Acronym rittip Name rectified-tesseract prism Circumradius sqrt(7)/2 = 1.322876 Lace cityin approx. ASCII-art ``` x3o x x3x x o3x x -- o3x4o x (cope) o3o x u3o x o3u x o3o x -- o3o4q x ((q,q,q,x)-tes) x3o x x3x x o3x x -- o3x4o x (cope) \ \ \ \ \ \ \ +-- x3o3o x (tepe) \ \ +--------- x3x3o x (tuttip) \ +---------------- o3x3x x (inv. tuttip) +----------------------- o3o3x x (inv. tepe) ``` ```x4o x o4q x x4o x -- o3x4o x (cope) o4q x o4q x -- o3o4q x ((q,q,q,x)-tes) x4o x o4q x x4o x -- o3x4o x (cope) ``` ```o3x4o o3o4q o3x4o -- o3o3x4o (rit) o3x4o o3o4q o3x4o -- o3o3x4o (rit) | | +-- o3x4o x (cope) | +---------- o3o4q x ((q,q,q,x)-tes) +------------------ o3x4o x (cope) ``` ```x3o3o x3x3o o3x3x o3o3x -- o3o3x4o (rit) x3o3o x3x3o o3x3x o3o3x -- o3o3x4o (rit) | | | +-- o3o3x x (tepe) | | +-------- o3x3x x (tuttip) | +-------------- x3x3o x (inv. tuttip) +-------------------- x3o3o x (inv. tepe) ``` Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 1/2)   & all permutations in all but last coord., all changes of sign Volume 23/6 = 3.833333 Confer segmentotera: tutcupip   general polytopal classes: segmentotera   lace simplices Externallinks

Incidence matrix according to Dynkin symbol

```x o3o3x4o

. . . . . | 64 |  1   6 |  6   6  3 |  6  3  2  3 |  2 3 1
----------+----+--------+-----------+-------------+-------
x . . . . |  2 | 32   * ♦  6   0  0 |  6  3  0  0 |  2 3 0
. . . x . |  2 |  * 192 |  1   2  1 |  2  1  1  2 |  1 2 1
----------+----+--------+-----------+-------------+-------
x . . x . |  4 |  2   2 | 96   *  * |  2  1  0  0 |  1 2 0
. . o3x . |  3 |  0   3 |  * 128  * |  1  0  1  1 |  1 1 1
. . . x4o |  4 |  0   4 |  *   * 48 |  0  1  0  2 |  0 2 1
----------+----+--------+-----------+-------------+-------
x . o3x . ♦  6 |  3   6 |  3   2  0 | 64  *  *  * |  1 1 0
x . . x4o ♦  8 |  4   8 |  4   0  2 |  * 24  *  * |  0 2 0
. o3o3x . ♦  4 |  0   6 |  0   4  0 |  *  * 32  * |  1 0 1
. . o3x4o ♦ 12 |  0  24 |  0   8  6 |  *  *  * 16 |  0 1 1
----------+----+--------+-----------+-------------+-------
x o3o3x . ♦  8 |  4  12 |  6   8  0 |  4  0  2  0 | 16 * *
x . o3x4o ♦ 24 | 12  48 | 24  16 12 |  8  6  0  2 |  * 8 *
. o3o3x4o ♦ 32 |  0  96 |  0  64 24 |  0  0 16  8 |  * * 2
```

```x x3o3x *c3o

. . . .    . | 64 |  1  3  3 |  3  3  3  3  3 |  3  3  3  3  1  1 | 3 1 1 1
-------------+----+----------+----------------+-------------------+--------
x . . .    . |  2 | 32  *  * ♦  3  3  0  0  0 |  3  3  3  0  0  0 | 3 1 1 0
. x . .    . |  2 |  * 96  * |  1  0  2  1  0 |  2  1  0  2  1  0 | 2 1 0 1
. . . x    . |  2 |  *  * 96 |  0  1  0  1  2 |  0  1  2  2  0  1 | 2 0 1 1
-------------+----+----------+----------------+-------------------+--------
x x . .    . |  4 |  2  2  0 | 48  *  *  *  * |  2  1  0  0  0  0 | 2 1 0 0
x . . x    . |  4 |  2  0  2 |  * 48  *  *  * |  0  1  2  0  0  0 | 2 0 1 0
. x3o .    . |  3 |  0  3  0 |  *  * 64  *  * |  1  0  0  1  1  0 | 1 1 0 1
. x . x    . |  4 |  0  2  2 |  *  *  * 48  * |  0  1  0  2  0  0 | 2 0 0 1
. . o3x    . |  3 |  0  0  3 |  *  *  *  * 64 |  0  0  1  1  0  1 | 1 0 1 1
-------------+----+----------+----------------+-------------------+--------
x x3o .    . ♦  6 |  3  6  0 |  3  0  2  0  0 | 32  *  *  *  *  * | 1 1 0 0
x x . x    . ♦  8 |  4  4  4 |  2  2  0  2  0 |  * 24  *  *  *  * | 2 0 0 0
x . o3x    . ♦  6 |  3  0  6 |  0  3  0  0  2 |  *  * 32  *  *  * | 1 0 1 0
. x3o3x    . ♦ 12 |  0 12 12 |  0  0  4  6  4 |  *  *  * 16  *  * | 1 0 0 1
. x3o . *c3o ♦  4 |  0  6  0 |  0  0  4  0  0 |  *  *  *  * 16  * | 0 1 0 1
. . o3x *c3o ♦  4 |  0  0  6 |  0  0  0  0  4 |  *  *  *  *  * 16 | 0 0 1 1
-------------+----+----------+----------------+-------------------+--------
x x3o3x    . ♦ 24 | 12 24 24 | 12 12  8 12  8 |  4  6  4  2  0  0 | 8 * * *
x x3o . *c3o ♦  8 |  4 12  0 |  6  0  8  0  0 |  4  0  0  0  2  0 | * 8 * *
x . o3x *c3o ♦  8 |  4  0 12 |  0  6  0  0  8 |  0  0  4  0  0  2 | * * 8 *
. x3o3x *c3o ♦ 32 |  0 48 48 |  0  0 32 24 32 |  0  0  0  8  8  8 | * * * 2
```

```xx3oo3xx *b3oo&#x   → height = 1
(rit || rit)

o.3o.3o. *b3o.    | 32  * |  3  3  1  0  0 |  3  3  3  3  3  0  0  0 | 3 1 1  3  3  3 0 0 0 | 1 3 1 1 0
.o3.o3.o *b3.o    |  * 32 |  0  0  1  3  3 |  0  0  0  3  3  3  3  3 | 0 0 0  3  3  3 3 1 1 | 0 3 1 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x. .. ..    ..    |  2  0 | 48  *  *  *  * |  2  1  0  1  0  0  0  0 | 2 1 0  2  1  0 0 0 0 | 1 2 1 0 0
.. .. x.    ..    |  2  0 |  * 48  *  *  * |  0  1  2  0  1  0  0  0 | 2 0 1  0  1  2 0 0 0 | 1 2 0 1 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 32  *  * ♦  0  0  0  3  3  0  0  0 | 0 0 0  3  3  3 0 0 0 | 0 3 1 1 0
.x .. ..    ..    |  0  2 |  *  *  * 48  * |  0  0  0  1  0  2  1  0 | 0 0 0  2  1  0 2 1 0 | 0 2 1 0 1
.. .. .x    ..    |  0  2 |  *  *  *  * 48 |  0  0  0  0  1  0  1  2 | 0 0 0  0  1  2 2 0 1 | 0 2 0 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3o. ..    ..    |  3  0 |  3  0  0  0  0 | 32  *  *  *  *  *  *  * | 1 1 0  1  0  0 0 0 0 | 1 1 1 0 0
x. .. x.    ..    |  4  0 |  2  2  0  0  0 |  * 24  *  *  *  *  *  * | 2 0 0  0  1  0 0 0 0 | 1 2 0 0 0
.. o.3x.    ..    |  3  0 |  0  3  0  0  0 |  *  * 32  *  *  *  *  * | 1 0 1  0  0  1 0 0 0 | 1 1 0 1 0
xx .. ..    ..&#x |  2  2 |  1  0  2  1  0 |  *  *  * 48  *  *  *  * | 0 0 0  2  1  0 0 0 0 | 0 2 1 0 0
.. .. xx    ..&#x |  2  2 |  0  1  2  0  1 |  *  *  *  * 48  *  *  * | 0 0 0  0  1  2 0 0 0 | 0 2 0 1 0
.x3.o ..    ..    |  0  3 |  0  0  0  3  0 |  *  *  *  *  * 32  *  * | 0 0 0  1  0  0 1 1 0 | 0 1 1 0 1
.x .. .x    ..    |  0  4 |  0  0  0  2  2 |  *  *  *  *  *  * 24  * | 0 0 0  0  1  0 2 0 0 | 0 2 0 0 1
.. .o3.x    ..    |  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 32 | 0 0 0  0  0  1 1 0 1 | 0 1 0 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3o.3x.    ..    ♦ 12  0 | 12 12  0  0  0 |  4  6  4  0  0  0  0  0 | 8 * *  *  *  * * * * | 1 1 0 0 0
x.3o. .. *b3o.    ♦  4  0 |  6  0  0  0  0 |  4  0  0  0  0  0  0  0 | * 8 *  *  *  * * * * | 1 0 1 0 0
.. o.3x. *b3o.    ♦  4  0 |  0  6  0  0  0 |  0  0  4  0  0  0  0  0 | * * 8  *  *  * * * * | 1 0 0 1 0
xx3oo ..    ..&#x ♦  3  3 |  3  0  3  3  0 |  1  0  0  3  0  1  0  0 | * * * 32  *  * * * * | 0 1 1 0 0
xx .. xx    ..&#x ♦  4  4 |  2  2  4  2  2 |  0  1  0  2  2  0  1  0 | * * *  * 24  * * * * | 0 2 0 0 0
.. oo3xx    ..&#x ♦  3  3 |  0  3  3  0  3 |  0  0  1  0  3  0  0  1 | * * *  *  * 32 * * * | 0 1 0 1 0
.x3.o3.x    ..    ♦  0 12 |  0  0  0 12 12 |  0  0  0  0  0  4  6  4 | * * *  *  *  * 8 * * | 0 1 0 0 1
.x3.o .. *b3.o    ♦  0  4 |  0  0  0  6  0 |  0  0  0  0  0  4  0  0 | * * *  *  *  * * 8 * | 0 0 1 0 1
.. .o3.x *b3.o    ♦  0  4 |  0  0  0  0  6 |  0  0  0  0  0  0  0  4 | * * *  *  *  * * * 8 | 0 0 0 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3o.3x. *b3o.    ♦ 32  0 | 48 48  0  0  0 | 32 24 32  0  0  0  0  0 | 8 8 8  0  0  0 0 0 0 | 1 * * * *
xx3oo3xx    ..&#x ♦ 12 12 | 12 12 12 12 12 |  4  6  4 12 12  4  6  4 | 1 0 0  4  6  4 1 0 0 | * 8 * * *
xx3oo .. *b3oo&#x ♦  4  4 |  6  0  4  6  0 |  4  0  0  6  0  4  0  0 | 0 1 0  4  0  0 0 1 0 | * * 8 * *
.. oo3xx *b3oo&#x ♦  4  4 |  0  6  4  0  6 |  0  0  4  0  6  0  0  4 | 0 0 1  0  0  4 0 0 1 | * * * 8 *
.x3.o3.x *b3.o    ♦  0 32 |  0  0  0 48 48 |  0  0  0  0  0 32 24 32 | 0 0 0  0  0  0 8 8 8 | * * * * 1
```