Acronym	rillip
Name	rectified-heptapeton prism, vertex figure of robay
Circumradius	sqrt(27/28) = 0.981981
Volume	19 sqrt(7)/1920 = 0.026182
Face vector	42, 231, 455, 455, 266, 91, 16
Confer	general polytopal classes: Wythoffian polyexa   segmentoexa
External links

Incidence matrix according to Dynkin symbol

x o3x3o3o3o3o

. . . . . . . | 42 |  1  10 |  10  5  20 |  5  20 10  20 | 10  20 10 10 | 10 10  5  2 | 5 2 1
--------------+----+--------+------------+---------------+--------------+-------------+------
x . . . . . . |  2 | 21   * ♦  10  0   0 |  5  20  0   0 | 10  20  0  0 | 10 10  0  0 | 5 2 0
. . x . . . . |  2 |  * 210 |   1  1   4 |  1   4  4   6 |  4   6  6  4 |  6  4  4  1 | 4 1 1
--------------+----+--------+------------+---------------+--------------+-------------+------
x . x . . . . |  4 |  2   2 | 105  *   * |  1   4  0   0 |  4   6  0  0 |  6  4  0  0 | 4 1 0
. o3x . . . . |  3 |  0   3 |   * 70   * |  1   0  4   0 |  4   0  6  0 |  6  0  4  0 | 4 0 1
. . x3o . . . |  3 |  0   3 |   *  * 280 |  0   1  1   3 |  1   3  3  3 |  3  3  3  1 | 3 1 1
--------------+----+--------+------------+---------------+--------------+-------------+------
x o3x . . . . ♦  6 |  3   6 |   3  2   0 | 35   *  *   * ♦  4   0  0  0 |  6  0  0  0 | 4 0 0
x . x3o . . . ♦  6 |  3   6 |   3  0   2 |  * 140  *   * |  1   3  0  0 |  3  3  0  0 | 3 1 0
. o3x3o . . . ♦  6 |  0  12 |   0  4   4 |  *   * 70   * |  1   0  3  0 |  3  0  3  0 | 3 0 1
. . x3o3o . . ♦  4 |  0   6 |   0  0   4 |  *   *  * 210 |  0   1  1  2 |  1  2  2  1 | 2 1 1
--------------+----+--------+------------+---------------+--------------+-------------+------
x o3x3o . . . ♦ 12 |  6  24 |  12  8   8 |  4   4  2   0 | 35   *  *  * |  3  0  0  0 | 3 0 0
x . x3o3o . . ♦  8 |  4  12 |   6  0   8 |  0   4  0   2 |  * 105  *  * |  1  2  0  0 | 2 1 0
. o3x3o3o . . ♦ 10 |  0  30 |   0 10  20 |  0   0  5   5 |  *   * 42  * |  1  0  2  0 | 2 0 1
. . x3o3o3o . ♦  5 |  0  10 |   0  0  10 |  0   0  0   5 |  *   *  * 84 |  0  1  1  1 | 1 1 1
--------------+----+--------+------------+---------------+--------------+-------------+------
x o3x3o3o . . ♦ 20 | 10  60 |  30 20  40 | 10  20 10  10 |  5   5  2  0 | 21  *  *  * | 2 0 0
x . x3o3o3o . ♦ 10 |  5  20 |  10  0  20 |  0  10  0  10 |  0   5  0  2 |  * 42  *  * | 1 1 0
. o3x3o3o3o . ♦ 15 |  0  60 |   0 20  60 |  0   0 15  30 |  0   0  6  6 |  *  * 14  * | 1 0 1
. . x3o3o3o3o ♦  6 |  0  15 |   0  0  20 |  0   0  0  15 |  0   0  0  6 |  *  *  * 14 | 0 1 1
--------------+----+--------+------------+---------------+--------------+-------------+------
x o3x3o3o3o . ♦ 30 | 15 120 |  60 40 120 | 20  60 30  60 | 15  30 12 12 |  6  6  2  0 | 7 * *
x . x3o3o3o3o ♦ 12 |  6  30 |  15  0  40 |  0  20  0  30 |  0  15  0 12 |  0  6  0  2 | * 7 *
. o3x3o3o3o3o ♦ 21 |  0 105 |   0 35 140 |  0   0 35 105 |  0   0 21 42 |  0  0  7  7 | * * 2

oo3xx3oo3oo3oo3oo&#x   → height = 1
(ril || ril)

o.3o.3o.3o.3o.3o.    | 21  * |  10  1   0 |  5  20  10  0   0 | 10  20  5  20  0   0 | 10 10 10  20  0  0 | 5 2 10 10 0 0 | 1 5 2 0
.o3.o3.o3.o3.o3.o    |  * 21 |   0  1  10 |  0   0  10  5  20 |  0   0  5  20 10  20 |  0  0 10  20 10 10 | 0 0 10 10 5 2 | 0 5 2 1
---------------------+-------+------------+-------------------+----------------------+--------------------+---------------+--------
.. x. .. .. .. ..    |  2  0 | 105  *   * |  1   4   1  0   0 |  4   6  1   4  0   0 |  6  4  4   6  0  0 | 4 1  6  4 0 0 | 1 4 1 0
oo3oo3oo3oo3oo3oo&#x |  1  1 |   * 21   * ♦  0   0  10  0   0 |  0   0  5  20  0   0 |  0  0 10  20  0  0 | 0 0 10 10 0 0 | 0 5 2 0
.. .x .. .. .. ..    |  0  2 |   *  * 105 |  0   0   1  1   4 |  0   0  1   4  4   6 |  0  0  4   6  6  4 | 0 0  6  4 4 1 | 0 4 1 1
---------------------+-------+------------+-------------------+----------------------+--------------------+---------------+--------
o.3x. .. .. .. ..    |  3  0 |   3  0   0 | 35   *   *  *   * |  4   0  1   0  0   0 |  6  0  4   0  0  0 | 4 0  6  0 0 0 | 1 4 0 0
.. x.3o. .. .. ..    |  3  0 |   3  0   0 |  * 140   *  *   * |  1   3  0   1  0   0 |  3  3  1   3  0  0 | 3 1  3  3 0 0 | 1 3 1 0
.. xx .. .. .. ..&#x |  2  2 |   1  2   1 |  *   * 105  *   * |  0   0  1   4  0   0 |  0  0  4   6  0  0 | 0 0  6  4 0 0 | 0 4 1 0
.o3.x .. .. .. ..    |  0  3 |   0  0   3 |  *   *   * 35   * |  0   0  1   0  4   0 |  0  0  4   0  6  0 | 0 0  6  0 4 0 | 0 4 0 1
.. .x3.o .. .. ..    |  0  3 |   0  0   3 |  *   *   *  * 140 |  0   0  0   1  1   3 |  0  0  1   3  3  3 | 0 0  3  3 3 1 | 0 3 1 1
---------------------+-------+------------+-------------------+----------------------+--------------------+---------------+--------
o.3x.3o. .. .. ..    ♦  6  0 |  12  0   0 |  4   4   0  0   0 | 35   *  *   *  *   * |  3  0  1   0  0  0 | 3 0  3  0 0 0 | 1 3 0 0
.. x.3o.3o. .. ..    ♦  4  0 |   6  0   0 |  0   4   0  0   0 |  * 105  *   *  *   * |  1  2  0   1  0  0 | 2 1  1  2 0 0 | 1 2 1 0
oo3xx .. .. .. ..&#x ♦  3  3 |   3  3   3 |  1   0   3  1   0 |  *   * 35   *  *   * ♦  0  0  4   0  0  0 | 0 0  6  0 0 0 | 0 4 0 0
.. xx3oo .. .. ..&#x ♦  3  3 |   3  3   3 |  0   1   3  0   1 |  *   *  * 140  *   * |  0  0  1   3  0  0 | 0 0  3  3 0 0 | 0 3 1 0
.o3.x3.o .. .. ..    ♦  0  6 |   0  0  12 |  0   0   0  4   4 |  *   *  *   * 35   * |  0  0  1   0  3  0 | 0 0  3  0 3 0 | 0 3 0 1
.. .x3.o3.o .. ..    ♦  0  4 |   0  0   6 |  0   0   0  0   4 |  *   *  *   *  * 105 |  0  0  0   1  1  2 | 0 0  1  2 2 1 | 0 2 1 1
---------------------+-------+------------+-------------------+----------------------+--------------------+---------------+--------
o.3x.3o.3o. .. ..    ♦ 10  0 |  30  0   0 | 10  20   0  0   0 |  5   5  0   0  0   0 | 21  *  *   *  *  * | 2 0  1  0 0 0 | 1 2 0 0
.. x.3o.3o.3o. ..    ♦  5  0 |  10  0   0 |  0  10   0  0   0 |  0   5  0   0  0   0 |  * 42  *   *  *  * | 1 1  0  1 0 0 | 1 1 1 0
oo3xx3oo .. .. ..&#x ♦  6  6 |  12  6  12 |  4   4  12  4   4 |  1   0  4   4  1   0 |  *  * 35   *  *  * | 0 0  3  0 0 0 | 0 3 0 0
.. xx3oo3oo .. ..&#x ♦  4  4 |   6  4   6 |  0   4   6  0   4 |  0   1  0   4  0   1 |  *  *  * 105  *  * | 0 0  1  2 0 0 | 0 2 1 0
.o3.x3.o3.o .. ..    ♦  0 10 |   0  0  30 |  0   0   0 10  20 |  0   0  0   0  5   5 |  *  *  *   * 21  * | 0 0  1  0 2 0 | 0 2 0 1
.. .x3.o3.o3.o ..    ♦  0  5 |   0  0  10 |  0   0   0  0  10 |  0   0  0   0  0   5 |  *  *  *   *  * 42 | 0 0  0  1 1 1 | 0 1 1 1
---------------------+-------+------------+-------------------+----------------------+--------------------+---------------+--------
o.3x.3o.3o.3o. ..    ♦ 15  0 |  60  0   0 | 20  60   0  0   0 | 15  30  0   0  0   0 |  6  6  0   0  0  0 | 7 *  *  * * * | 1 1 0 0
.. x.3o.3o.3o.3o.    ♦  6  0 |  15  0   0 |  0  20   0  0   0 |  0  15  0   0  0   0 |  0  6  0   0  0  0 | * 7  *  * * * | 1 0 1 0
oo3xx3oo3oo .. ..&#x ♦ 10 10 |  30 10  30 | 10  20  30 10  20 |  5   5 10  20  5   5 |  1  0  5   5  1  0 | * * 21  * * * | 0 2 0 0
.. xx3oo3oo3oo ..&#x ♦  5  5 |  10  5  10 |  0  10  10  0  10 |  0   5  0  10  0   5 |  0  1  0   5  0  1 | * *  * 42 * * | 0 1 1 0
.o3.x3.o3.o3.o ..    ♦  0 15 |   0  0  60 |  0   0   0 20  60 |  0   0  0   0 15  30 |  0  0  0   0  6  6 | * *  *  * 7 * | 0 1 0 1
.. .x3.o3.o3.o3.o    ♦  0  6 |   0  0  15 |  0   0   0  0  20 |  0   0  0   0  0  15 |  0  0  0   0  0  6 | * *  *  * * 7 | 0 0 1 1
---------------------+-------+------------+-------------------+----------------------+--------------------+---------------+--------
o.3x.3o.3o.3o.3o.    ♦ 21  0 | 105  0   0 | 35 140   0  0   0 | 35 105  0   0  0   0 | 21 42  0   0  0  0 | 7 7  0  0 0 0 | 1 * * *
oo3xx3oo3oo3oo ..&#x ♦ 15 15 |  60 15  60 | 20  60  60 20  60 | 15  30 20  60 15  30 |  6  6 15  30  6  6 | 1 0  6  6 1 0 | * 7 * *
.. xx3oo3oo3oo3oo&#x ♦  6  6 |  15  6  15 |  0  20  15  0  20 |  0  15  0  20  0  15 |  0  6  0  15  0  6 | 0 1  0  6 0 1 | * * 7 *
.o3.x3.o3.o3.o3.o    ♦  0 21 |   0  0 105 |  0   0   0 35 140 |  0   0  0   0 35 105 |  0  0  0   0 21 42 | 0 0  0  0 7 7 | * * * 1