Acronym rasa (old: ras)
Name rectified hepteract
wrt. hop
6/sqrt(14) = 1.603567
wrt. rax
1/sqrt(2) = 0.707107
Lace city
in approx. ASCII-art
 ``` ©   ``` ```r Q r - o3o3o3o3x4o (rax) Q Q - o3o3o3o3o4q (q-ax) r Q r - o3o3o3o3x4o (rax) where: r - o3o3o3x4o (rin) Q - o3o3o3o4q (q-pent) ```
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
Volume 5039 sqrt(2)/630 = 11.311464
Dihedral angles
• at hix between hop and rax:   arccos[-1/sqrt(7)] = 112.207654°
• at rin between rax and rax:   90°
Confer
analogs:
rectified hypercube rCn
External

Incidence matrix according to Dynkin symbol

```o3o3o3o3o3x4o

. . . . . . . | 448 |   12 |   30   6 |   40  15 |   30  20 |  12 15 |   2  6
--------------+-----+------+----------+----------+----------+--------+-------
. . . . . x . |   2 | 2688 |    5   1 |   10   5 |   10  10 |   5 10 |   1  5
--------------+-----+------+----------+----------+----------+--------+-------
. . . . o3x . |   3 |    3 | 4480   * |    4   1 |    6   4 |   4  6 |   1  4
. . . . . x4o |   4 |    4 |    * 672 ♦    0   5 |    0  10 |   0 10 |   0  5
--------------+-----+------+----------+----------+----------+--------+-------
. . . o3o3x . ♦   4 |    6 |    4   0 | 4480   * |    3   1 |   3  3 |   1  3
. . . . o3x4o ♦  12 |   24 |    8   6 |    * 560 ♦    0   4 |   0  6 |   0  4
--------------+-----+------+----------+----------+----------+--------+-------
. . o3o3o3x . ♦   5 |   10 |   10   0 |    5   0 | 2688   * |   2  1 |   1  2
. . . o3o3x4o ♦  32 |   96 |   64  24 |   16   8 |    * 280 |   0  3 |   0  3
--------------+-----+------+----------+----------+----------+--------+-------
. o3o3o3o3x . ♦   6 |   15 |   20   0 |   15   0 |    6   0 | 896  * |   1  1
. . o3o3o3x4o ♦  80 |  320 |  320  80 |  160  40 |   32  10 |   * 84 |   0  2
--------------+-----+------+----------+----------+----------+--------+-------
o3o3o3o3o3x . ♦   7 |   21 |   35   0 |   35   0 |   21   0 |   7  0 | 128  *
. o3o3o3o3x4o ♦ 192 |  960 | 1280 240 |  960 160 |  384  60 |  64 12 |   * 14
```

```x3o3x *b3o3o3o3o

. . .    . . . . | 448 |    6    6 |   15   6   15 |  15   20   20 |  20   15   15 | 15   6   6 |  6  1  1
-----------------+-----+-----------+---------------+---------------+---------------+------------+---------
x . .    . . . . |   2 | 1344    * |    5   1    0 |   5   10    0 |  10   10    0 | 10   5   0 |  5  1  0
. . x    . . . . |   2 |    * 1344 |    0   1    5 |   5    0   10 |  10    0   10 | 10   0   5 |  5  0  1
-----------------+-----+-----------+---------------+---------------+---------------+------------+---------
x3o .    . . . . |   3 |    3    0 | 2240   *    * |   1    4    0 |   4    6    0 |  6   4   0 |  4  1  0
x . x    . . . . |   4 |    2    2 |    * 672    * ♦   5    0    0 |  10    0    0 | 10   0   0 |  5  0  0
. o3x    . . . . |   3 |    0    3 |    *   * 2240 |   1    0    4 |   4    0    6 |  6   0   4 |  4  0  1
-----------------+-----+-----------+---------------+---------------+---------------+------------+---------
x3o3x    . . . . ♦  12 |   12   12 |    4   6    4 | 560    *    * ♦   4    0    0 |  6   0   0 |  4  0  0
x3o . *b3o . . . ♦   4 |    6    0 |    4   0    0 |   * 2240    * |   1    3    0 |  3   3   0 |  3  1  0
. o3x *b3o . . . ♦   4 |    0    6 |    0   0    4 |   *    * 2240 |   1    0    3 |  3   0   3 |  3  0  1
-----------------+-----+-----------+---------------+---------------+---------------+------------+---------
x3o3x *b3o . . . ♦  32 |   48   48 |   32  24   32 |   8    8    8 | 280    *    * |  3   0   0 |  3  0  0
x3o . *b3o3o . . ♦   5 |   10    0 |   10   0    0 |   0    5    0 |   * 1344    * |  1   2   0 |  2  1  0
. o3x *b3o3o . . ♦   5 |    0   10 |    0   0   10 |   0    0    5 |   *    * 1344 |  1   0   2 |  2  0  1
-----------------+-----+-----------+---------------+---------------+---------------+------------+---------
x3o3x *b3o3o . . ♦  80 |  160  160 |  160  80  160 |  40   80   80 |  10   16   16 | 84   *   * |  2  0  0
x3o . *b3o3o3o . ♦   6 |   15    0 |   20   0    0 |   0   15    0 |   0    6    0 |  * 448   * |  1  1  0
. o3x *b3o3o3o . ♦   6 |    0   15 |    0   0   20 |   0    0   15 |   0    0    6 |  *   * 448 |  1  0  1
-----------------+-----+-----------+---------------+---------------+---------------+------------+---------
x3o3x *b3o3o3o . ♦ 192 |  480  480 |  640 240  640 | 160  480  480 |  60  192  192 | 12  32  32 | 14  *  *
x3o . *b3o3o3o3o ♦   7 |   21    0 |   35   0    0 |   0   35    0 |   0   21    0 |  0   7   0 |  * 64  *
. o3x *b3o3o3o3o ♦   7 |    0   21 |    0   0   35 |   0    0   35 |   0    0   21 |  0   0   7 |  *  * 64
```

```qo oo3oo3oo3oo3xo4oq&#zx   → height = 0
(tegum sum of a q-height raxip and an equatorial q-ax)

o. o.3o.3o.3o.3o.4o.     | 384  * |   10   2 |   20   5   1   10 |   20  10   5   20 |  10  10  10   20 |   2  5 10  10 | 1  5   2
.o .o3.o3.o3.o3.o4.o     |   * 64 |    0  12 |    0   0   6   30 |    0   0  15   40 |   0   0  20   30 |   0  0 15  12 | 0  6   2
-------------------------+--------+----------+-------------------+-------------------+------------------+---------------+---------
.. .. .. .. .. x. ..     |   2  0 | 1920   * |    4   1   0    1 |    6   4   1    4 |   4   6   4    6 |   1  4  6   4 | 1  4   1
oo oo3oo3oo3oo3oo4oo&#x  |   1  1 |    * 768 |    0   0   1    5 |    0   0   5   10 |   0   0  10   10 |   0  0 10   5 | 0  5   1
-------------------------+--------+----------+-------------------+-------------------+------------------+---------------+---------
.. .. .. .. o.3x. ..     |   3  0 |    3   0 | 2560   *   *    * |    3   1   0    1 |   3   3   1    3 |   1  3  3   3 | 1  3   1
.. .. .. .. .. x.4o.     |   4  0 |    4   0 |    * 480   *    * ♦    0   4   1    0 |   0   6   4    0 |   0  4  6   0 | 1  4   0
qo .. .. .. .. .. oq&#zx |   2  2 |    0   4 |    *   * 192    * ♦    0   0   5    0 |   0   0  10    0 |   0  0 10   0 | 0  5   0
.. .. .. .. .. xo ..&#x  |   2  1 |    1   2 |    *   *   * 1920 |    0   0   1    4 |   0   0   4    6 |   0  0  6   4 | 0  4   1
-------------------------+--------+----------+-------------------+-------------------+------------------+---------------+---------
.. .. .. o.3o.3x. ..     ♦   4  0 |    6   0 |    4   0   0    0 | 1920   *   *    * |   2   1   0    1 |   1  2  1   2 | 1  2   1
.. .. .. .. o.3x.4o.     ♦  12  0 |   24   0 |    8   6   0    0 |    * 320   *    * ♦   0   3   1    0 |   0  3  3   0 | 1  3   0
qo .. .. .. .. xo4oq&#zx ♦   8  4 |    8  16 |    0   2   4    8 |    *   * 240    * ♦   0   0   4    0 |   0  0  6   0 | 0  4   0
.. .. .. .. oo3xo ..&#x  ♦   3  1 |    3   3 |    1   0   0    3 |    *   *   * 2560 |   0   0   1    3 |   0  0  3   3 | 0  3   1
-------------------------+--------+----------+-------------------+-------------------+------------------+---------------+---------
.. .. o.3o.3o.3x. ..     ♦   5  0 |   10   0 |   10   0   0    0 |    5   0   0    0 | 768   *   *    * |   1  1  0   1 | 1  1   1
.. .. .. o.3o.3x.4o.     ♦  32  0 |   96   0 |   64  24   0    0 |   16   8   0    0 |   * 120   *    * |   0  2  1   0 | 1  2   0
qo .. .. .. oo3xo4oq&#zx ♦  24  8 |   48  48 |   16  12  12   48 |    0   2   6   16 |   *   * 160    * |   0  0  3   0 | 0  3   0
.. .. .. oo3oo3xo ..&#x  ♦   4  1 |    6   4 |    4   0   0    6 |    1   0   0    4 |   *   *   * 1920 |   0  0  1   2 | 0  2   1
-------------------------+--------+----------+-------------------+-------------------+------------------+---------------+---------
.. o.3o.3o.3o.3x. ..     ♦   6  0 |   15   0 |   20   0   0    0 |   15   0   0    0 |   6   0   0    0 | 128  *  *   * | 1  0   1
.. .. o.3o.3o.3x.4o.     ♦  80  0 |  320   0 |  320  80   0    0 |  160  40   0    0 |  32  10   0    0 |   * 24  *   * | 1  1   0
qo .. .. oo3oo3xo4oq&#zx ♦  64 16 |  192 128 |  128  48  32  192 |   32  16  24  128 |   0   2   8   32 |   *  * 60   * | 0  2   0
.. .. oo3oo3oo3xo ..&#x  ♦   5  1 |   10   5 |   10   0   0   10 |    5   0   0   10 |   1   0   0    5 |   *  *  * 768 | 0  1   1
-------------------------+--------+----------+-------------------+-------------------+------------------+---------------+---------
.. o.3o.3o.3o.3x.4o.     ♦ 192  0 |  960   0 | 1280 240   0    0 |  960 160   0    0 | 384  60   0    0 |  64 12  0   0 | 2  *   *
qo .. oo3oo3oo3xo4oq&#zx ♦ 160 32 |  640 320 |  640 160  80  640 |  320  80  80  640 |  64  20  40  320 |   0  2 10  64 | * 12   *
.. oo3oo3oo3oo3xo ..&#x  ♦   6  1 |   15   6 |   20   0   0   15 |   15   0   0   20 |   6   0   0   15 |   1  0  0   6 | *  * 128
```

```ooo3ooo3ooo3ooo3xox4oqo&#xt   → both heights =  = 1/sqrt(2) = 0.707107
(rax || pseudo q-ax || rax)

o..3o..3o..3o..3o..4o..     | 192  *   * |  10   2   0   0 |   20   5  10   1   0    0   0 |  20  10   20   5    0   0   0 |  10 10  20  10   0   0  0 |  2  5  10 10   0  0  0 | 1  2  5  0 0
.o.3.o.3.o.3.o.3.o.4.o.     |   * 64   * |   0   6   6   0 |    0   0  15   6  15    0   0 |   0   0   20  15   20   0   0 |   0  0  15  20  15   0  0 |  0  0   6 15   6  0  0 | 0  1  6  1 0
..o3..o3..o3..o3..o4..o     |   *  * 192 |   0   0   2  10 |    0   0   0   1  10   20   5 |   0   0    0   5   20  20  10 |   0  0   0  10  20  10 10 |  0  0   0 10  10  2  5 | 0  0  5  2 1
----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+-------------
... ... ... ... x.. ...     |   2  0   0 | 960   *   *   * |    4   1   1   0   0    0   0 |   6   4    4   1    0   0   0 |   4  6   6   4   0   0  0 |  1  4   4  6   0  0  0 | 1  1  4  0 0
oo.3oo.3oo.3oo.3oo.4oo.&#x  |   1  1   0 |   * 384   *   * |    0   0   5   1   0    0   0 |   0   0   10   5    0   0   0 |   0  0  10  10   0   0  0 |  0  0   5 10   0  0  0 | 0  1  5  0 0
.oo3.oo3.oo3.oo3.oo4.oo&#x  |   0  1   1 |   *   * 384   * |    0   0   0   1   5    0   0 |   0   0    0   5   10   0   0 |   0  0   0  10  10   0  0 |  0  0   0 10   5  0  0 | 0  0  5  1 0
... ... ... ... ..x ...     |   0  0   2 |   *   *   * 960 |    0   0   0   0   1    4   1 |   0   0    0   1    4   6   4 |   0  0   0   4   6   4  6 |  0  0   0  6   4  1  4 | 0  0  4  1 1
----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+-------------
... ... ... o..3x.. ...     |   3  0   0 |   3   0   0   0 | 1280   *   *   *   *    *   * |   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
... ... ... ... x..4o..     |   4  0   0 |   4   0   0   0 |    * 240   *   *   *    *   * ♦   0   4    0   1    0   0   0 |   0  6   0   4   0   0  0 |  0  4   0  6   0  0  0 | 1  0  4  0 0
... ... ... ... xo. ...&#x  |   2  1   0 |   1   2   0   0 |    *   * 960   *   *    *   * |   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
... ... ... ... ... oqo&#xt |   1  2   1 |   0   2   2   0 |    *   *   * 192   *    *   * ♦   0   0    0   5    0   0   0 |   0  0   0  10   0   0  0 |  0  0   0 10   0  0  0 | 0  0  5  0 0
... ... ... ... .ox ...&#x  |   0  1   2 |   0   0   2   1 |    *   *   *   * 960    *   * |   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
... ... ... ..o3..x ...     |   0  0   3 |   0   0   0   3 |    *   *   *   *   * 1280   * |   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
... ... ... ... ..x4..o     |   0  0   4 |   0   0   0   4 |    *   *   *   *   *    * 240 ♦   0   0    0   1    0   0   4 |   0  0   0   4   0   0  6 |  0  0   0  6   0  0  4 | 0  0  4  0 1
----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+-------------
... ... o..3o..3x.. ...     ♦   4  0   0 |   6   0   0   0 |    4   0   0   0   0    0   0 | 960   *    *   *    *   *   * |   2  1   1   0   0   0  0 |  1  2   2  1   0  0  0 | 1  1  2  0 0
... ... ... o..3x..4o..     ♦  12  0   0 |  24   0   0   0 |    8   6   0   0   0    0   0 |   * 160    *   *    *   *   * ♦   0  3   0   1   0   0  0 |  0  3   0  3   0  0  0 | 1  0  3  0 0
... ... ... oo.3xo. ...&#x  ♦   3  1   0 |   3   3   0   0 |    1   0   3   0   0    0   0 |   *   * 1280   *    *   *   * |   0  0   3   1   0   0  0 |  0  0   3  3   0  0  0 | 0  1  3  0 0
... ... ... ... xox4oqo&#xt ♦   4  4   4 |   4   8   8   4 |    0   1   4   4   4    0   1 |   *   *    * 240    *   *   * ♦   0  0   0   4   0   0  0 |  0  0   0  6   0  0  0 | 0  0  4  0 0
... ... ... .oo3.ox ...&#x  ♦   0  1   3 |   0   0   3   3 |    0   0   0   0   3    1   0 |   *   *    *   * 1280   *   * |   0  0   0   1   3   0  0 |  0  0   0  3   3  0  0 | 0  0  3  1 0
... ... ..o3..o3..x ...     ♦   0  0   4 |   0   0   0   6 |    0   0   0   0   0    4   0 |   *   *    *   *    * 960   * |   0  0   0   0   1   2  1 |  0  0   0  1   2  1  2 | 0  0  2  1 1
... ... ... ..o3..x4..o     ♦   0  0  12 |   0   0   0  24 |    0   0   0   0   0    8   6 |   *   *    *   *    *   * 160 ♦   0  0   0   1   0   0  3 |  0  0   0  3   0  0  3 | 0  0  3  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 | 384  *   *   *   *   *  * |  1  1   1  0   0  0  0 | 1  1  1  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 |   * 60   *   *   *   *  * |  0  2   0  1   0  0  0 | 1  0  2  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 |   *  * 960   *   *   *  * |  0  0   2  1   0  0  0 | 0  1  2  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 |   *  *   * 160   *   *  * |  0  0   0  3   0  0  0 | 0  0  3  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 |   *  *   *   * 960   *  * |  0  0   0  1   2  0  0 | 0  0  2  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 |   *  *   *   *   * 384  * |  0  0   0  0   1  1  1 | 0  0  1  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 |   *  *   *   *   *   * 60 |  0  0   0  1   0  0  2 | 0  0  2  0 1
----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+-------------
o..3o..3o..3o..3x.. ...     ♦   6  0   0 |  15   0   0   0 |   20   0   0   0   0    0   0 |  15   0    0   0    0   0   0 |   6  0   0   0   0   0  0 | 64  *   *  *   *  *  * | 1  1  0  0 0
... 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 |  * 12   *  *   *  *  * | 1  0  1  0 0
... 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 |  *  * 384  *   *  *  * | 0  1  1  0 0
... ... 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 |  *  *   * 60   *  *  * | 0  0  2  0 0
... .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 |  *  *   *  * 384  *  * | 0  0  1  1 0
..o3..o3..o3..o3..x ...     ♦   0  0   6 |   0   0   0  15 |    0   0   0   0   0   20   0 |   0   0    0   0    0  15   0 |   0  0   0   0   0   6  0 |  *  *   *  *   * 64  * | 0  0  0  1 1
... ..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 |  *  *   *  *   *  * 12 | 0  0  1  0 1
----------------------------+------------+-----------------+-------------------------------+-------------------------------+---------------------------+------------------------+-------------
o..3o..3o..3o..3x..4o..     ♦ 192  0   0 | 960   0   0   0 | 1280 240   0   0   0    0   0 | 960 160    0   0    0   0   0 | 384 60   0   0   0   0  0 | 64 12   0  0   0  0  0 | 1  *  *  * *
oo.3oo.3oo.3oo.3xo. ...&#x  ♦   6  1   0 |  15   6   0   0 |   20   0  15   0   0    0   0 |  15   0   20   0    0   0   0 |   6  0  15   0   0   0  0 |  1  0   6  0   0  0  0 | * 64  *  * *
... ooo3ooo3ooo3xox4oqo&#xt ♦  80 32  80 | 320 160 160 320 |  320  80 320  80 320  320  80 | 160  40  320  80  320 160  40 |  32 10 160  40 160  32 10 |  0  1  32 10  32  0  1 | *  * 12  * *
.oo3.oo3.oo3.oo3.ox ...&#x  ♦   0  1   6 |   0   0   6  15 |    0   0   0   0  15   20   0 |   0   0    0   0   20  15   0 |   0  0   0   0  15   6  0 |  0  0   0  0   6  1  0 | *  *  * 64 *
..o3..o3..o3..o3..x4..o     ♦   0  0 192 |   0   0   0 960 |    0   0   0   0   0 1280 240 |   0   0    0   0    0 960 160 |   0  0   0   0   0 384 60 |  0  0   0  0   0 64 12 | *  *  *  * 1
```