3o ♦  8 |  0  24 |  0  32 |  0  16 |  * 10
```

```o3o3o *b3x3x

. . .    . . | 80 |   6  1 |  12  6 |  4  4 12 |  1  4  4
-------------+----+--------+--------+----------+---------
. . .    x . |  2 | 240  * |   4  1 |  2  2  4 |  1  2  2
. . .    . x |  2 |   * 40 ♦   0  6 |  0  0 12 |  0  4  4
-------------+----+--------+--------+----------+---------
. o . *b3x . |  3 |   3  0 | 320  * |  1  1  1 |  1  1  1
. . .    x3x |  6 |   3  3 |   * 80 |  0  0  4 |  0  2  2
-------------+----+--------+--------+----------+---------
o3o . *b3x . ♦  4 |   6  0 |   4  0 | 80  *  * |  1  1  0
. o3o *b3x . ♦  4 |   6  0 |   4  0 |  * 80  * |  1  0  1
. o . *b3x3x ♦ 12 |  12  6 |   4  4 |  *  * 80 |  0  1  1
-------------+----+--------+--------+----------+---------
o3o3o *b3x . ♦  8 |  24  0 |  32  0 |  8  8  0 | 10  *  *
o3o . *b3x3x ♦ 20 |  30 10 |  20 10 |  5  0  5 |  * 16  *
. o3o *b3x3x ♦ 20 |  30 10 |  20 10 |  0  5  5 |  *  * 16
```

```xuxux3ooxoo3ooooo4ooooo&#xt   → all heights = 1/sqrt(2) = 0.707107
(hex || pseudo u-hex || pseudo thex || pseudo u-hex || hex)

o....3o....3o....4o....     | 8 *  * * * |  6 1  0  0  0  0 0  0 | 12  6  0  0  0  0  0  0 |  8 12  0  0  0  0  0 | 1  8 0  0 0
.o...3.o...3.o...4.o...     | * 8  * * * |  0 1  6  0  0  0 0  0 |  0  6 12  0  0  0  0  0 |  0 12  8  0  0  0  0 | 0  8 1  0 0
..o..3..o..3..o..4..o..     | * * 48 * * |  0 0  1  1  4  1 0  0 |  0  1  4  4  4  1  4  0 |  0  4  4  4  4  4  0 | 0  4 1  4 0
...o.3...o.3...o.4...o.     | * *  * 8 * |  0 0  0  0  0  6 1  0 |  0  0  0  0  0  6 12  0 |  0  0  0  0 12  8  0 | 0  0 1  8 0
....o3....o3....o4....o     | * *  * * 8 |  0 0  0  0  0  0 1  6 |  0  0  0  0  0  6  0 12 |  0  0  0  0 12  0  8 | 0  0 0  8 1
----------------------------+------------+-----------------------+-------------------------+----------------------+------------
x.... ..... ..... .....     | 2 0  0 0 0 | 24 *  *  *  *  * *  * |  4  1  0  0  0  0  0  0 |  4  4  0  0  0  0  0 | 1  4 0  0 0
oo...3oo...3oo...4oo...&#x  | 1 1  0 0 0 |  * 8  *  *  *  * *  * ♦  0  6  0  0  0  0  0  0 |  0 12  0  0  0  0  0 | 0  8 0  0 0
.oo..3.oo..3.oo..4.oo..&#x  | 0 1  1 0 0 |  * * 48  *  *  * *  * |  0  1  4  0  0  0  0  0 |  0  4  4  0  0  0  0 | 0  4 1  0 0
..x.. ..... ..... .....     | 0 0  2 0 0 |  * *  * 24  *  * *  * ♦  0  1  0  4  0  1  0  0 |  0  4  0  4  4  0  0 | 0  4 0  4 0
..... ..x.. ..... .....     | 0 0  2 0 0 |  * *  *  * 96  * *  * |  0  0  1  1  2  0  1  0 |  0  1  2  2  1  2  0 | 0  2 1  2 0
..oo.3..oo.3..oo.4..oo.&#x  | 0 0  1 1 0 |  * *  *  *  * 48 *  * |  0  0  0  0  0  1  4  0 |  0  0  0  0  4  4  0 | 0  0 1  4 0
...oo3...oo3...oo4...oo&#x  | 0 0  0 1 1 |  * *  *  *  *  * 8  * ♦  0  0  0  0  0  6  0  0 |  0  0  0  0 12  0  0 | 0  0 0  8 0
....x ..... ..... .....     | 0 0  0 0 2 |  * *  *  *  *  * * 24 |  0  0  0  0  0  1  0  4 |  0  0  0  0  4  0  4 | 0  0 0  4 1
----------------------------+------------+-----------------------+-------------------------+----------------------+------------
x....3o.... ..... .....     | 3 0  0 0 0 |  3 0  0  0  0  0 0  0 | 32  *  *  *  *  *  *  * |  2  1  0  0  0  0  0 | 1  2 0  0 0
xux.. ..... ..... .....&#xt | 2 2  2 0 0 |  1 2  2  1  0  0 0  0 |  * 24  *  *  *  *  *  * |  0  4  0  0  0  0  0 | 0  4 0  0 0
..... .ox.. ..... .....&#x  | 0 1  2 0 0 |  0 0  2  0  1  0 0  0 |  *  * 96  *  *  *  *  * |  0  1  2  0  0  0  0 | 0  2 1  0 0
..x..3..x.. ..... .....     | 0 0  6 0 0 |  0 0  0  3  3  0 0  0 |  *  *  * 32  *  *  *  * |  0  1  0  2  1  0  0 | 0  2 0  2 0
..... ..x..3..o.. .....     | 0 0  3 0 0 |  0 0  0  0  3  0 0  0 |  *  *  *  * 64  *  *  * |  0  0  1  1  0  1  0 | 0  1 1  1 0
..xux ..... ..... .....&#xt | 0 0  2 2 2 |  0 0  0  1  0  2 2  1 |  *  *  *  *  * 24  *  * |  0  0  0  0  4  0  0 | 0  0 0  4 0
..... ..xo. ..... .....&#xt | 0 0  2 1 0 |  0 0  0  0  1  2 0  0 |  *  *  *  *  *  * 96  * |  0  0  0  0  1  2  0 | 0  0 1  2 0
....x3....o ..... .....     | 0 0  0 0 3 |  0 0  0  0  0  0 0  3 |  *  *  *  *  *  *  * 32 |  0  0  0  0  1  0  2 | 0  0 0  2 1
----------------------------+------------+-----------------------+-------------------------+----------------------+------------
x....3o....3o.... .....     ♦ 4 0  0 0 0 |  6 0  0  0  0  0 0  0 |  4  0  0  0  0  0  0  0 | 16  *  *  *  *  *  * | 1  1 0  0 0
xux..3oox.. ..... .....&#xt ♦ 3 3  6 0 0 |  3 3  6  3  3  0 0  0 |  1  3  3  1  0  0  0  0 |  * 32  *  *  *  *  * | 0  2 0  0 0
..... .ox..3.oo.. .....&#x  ♦ 0 1  3 0 0 |  0 0  3  0  3  0 0  0 |  0  0  3  0  1  0  0  0 |  *  * 64  *  *  *  * | 0  1 1  0 0
..x..3..x..3..o.. .....     ♦ 0 0 12 0 0 |  0 0  0  6 12  0 0  0 |  0  0  0  4  4  0  0  0 |  *  *  * 16  *  *  * | 0  1 0  1 0
..xux3..xoo ..... .....&#xt ♦ 0 0  6 3 3 |  0 0  0  3  3  6 3  3 |  0  0  0  1  0  3  3  1 |  *  *  *  * 32  *  * | 0  0 0  2 0
..... ..xo.3..oo. .....&#x  ♦ 0 0  3 1 0 |  0 0  0  0  3  3 0  0 |  0  0  0  0  1  0  3  0 |  *  *  *  *  * 64  * | 0  0 1  1 0
....x3....o3....o .....     ♦ 0 0  0 0 4 |  0 0  0  0  0  0 0  6 |  0  0  0  0  0  0  0  4 |  *  *  *  *  *  * 16 | 0  0 0  1 1
----------------------------+------------+-----------------------+-------------------------+----------------------+------------
x....3o....3o....4o....     ♦ 8 0  0 0 0 | 24 0  0  0  0  0 0  0 | 32  0  0  0  0  0  0  0 | 16  0  0  0  0  0  0 | 1  * *  * *
xux..3oox..3ooo.. .....&#xt ♦ 4 4 12 0 0 |  6 4 12  6 12  0 0  0 |  4  6 12  4  4  0  0  0 |  1  4  4  1  0  0  0 | * 16 *  * *
..... .oxo.3.ooo.4.ooo.&#xt ♦ 0 1  6 1 0 |  0 0  6  0 12  6 0  0 |  0  0 12  0  8  0 12  0 |  0  0  8  0  0  8  0 | *  * 8  * *
..xux3..xoo3..ooo .....&#xt ♦ 0 0 12 4 4 |  0 0  0  6 12 12 4  6 |  0  0  0  4  4  6 12  4 |  0  0  0  1  4  4  1 | *  * * 16 *
....x3....o3....o4....o     ♦ 0 0  0 0 8 |  0 0  0  0  0  0 0 24 |  0  0  0  0  0  0  0 32 |  0  0  0  0  0  0 16 | *  * *  * 1
```
```or
o....3o....3o....4o....     & | 16  *  * |  6  1  0  0  0 | 12  6   0  0  0 |  8 12   0  0 | 1  8 0
.o...3.o...3.o...4.o...     & |  * 16  * |  0  1  6  0  0 |  0  6  12  0  0 |  0 12   8  0 | 0  8 1
..o..3..o..3..o..4..o..       |  *  * 48 |  0  0  2  1  4 |  0  2   8  4  4 |  0  8   8  4 | 0  8 1
------------------------------+----------+----------------+-----------------+--------------+-------
x.... ..... ..... .....     & |  2  0  0 | 48  *  *  *  * |  4  1   0  0  0 |  4  4   0  0 | 1  4 0
oo...3oo...3oo...4oo...&#x  & |  1  1  0 |  * 16  *  *  * ♦  0  6   0  0  0 |  0 12   0  0 | 0  8 0
.oo..3.oo..3.oo..4.oo..&#x  & |  0  1  1 |  *  * 96  *  * |  0  1   4  0  0 |  0  4   4  0 | 0  4 1
..x.. ..... ..... .....       |  0  0  2 |  *  *  * 24  * ♦  0  2   0  4  0 |  0  8   0  4 | 0  8 0
..... ..x.. ..... .....       |  0  0  2 |  *  *  *  * 96 |  0  0   2  1  2 |  0  2   4  2 | 0  4 1
------------------------------+----------+----------------+-----------------+--------------+-------
x....3o.... ..... .....     & |  3  0  0 |  3  0  0  0  0 | 64  *   *  *  * |  2  1   0  0 | 1  2 0
xux.. ..... ..... .....&#xt & |  2  2  2 |  1  2  2  1  0 |  * 48   *  *  * |  0  4   0  0 | 0  4 0
..... .ox.. ..... .....&#x  & |  0  1  2 |  0  0  2  0  1 |  *  * 192  *  * |  0  1   2  0 | 0  2 1
..x..3..x.. ..... .....       |  0  0  6 |  0  0  0  3  3 |  *  *   * 32  * |  0  2   0  2 | 0  4 0
..... ..x..3..o.. .....       |  0  0  3 |  0  0  0  0  3 |  *  *   *  * 64 |  0  0   2  1 | 0  2 1
------------------------------+----------+----------------+-----------------+--------------+-------
x....3o....3o.... .....     & ♦  4  0  0 |  6  0  0  0  0 |  4  0   0  0  0 | 32  *   *  * | 1  1 0
xux..3oox.. ..... .....&#xt & ♦  3  3  6 |  3  3  6  3  3 |  1  3   3  1  0 |  * 64   *  * | 0  2 0
..... .ox..3.oo.. .....&#x  & ♦  0  1  3 |  0  0  3  0  3 |  0  0   3  0  1 |  *  * 128  * | 0  1 1
..x..3..x..3..o.. .....       ♦  0  0 12 |  0  0  0  6 12 |  0  0   0  4  4 |  *  *   * 16 | 0  2 0
------------------------------+----------+----------------+-----------------+--------------+-------
x....3o....3o....4o....     & ♦  8  0  0 | 24  0  0  0  0 | 32  0   0  0  0 | 16  0   0  0 | 2  * *
xux..3oox..3ooo.. .....&#xt & ♦  4  4 12 |  6  4 12  6 12 |  4  6  12  4  4 |  1  4   4  1 | * 32 *
..... .oxo.3.ooo.4.ooo.&#xt   ♦  0  2  6 |  0  0 12  0 12 |  0  0  24  0  8 |  0  0  16  0 | *  * 8
```

```Qqo xux3oox3ooo4ooo&#zxt

o.. o..3o..3o..4o..      | 16  *  * |  6  1  0  0  0 | 12  6   0  0  0 |  8 12   0  0 | 1  8 0
.o. .o.3.o.3.o.4.o.      |  * 16  * |  0  1  6  0  0 |  0  6  12  0  0 |  0 12   8  0 | 0  8 1
..o ..o3..o3..o4..o      |  *  * 48 |  0  0  2  1  4 |  0  2   8  4  4 |  0  8   8  4 | 0  8 1
-------------------------+----------+----------------+-----------------+--------------+-------
... x.. ... ... ...      |  2  0  0 | 48  *  *  *  * |  4  1   0  0  0 |  4  4   0  0 | 1  4 0
oo. oo.3oo.3oo.4oo.&#x   |  1  1  0 |  * 16  *  *  * ♦  0  6   0  0  0 |  0 12   0  0 | 0  8 0
.oo .oo3.oo3.oo4.oo&#x   |  0  1  1 |  *  * 96  *  * |  0  1   4  0  0 |  0  4   4  0 | 0  4 1
... ..x ... ... ...      |  0  0  2 |  *  *  * 24  * ♦  0  2   0  4  0 |  0  8   0  4 | 0  8 0
... ... ..x ... ...      |  0  0  2 |  *  *  *  * 96 |  0  0   2  1  2 |  0  2   4  2 | 0  4 1
-------------------------+----------+----------------+-----------------+--------------+-------
... x..3o.. ... ...      |  3  0  0 |  3  0  0  0  0 | 64  *   *  *  * |  2  1   0  0 | 1  2 0
... xux ... ... ...&#xt  |  2  2  2 |  1  2  2  1  0 |  * 48   *  *  * |  0  4   0  0 | 0  4 0
... ... .ox ... ...&#x   |  0  1  2 |  0  0  2  0  1 |  *  * 192  *  * |  0  1   2  0 | 0  2 1
... ..x3..x ... ...      |  0  0  6 |  0  0  0  3  3 |  *  *   * 32  * |  0  2   0  2 | 0  4 0
... ... ..x3..o ...      |  0  0  3 |  0  0  0  0  3 |  *  *   *  * 64 |  0  0   2  1 | 0  2 1
-------------------------+----------+----------------+-----------------+--------------+-------
... x..3o..3o.. ...      ♦  4  0  0 |  6  0  0  0  0 |  4  0   0  0  0 | 32  *   *  * | 1  1 0
... xux3oox ... ...&#xt  ♦  3  3  6 |  3  3  6  3  3 |  1  3   3  1  0 |  * 64   *  * | 0  2 0
... ... .ox3.oo ...&#x   ♦  0  1  3 |  0  0  3  0  3 |  0  0   3  0  1 |  *  * 128  * | 0  1 1
... ..x3..x3..o ...      ♦  0  0 12 |  0  0  0  6 12 |  0  0   0  4  4 |  *  *   * 16 | 0  2 0
-------------------------+----------+----------------+-----------------+--------------+-------
... x..3o..3o..4o..      ♦  8  0  0 | 24  0  0  0  0 | 32  0   0  0  0 | 16  0   0  0 | 2  * *
... xux3oox3ooo ...&#xt  ♦  4  4 12 |  6  4 12  6 12 |  4  6  12  4  4 |  1  4   4  1 | * 32 *
.qo ... .ox3.oo4.oo&#zx  ♦  0  2  6 |  0  0 12  0 12 |  0  0  24  0  8 |  0  0  16  0 | *  * 8
```

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