Acronym	siddic
Name	small distetracontoctachoron
Cross sections	©
Circumradius	sqrt[2+sqrt(2)] = 1.847759
Coordinates	(0, 0, sqrt(2)/2, (2+sqrt(2))/2)                   & all permutations, all changes of sign (1/2, 1/2, (1+sqrt(2))/2, (1+sqrt(2))/2)       & all permutations, all changes of sign (vertex inscribed srit)
General of army	spic
Colonel of regiment	spic
Face vector	144, 576, 528, 96
Confer	general polytopal classes: Wythoffian polychora
External links

As abstract polytope siddic is isomorphic to giddic, thereby replacing octagons by octagrams, and thus tic by quith. – As such siddic is a lieutenant.

Incidence matrix according to Dynkin symbol

x3o4o3/2x4*a

. . .   .    | 144 |   4   4 |   4   8   4 |  1  4  4  1
-------------+-----+---------+-------------+------------
x . .   .    |   2 | 288   * |   2   2   0 |  1  2  1  0
. . .   x    |   2 |   * 288 |   0   2   2 |  0  1  2  1
-------------+-----+---------+-------------+------------
x3o .   .    |   3 |   3   0 | 192   *   * |  1  1  0  0
x . .   x4*a |   8 |   4   4 |   * 144   * |  0  1  1  0
. . o3/2x    |   3 |   0   3 |   *   * 192 |  0  0  1  1
-------------+-----+---------+-------------+------------
x3o4o   .    ♦   6 |  12   0 |   8   0   0 | 24  *  *  *
x3o .   x4*a ♦  24 |  24  12 |   8   6   0 |  * 24  *  *
x . o3/2x4*a ♦  24 |  12  24 |   0   6   8 |  *  * 24  *
. o4o3/2x    ♦   6 |   0  12 |   0   0   8 |  *  *  * 24

x3o4/3o3x4*a

. .   . .    | 144 |   4   4 |   4   8   4 |  1  4  4  1
-------------+-----+---------+-------------+------------
x .   . .    |   2 | 288   * |   2   2   0 |  1  2  1  0
. .   . x    |   2 |   * 288 |   0   2   2 |  0  1  2  1
-------------+-----+---------+-------------+------------
x3o   . .    |   3 |   3   0 | 192   *   * |  1  1  0  0
x .   . x4*a |   8 |   4   4 |   * 144   * |  0  1  1  0
. .   o3x    |   3 |   0   3 |   *   * 192 |  0  0  1  1
-------------+-----+---------+-------------+------------
x3o4/3o .    ♦   6 |  12   0 |   8   0   0 | 24  *  *  *
x3o   . x4*a ♦  24 |  24  12 |   8   6   0 |  * 24  *  *
x .   o3x4*a ♦  24 |  12  24 |   0   6   8 |  *  * 24  *
. o4/3o3x    ♦   6 |   0  12 |   0   0   8 |  *  *  * 24

or
. .   . .       | 144 |   8 |   8   8 |  2  8
----------------+-----+-----+---------+------
x .   . .     & |   2 | 576 |   2   2 |  1  3
----------------+-----+-----+---------+------
x3o   . .     & |   3 |   3 | 384   * |  1  1
x .   . x4*a    |   8 |   8 |   * 144 |  0  2
----------------+-----+-----+---------+------
x3o4/3o .     & ♦   6 |  12 |   8   0 | 48  *
x3o   . x4*a  & ♦  24 |  36 |   8   6 |  * 48

x3/2o4/3o3/2x4*a

.   .   .   .    | 144 |   4   4 |   4   8   4 |  1  4  4  1
-----------------+-----+---------+-------------+------------
x   .   .   .    |   2 | 288   * |   2   2   0 |  1  2  1  0
.   .   .   x    |   2 |   * 288 |   0   2   2 |  0  1  2  1
-----------------+-----+---------+-------------+------------
x3/2o   .   .    |   3 |   3   0 | 192   *   * |  1  1  0  0
x   .   .   x4*a |   8 |   4   4 |   * 144   * |  0  1  1  0
.   .   o3/2x    |   3 |   0   3 |   *   * 192 |  0  0  1  1
-----------------+-----+---------+-------------+------------
x3/2o4/3o   .    ♦   6 |  12   0 |   8   0   0 | 24  *  *  *
x3/2o   .   x4*a ♦  24 |  24  12 |   8   6   0 |  * 24  *  *
x   .   o3/2x4*a ♦  24 |  12  24 |   0   6   8 |  *  * 24  *
.   o4/3o3/2x    ♦   6 |   0  12 |   0   0   8 |  *  *  * 24

or
.   .   .   .       | 144 |   8 |   8   8 |  2  8
--------------------+-----+-----+---------+------
x   .   .   .     & |   2 | 576 |   2   2 |  1  3
--------------------+-----+-----+---------+------
x3/2o   .   .     & |   3 |   3 | 384   * |  1  1
x   .   .   x4*a    |   8 |   8 |   * 144 |  0  2
--------------------+-----+-----+---------+------
x3/2o4/3o   .     & ♦   6 |  12 |   8   0 | 48  *
x3/2o   .   x4*a  & ♦  24 |  36 |   8   6 |  * 48