Acronym bittix (old: dittox) Name bitruncated hexateron Field of sections ` ©` Circumradius sqrt(29/12) = 1.554563 Inradiuswrt. tip 7/sqrt(60) = 0.903696 Inradiuswrt. deca sqrt(5/12) = 0.645497 Vertex figure ` ©   ©` Lace cityin approx. ASCII-art ```o3o3x o3o3u o3x3x -- o3o3x3x (tip) o3o3u o3u3o -- o3o3u3o (u-rap) o3x3x o3u3o x3x3o -- o3x3x3o (deca) ``` Volume 841 sqrt(3)/240 = 6.069395 Surface 153 sqrt(5)/8 = 42.764800 Dihedral angles (at margins) at tut between deca and tip:   arccos(-1/5) = 101.536959° at tet between tip and tip:   arccos(1/5) = 78.463041° at tut between deca and deca:   arccos(1/5) = 78.463041° Confer general polytopal classes: lace simplices Externallinks

Incidence matrix according to Dynkin symbol

```o3x3x3o3o

. . . . . | 60 |  2  3 |  1  6  3 |  3  6  1 | 3 2
----------+----+-------+----------+----------+----
. x . . . |  2 | 60  * |  1  3  0 |  3  3  0 | 3 1
. . x . . |  2 |  * 90 |  0  2  2 |  1  4  1 | 2 2
----------+----+-------+----------+----------+----
o3x . . . |  3 |  3  0 | 20  *  * |  3  0  0 | 3 0
. x3x . . |  6 |  3  3 |  * 60  * |  1  2  0 | 2 1
. . x3o . |  3 |  0  3 |  *  * 60 |  0  2  1 | 1 2
----------+----+-------+----------+----------+----
o3x3x . . ♦ 12 | 12  6 |  4  4  0 | 15  *  * | 2 0
. x3x3o . ♦ 12 |  6 12 |  0  4  4 |  * 30  * | 1 1
. . x3o3o ♦  4 |  0  6 |  0  0  4 |  *  * 15 | 0 2
----------+----+-------+----------+----------+----
o3x3x3o . ♦ 30 | 30 30 | 10 20 10 |  5  5  0 | 6 *
. x3x3o3o ♦ 20 | 10 30 |  0 10 20 |  0  5  5 | * 6
```

```o3/2x3x3o3o

.   . . . . | 60 |  2  3 |  1  6  3 |  3  6  1 | 3 2
------------+----+-------+----------+----------+----
.   x . . . |  2 | 60  * |  1  3  0 |  3  3  0 | 3 1
.   . x . . |  2 |  * 90 |  0  2  2 |  1  4  1 | 2 2
------------+----+-------+----------+----------+----
o3/2x . . . |  3 |  3  0 | 20  *  * |  3  0  0 | 3 0
.   x3x . . |  6 |  3  3 |  * 60  * |  1  2  0 | 2 1
.   . x3o . |  3 |  0  3 |  *  * 60 |  0  2  1 | 1 2
------------+----+-------+----------+----------+----
o3/2x3x . . ♦ 12 | 12  6 |  4  4  0 | 15  *  * | 2 0
.   x3x3o . ♦ 12 |  6 12 |  0  4  4 |  * 30  * | 1 1
.   . x3o3o ♦  4 |  0  6 |  0  0  4 |  *  * 15 | 0 2
------------+----+-------+----------+----------+----
o3/2x3x3o . ♦ 30 | 30 30 | 10 20 10 |  5  5  0 | 6 *
.   x3x3o3o ♦ 20 | 10 30 |  0 10 20 |  0  5  5 | * 6
```

```o3x3x3o3/2o

. . . .   . | 60 |  2  3 |  1  6  3 |  3  6  1 | 3 2
------------+----+-------+----------+----------+----
. x . .   . |  2 | 60  * |  1  3  0 |  3  3  0 | 3 1
. . x .   . |  2 |  * 90 |  0  2  2 |  1  4  1 | 2 2
------------+----+-------+----------+----------+----
o3x . .   . |  3 |  3  0 | 20  *  * |  3  0  0 | 3 0
. x3x .   . |  6 |  3  3 |  * 60  * |  1  2  0 | 2 1
. . x3o   . |  3 |  0  3 |  *  * 60 |  0  2  1 | 1 2
------------+----+-------+----------+----------+----
o3x3x .   . ♦ 12 | 12  6 |  4  4  0 | 15  *  * | 2 0
. x3x3o   . ♦ 12 |  6 12 |  0  4  4 |  * 30  * | 1 1
. . x3o3/2o ♦  4 |  0  6 |  0  0  4 |  *  * 15 | 0 2
------------+----+-------+----------+----------+----
o3x3x3o   . ♦ 30 | 30 30 | 10 20 10 |  5  5  0 | 6 *
. x3x3o3/2o ♦ 20 | 10 30 |  0 10 20 |  0  5  5 | * 6
```

```oox3xux3xoo3ooo&#xt   → both heights = sqrt(3/5) = 0.774597
(deca || pseudo u-rap || tip)

o..3o..3o..3o..     | 30  *  * |  2  2  1  0  0  0 |  1  4  1  2  2  0  0  0 | 2 2  1  1  4 0 0 | 1 2 2 0
.o.3.o.3.o.3.o.     |  * 10  * |  0  0  3  2  0  0 |  0  0  0  3  6  1  0  0 | 0 0  1  3  6 0 0 | 0 3 2 0
..o3..o3..o3..o     |  *  * 20 |  0  0  0  1  1  3 |  0  0  0  0  3  1  3  3 | 0 0  0  3  3 3 1 | 0 3 1 1
--------------------+----------+-------------------+-------------------------+------------------+--------
... x.. ... ...     |  2  0  0 | 30  *  *  *  *  * |  1  2  0  0  1  0  0  0 | 2 1  0  1  2 0 0 | 1 2 1 0
... ... x.. ...     |  2  0  0 |  * 30  *  *  *  * |  0  2  1  1  0  0  0  0 | 1 2  1  0  2 0 0 | 1 1 2 0
oo.3oo.3oo.3oo.&#x  |  1  1  0 |  *  * 30  *  *  * |  0  0  0  2  2  0  0  0 | 0 0  1  1  4 0 0 | 0 2 2 0
.oo3.oo3.oo3.oo&#x  |  0  1  1 |  *  *  * 20  *  * |  0  0  0  0  3  1  0  0 | 0 0  0  3  3 0 0 | 0 3 1 0
..x ... ... ...     |  0  0  2 |  *  *  *  * 10  * |  0  0  0  0  0  1  3  0 | 0 0  0  3  0 3 0 | 0 3 0 1
... ..x ... ...     |  0  0  2 |  *  *  *  *  * 30 |  0  0  0  0  1  0  1  2 | 0 0  0  1  2 2 1 | 0 2 1 1
--------------------+----------+-------------------+-------------------------+------------------+--------
o..3x.. ... ...     |  3  0  0 |  3  0  0  0  0  0 | 10  *  *  *  *  *  *  * | 2 0  0  1  0 0 0 | 1 2 0 0
... x..3x.. ...     |  6  0  0 |  3  3  0  0  0  0 |  * 20  *  *  *  *  *  * | 1 1  0  0  1 0 0 | 1 1 1 0
... ... x..3o..     |  3  0  0 |  0  3  0  0  0  0 |  *  * 10  *  *  *  *  * | 0 2  1  0  0 0 0 | 1 0 2 0
... ... xo. ...&#x  |  2  1  0 |  0  1  2  0  0  0 |  *  *  * 30  *  *  *  * | 0 0  1  0  2 0 0 | 0 1 2 0
... xux ... ...&#xt |  2  2  2 |  1  0  2  2  0  1 |  *  *  *  * 30  *  *  * | 0 0  0  1  2 0 0 | 0 2 1 0
.ox ... ... ...&#x  |  0  1  2 |  0  0  0  2  1  0 |  *  *  *  *  * 10  *  * | 0 0  0  3  0 0 0 | 0 3 0 0
..x3..x ... ...     |  0  0  6 |  0  0  0  0  3  3 |  *  *  *  *  *  * 10  * | 0 0  0  1  0 2 0 | 0 2 0 1
... ..x3..o ...     |  0  0  3 |  0  0  0  0  0  3 |  *  *  *  *  *  *  * 20 | 0 0  0  0  1 1 1 | 0 1 1 1
--------------------+----------+-------------------+-------------------------+------------------+--------
o..3x..3x.. ...     ♦ 12  0  0 | 12  6  0  0  0  0 |  4  4  0  0  0  0  0  0 | 5 *  *  *  * * * | 1 1 0 0
... x..3x..3o..     ♦ 12  0  0 |  6 12  0  0  0  0 |  0  4  4  0  0  0  0  0 | * 5  *  *  * * * | 1 0 1 0
... ... xo.3oo.&#x  ♦  3  1  0 |  0  3  3  0  0  0 |  0  0  1  3  0  0  0  0 | * * 10  *  * * * | 0 0 2 0
oox3xux ... ...&#xt ♦  3  3  6 |  3  0  3  6  3  3 |  1  0  0  0  3  3  1  0 | * *  * 10  * * * | 0 2 0 0
... xux3xoo ...&#xt ♦  6  3  3 |  3  3  6  3  0  3 |  0  1  0  3  3  0  0  1 | * *  *  * 20 * * | 0 1 1 0
..x3..x3..o ...     ♦  0  0 12 |  0  0  0  0  6 12 |  0  0  0  0  0  0  4  4 | * *  *  *  * 5 * | 0 1 0 1
... ..x3..o3..o     ♦  0  0  4 |  0  0  0  0  0  6 |  0  0  0  0  0  0  0  4 | * *  *  *  * * 5 | 0 0 1 1
--------------------+----------+-------------------+-------------------------+------------------+--------
o..3x..3x..3o..     ♦ 30  0  0 | 30 30  0  0  0  0 | 10 20 10  0  0  0  0  0 | 5 5  0  0  0 0 0 | 1 * * *
oox3xux3xoo ...&#xt ♦ 12  6 12 | 12  6 12 12  6 12 |  4  4  0  6 12  6  4  4 | 1 0  0  4  4 1 0 | * 5 * *
... xux3xoo3ooo&#xt ♦ 12  4  4 |  6 12 12  4  0  6 |  0  4  4 12  6  0  0  4 | 0 1  4  0  4 0 1 | * * 5 *
..x3..x3..o3..o     ♦  0  0 20 |  0  0  0  0 10 30 |  0  0  0  0  0  0 10 20 | 0 0  0  0  0 5 5 | * * * 1
```

 © 2004-2022 top of page