Acronym rax
Name rectified hexeract,
rectified dodecapeton
wrt. hix
5/sqrt(12) = 1.443376
wrt. rin
1/sqrt(2) = 0.707107
Lace city
in approx. ASCII-art
 ``` ©   ``` ```r Q r -- o3o3o3x4o (rin) Q Q -- o3o3o3o4q (q-pent) r Q r -- o3o3o3x4o (rin) where: r - o3o3x4o (rit) Q - o3o3o4q (q-tes) ```
```           +----------------		o3o3o3x4o (rin)
/       +---------		o3o3o3o4q (q-pent)
/       /       +--		o3o3o3x4o (rin)
/
x3o3o3o o3o3o3o     		-- x3o3o3o3o (hix)

x3x3o3o u3o3o3o x3o3o3o		-- x3x3o3o3o (tix)

o3x3x3o o3u3o3o x3x3o3o 		-- o3x3x3o3o (bittix)

o3o3x3x o3o3u3o o3x3x3o  		-- o3o3x3x3o (alt. bittix)

o3o3o3x o3o3o3u o3o3x3x  		-- o3o3o3x3x (alt. tix)

o3o3o3o o3o3o3x   		-- o3o3o3o3x (dual hix)
```
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
Volume 719/90 = 7.988889
Surface (714 sqrt(2)+2 sqrt(3))/15 = 67.547506
Dihedral angles
(at margins)
• at pen between hix and rin:   arccos[-1/sqrt(6)] = 114.094843°
• at rit between rin and rin:   90°
Confer
analogs:
rectified hypercube rCn
External

Incidence matrix according to Dynkin symbol

```o3o3o3o3x4o

. . . . . . | 192 ♦  10 |   20   5 |  20  10 |  10 10 |  2  5
------------+-----+-----+----------+---------+--------+------
. . . . x . |   2 | 960 |    4   1 |   6   4 |   4  6 |  1  4
------------+-----+-----+----------+---------+--------+------
. . . o3x . |   3 |   3 | 1280   * |   3   1 |   3  3 |  1  3
. . . . x4o |   4 |   4 |    * 240 ♦   0   4 |   0  6 |  0  4
------------+-----+-----+----------+---------+--------+------
. . o3o3x . ♦   4 |   6 |    4   0 | 960   * |   2  1 |  1  2
. . . o3x4o ♦  12 |  24 |    8   6 |   * 160 |   0  3 |  0  3
------------+-----+-----+----------+---------+--------+------
. o3o3o3x . ♦   5 |  10 |   10   0 |   5   0 | 384  * |  1  1
. . o3o3x4o ♦  32 |  96 |   64  24 |  16   8 |   * 60 |  0  2
------------+-----+-----+----------+---------+--------+------
o3o3o3o3x . ♦   6 |  15 |   20   0 |  15   0 |   6  0 | 64  *
. o3o3o3x4o ♦  80 | 320 |  320  80 | 160  40 |  32 10 |  * 12
```

```o3o3o3o3x4/3o

. . . . .   . | 192 ♦  10 |   20   5 |  20  10 |  10 10 |  2  5
--------------+-----+-----+----------+---------+--------+------
. . . . x   . |   2 | 960 |    4   1 |   6   4 |   4  6 |  1  4
--------------+-----+-----+----------+---------+--------+------
. . . o3x   . |   3 |   3 | 1280   * |   3   1 |   3  3 |  1  3
. . . . x4/3o |   4 |   4 |    * 240 ♦   0   4 |   0  6 |  0  4
--------------+-----+-----+----------+---------+--------+------
. . o3o3x   . ♦   4 |   6 |    4   0 | 960   * |   2  1 |  1  2
. . . o3x4/3o ♦  12 |  24 |    8   6 |   * 160 |   0  3 |  0  3
--------------+-----+-----+----------+---------+--------+------
. o3o3o3x   . ♦   5 |  10 |   10   0 |   5   0 | 384  * |  1  1
. . o3o3x4/3o ♦  32 |  96 |   64  24 |  16   8 |   * 60 |  0  2
--------------+-----+-----+----------+---------+--------+------
o3o3o3o3x   . ♦   6 |  15 |   20   0 |  15   0 |   6  0 | 64  *
. o3o3o3x4/3o ♦  80 | 320 |  320  80 | 160  40 |  32 10 |  * 12
```

```x3o3x *b3o3o3o

. . .    . . . | 192 |   5   5 |  10   5  10 |  10  10  10 | 10   5   5 |  5  1  1
---------------+-----+---------+-------------+-------------+------------+---------
x . .    . . . |   2 | 480   * |   4   1   0 |   4   6   0 |  6   4   0 |  4  1  0
. . x    . . . |   2 |   * 480 |   0   1   4 |   4   0   6 |  6   0   4 |  4  0  1
---------------+-----+---------+-------------+-------------+------------+---------
x3o .    . . . |   3 |   3   0 | 640   *   * |   1   3   0 |  3   3   0 |  3  1  0
x . x    . . . |   4 |   2   2 |   * 240   * ♦   4   0   0 |  6   0   0 |  4  0  0
. o3x    . . . |   3 |   0   3 |   *   * 640 |   1   0   3 |  3   0   3 |  3  0  1
---------------+-----+---------+-------------+-------------+------------+---------
x3o3x    . . . ♦  12 |  12  12 |   4   6   4 | 160   *   * |  3   0   0 |  3  0  0
x3o . *b3o . . ♦   4 |   6   0 |   4   0   0 |   * 480   * |  1   2   0 |  2  1  0
. o3x *b3o . . ♦   4 |   0   6 |   0   0   4 |   *   * 480 |  1   0   2 |  2  0  1
---------------+-----+---------+-------------+-------------+------------+---------
x3o3x *b3o . . ♦  32 |  48  48 |  32  24  32 |   8   8   8 | 60   *   * |  2  0  0
x3o . *b3o3o . ♦   5 |  10   0 |  10   0   0 |   0   5   0 |  * 192   * |  1  1  0
. o3x *b3o3o . ♦   5 |   0  10 |   0   0  10 |   0   0   5 |  *   * 192 |  1  0  1
---------------+-----+---------+-------------+-------------+------------+---------
x3o3x *b3o3o . ♦  80 | 160 160 | 160  80 160 |  40  80  80 | 10  16  16 | 12  *  *
x3o . *b3o3o3o ♦   6 |  15   0 |  20   0   0 |   0  15   0 |  0   6   0 |  * 32  *
. o3x *b3o3o3o ♦   6 |   0  15 |   0   0  20 |   0   0  15 |  0   0   6 |  *  * 32
```

```qo oo3oo3oo3xo4oq&#zx   → height = 0
(tegum sum of a q-height rinnip and an equatorial q-pent)

o. o.3o.3o.3o.4o.     | 160  * |   8   2 |  12   4  1   8 |   8  6  4  12 |  2  4  6   8 | 1  4  2
.o .o3.o3.o3.o4.o     |   * 32 |   0  10 |   0   0  5  20 |   0  0 10  20 |  0  0 10  10 | 0  5  2
----------------------+--------+---------+----------------+---------------+--------------+--------
.. .. .. .. x. ..     |   2  0 | 640   * |   3   1  0   1 |   3  3  1   3 |  1  3  3   3 | 1  3  1
oo oo3oo3oo3oo4oo&#x  |   1  1 |   * 320 |   0   0  1   4 |   0  0  4   6 |  0  0  6   4 | 0  4  1
----------------------+--------+---------+----------------+---------------+--------------+--------
.. .. .. o.3x. ..     |   3  0 |   3   0 | 640   *  *   * |   2  1  0   1 |  1  2  1   2 | 1  2  1
.. .. .. .. x.4o.     |   4  0 |   4   0 |   * 160  *   * ♦   0  3  1   0 |  0  3  3   0 | 1  3  0
qo .. .. .. .. oq&#zx |   2  2 |   0   4 |   *   * 80   * ♦   0  0  4   0 |  0  0  6   0 | 0  4  0
.. .. .. .. xo ..&#x  |   2  1 |   1   2 |   *   *  * 640 |   0  0  1   3 |  0  0  3   3 | 0  3  1
----------------------+--------+---------+----------------+---------------+--------------+--------
.. .. o.3o.3x. ..     ♦   4  0 |   6   0 |   4   0  0   0 | 320  *  *   * |  1  1  0   1 | 1  1  1
.. .. .. o.3x.4o.     ♦  12  0 |  24   0 |   8   6  0   0 |   * 80  *   * |  0  2  1   0 | 1  2  0
qo .. .. .. xo4oq&#zx ♦   8  4 |   8  16 |   0   2  4   8 |   *  * 80   * |  0  0  3   0 | 0  3  0
.. .. .. oo3xo ..&#x  ♦   3  1 |   3   3 |   1   0  0   3 |   *  *  * 640 |  0  0  1   2 | 0  2  1
----------------------+--------+---------+----------------+---------------+--------------+--------
.. o.3o.3o.3x. ..     ♦   5  0 |  10   0 |  10   0  0   0 |   5  0  0   0 | 64  *  *   * | 1  0  1
.. .. o.3o.3x.4o.     ♦  32  0 |  96   0 |  64  24  0   0 |  16  8  0   0 |  * 20  *   * | 1  1  0
qo .. .. oo3xo4oq&#zx ♦  24  8 |  48  48 |  16  12 12  48 |   0  2  6  16 |  *  * 40   * | 0  2  0
.. .. oo3oo3xo ..&#x  ♦   4  1 |   6   4 |   4   0  0   6 |   1  0  0   4 |  *  *  * 320 | 0  1  1
----------------------+--------+---------+----------------+---------------+--------------+--------
.. o.3o.3o.3x.4o.     ♦  80  0 | 320   0 | 320  80  0   0 | 160 40  0   0 | 32 10  0   0 | 2  *  *
qo .. oo3oo3xo4oq&#zx ♦  64 16 | 192 128 | 128  48 32 192 |  32 16 24 128 |  0  2  8  32 | * 10  *
.. oo3oo3oo3xo ..&#x  ♦   5  1 |  10   5 |  10   0  0  10 |   5  0  0  10 |  1  0  0   5 | *  * 64
```

```ooo3ooo3ooo3xox4oqo&#xt   → both heights =  = 1/sqrt(2) = 0.707107
(rin || pseudo q-pent || rin)

o..3o..3o..3o..4o..     | 80  *  * |   8   2   0   0 |  12  4   8  1   0   0  0 |   8  6  12  4   0   0  0 |  2  4   8  6   0  0  0 | 1  2  4  0 0
.o.3.o.3.o.3.o.4.o.     |  * 32  * |   0   5   5   0 |   0  0  10  5  10   0  0 |   0  0  10 10  10   0  0 |  0  0   5 10   5  0  0 | 0  1  5  1 0
..o3..o3..o3..o4..o     |  *  * 80 |   0   0   2   8 |   0  0   0  1   8  12  4 |   0  0   0  4  12   8  6 |  0  0   0  6   8  2  4 | 0  0  4  2 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
... ... ... x.. ...     |  2  0  0 | 320   *   *   * |   3  1   1  0   0   0  0 |   3  3   3  1   0   0  0 |  1  3   3  3   0  0  0 | 1  1  3  0 0
oo.3oo.3oo.3oo.4oo.&#x  |  1  1  0 |   * 160   *   * |   0  0   4  1   0   0  0 |   0  0   6  4   0   0  0 |  0  0   4  6   0  0  0 | 0  1  4  0 0
.oo3.oo3.oo3.oo4.oo&#x  |  0  1  1 |   *   * 160   * |   0  0   0  1   4   0  0 |   0  0   0  4   6   0  0 |  0  0   0  6   4  0  0 | 0  0  4  1 0
... ... ... ..x ...     |  0  0  2 |   *   *   * 320 |   0  0   0  0   1   3  1 |   0  0   0  1   3   3  3 |  0  0   0  3   3  1  3 | 0  0  3  1 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
... ... o..3x.. ...     |  3  0  0 |   3   0   0   0 | 320  *   *  *   *   *  * |   2  1   1  0   0   0  0 |  1  2   2  1   0  0  0 | 1  1  2  0 0
... ... ... x..4o..     |  4  0  0 |   4   0   0   0 |   * 80   *  *   *   *  * ♦   0  3   0  1   0   0  0 |  0  3   0  3   0  0  0 | 1  0  3  0 0
... ... ... xo. ...&#x  |  2  1  0 |   1   2   0   0 |   *  * 320  *   *   *  * |   0  0   3  1   0   0  0 |  0  0   3  3   0  0  0 | 0  1  3  0 0
... ... ... ... oqo&#xt |  1  2  1 |   0   2   2   0 |   *  *   * 80   *   *  * ♦   0  0   0  4   0   0  0 |  0  0   0  6   0  0  0 | 0  0  4  0 0
... ... ... .ox ...&#x  |  0  1  2 |   0   0   2   1 |   *  *   *  * 320   *  * |   0  0   0  1   3   0  0 |  0  0   0  3   3  0  0 | 0  0  3  1 0
... ... ..o3..x ...     |  0  0  3 |   0   0   0   3 |   *  *   *  *   * 320  * |   0  0   0  0   1   2  1 |  0  0   0  1   2  1  2 | 0  0  2  1 1
... ... ... ..x4..o     |  0  0  4 |   0   0   0   4 |   *  *   *  *   *   * 80 ♦   0  0   0  1   0   0  3 |  0  0   0  3   0  0  3 | 0  0  3  0 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
... o..3o..3x.. ...     ♦  4  0  0 |   6   0   0   0 |   4  0   0  0   0   0  0 | 160  *   *  *   *   *  * |  1  1   1  0   0  0  0 | 1  1  1  0 0
... ... o..3x..4o..     ♦ 12  0  0 |  24   0   0   0 |   8  6   0  0   0   0  0 |   * 40   *  *   *   *  * |  0  2   0  1   0  0  0 | 1  0  2  0 0
... ... oo.3xo. ...&#x  ♦  3  1  0 |   3   3   0   0 |   1  0   3  0   0   0  0 |   *  * 320  *   *   *  * |  0  0   2  1   0  0  0 | 0  1  2  0 0
... ... ... xox4oqo&#xt ♦  4  4  4 |   4   8   8   4 |   0  1   4  4   4   0  1 |   *  *   * 80   *   *  * |  0  0   0  3   0  0  0 | 0  0  3  0 0
... ... .oo3.ox ...&#x  ♦  0  1  3 |   0   0   3   3 |   0  0   0  0   3   1  0 |   *  *   *  * 320   *  * |  0  0   0  1   2  0  0 | 0  0  2  1 0
... ..o3..o3..x ...     ♦  0  0  4 |   0   0   0   6 |   0  0   0  0   0   4  0 |   *  *   *  *   * 160  * |  0  0   0  0   1  1  1 | 0  0  1  1 1
... ... ..o3..x4..o     ♦  0  0 12 |   0   0   0  24 |   0  0   0  0   0   8  6 |   *  *   *  *   *   * 40 |  0  0   0  1   0  0  2 | 0  0  2  0 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
o..3o..3o..3x.. ...     ♦  5  0  0 |  10   0   0   0 |  10  0   0  0   0   0  0 |   5  0   0  0   0   0  0 | 32  *   *  *   *  *  * | 1  1  0  0 0
... o..3o..3x..4o..     ♦ 32  0  0 |  96   0   0   0 |  64 24   0  0   0   0  0 |  16  8   0  0   0   0  0 |  * 10   *  *   *  *  * | 1  0  1  0 0
... oo.3oo.3xo. ...&#x  ♦  4  1  0 |   6   4   0   0 |   4  0   6  0   0   0  0 |   1  0   4  0   0   0  0 |  *  * 160  *   *  *  * | 0  1  1  0 0
... ... ooo3xox4oqo&#xt ♦ 12  8 12 |  24  24  24  24 |   8  6  24 12  24   8  6 |   0  1   8  6   8   0  1 |  *  *   * 40   *  *  * | 0  0  2  0 0
... .oo3.oo3.ox ...&#x  ♦  0  1  4 |   0   0   4   6 |   0  0   0  0   6   4  0 |   0  0   0  0   4   1  0 |  *  *   *  * 160  *  * | 0  0  1  1 0
..o3..o3..o3..x ...     ♦  0  0  5 |   0   0   0  10 |   0  0   0  0   0  10  0 |   0  0   0  0   0   5  0 |  *  *   *  *   * 32  * | 0  0  0  1 1
... ..o3..o3..x4..o     ♦  0  0 32 |   0   0   0  96 |   0  0   0  0   0  64 24 |   0  0   0  0   0  16  8 |  *  *   *  *   *  * 10 | 0  0  1  0 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
o..3o..3o..3x..4o..     ♦ 80  0  0 | 320   0   0   0 | 320 80   0  0   0   0  0 | 160 40   0  0   0   0  0 | 32 10   0  0   0  0  0 | 1  *  *  * *
oo.3oo.3oo.3xo. ...&#x  ♦  5  1  0 |  10   5   0   0 |  10  0  10  0   0   0  0 |   5  0  10  0   0   0  0 |  1  0   5  0   0  0  0 | * 32  *  * *
... ooo3ooo3xox4oqo&#xt ♦ 32 16 32 |  96  64  64  96 |  64 24  96 32  96  64 24 |  16  8  64 24  64  16  8 |  0  1  16  8  16  0  1 | *  * 10  * *
.oo3.oo3.oo3.ox ...&#x  ♦  0  1  5 |   0   0   5  10 |   0  0   0  0  10  10  0 |   0  0   0  0  10   5  0 |  0  0   0  0   5  1  0 | *  *  * 32 *
..o3..o3..o3..x4..o     ♦  0  0 80 |   0   0   0 320 |   0  0   0  0   0 320 80 |   0  0   0  0   0 160 40 |  0  0   0  0   0 32 10 | *  *  *  * 1
```