Acronym	squiddaf
Name	square duoantifastegium, digonal-square duoantiwedge, square prism atop bidual square prism
	©
Circumradius	sqrt[(5+sqrt(2))/8] = 0.895420
Lace city in approx. ASCII-art	4 4 = o o4x (square) P P = x x4o (gyro {4}-prism) 4
Lace hyper city in approx. ASCII-art	x4o x4o o4x o4x (disphenoid in configuration space)
Face vector	16, 56, 76, 46, 12
Confer	more general: n/d-daf related segmentotera: cubaope   general polytopal classes: segmentotera   scaliform
External links

This polyteron well can be obtained from cubaope. For if at its base ope both oct bases in turn would get diminished down to a diametral square, then that whole base would become a cube too (the bidual {4}-prism).

Incidence matrix according to Dynkin symbol

xo ox xo4ox&#x   → height = sqrt[(sqrt(2)-1)/2] = 0.455090
({4}-prism || bidual {4}-prism)

o. o. o.4o.    | 8 * | 1 2  4 0 0 | 2 1  4  2  4  2 0 0 | 1 2 4 2 2 1 2 0 | 2 1 2 1
.o .o .o4.o    | * 8 | 0 0  4 1 2 | 0 0  2  4  2  4 2 1 | 0 2 1 2 2 4 2 1 | 1 2 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. .. ..    | 2 0 | 4 *  * * * | 2 0  4  0  0  0 0 0 | 1 2 4 2 0 0 0 0 | 2 1 2 0
.. .. x. ..    | 2 0 | * 8  * * * | 1 1  0  0  2  0 0 0 | 1 0 2 0 1 0 2 0 | 1 0 2 1
oo oo oo4oo&#x | 1 1 | * * 32 * * | 0 0  1  1  1  1 0 0 | 0 1 1 1 1 1 1 0 | 1 1 1 1
.. .x .. ..    | 0 2 | * *  * 4 * | 0 0  0  4  0  0 2 0 | 0 2 0 0 2 4 0 1 | 1 2 0 2
.. .. .. .x    | 0 2 | * *  * * 8 | 0 0  0  0  0  2 1 1 | 0 0 0 1 0 2 2 1 | 0 1 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. x. ..    | 4 0 | 2 2  0 0 0 | 4 *  *  *  *  * * * | 1 0 2 0 0 0 0 0 | 1 0 2 0
.. .. x.4o.    | 4 0 | 0 4  0 0 0 | * 2  *  *  *  * * * | 1 0 0 0 0 0 2 0 | 0 0 2 1
xo .. .. ..&#x | 2 1 | 1 0  2 0 0 | * * 16  *  *  * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
.. ox .. ..&#x | 1 2 | 0 0  2 1 0 | * *  * 16  *  * * * | 0 1 0 0 1 1 0 0 | 1 1 0 1
.. .. xo ..&#x | 2 1 | 0 1  2 0 0 | * *  *  * 16  * * * | 0 0 1 0 1 0 1 0 | 1 0 1 1
.. .. .. ox&#x | 1 2 | 0 0  2 0 1 | * *  *  *  * 16 * * | 0 0 0 1 0 1 1 0 | 0 1 1 1
.. .x .. .x    | 0 4 | 0 0  0 2 2 | * *  *  *  *  * 4 * | 0 0 0 0 0 2 0 1 | 0 1 0 2
.. .. .o4.x    | 0 4 | 0 0  0 0 4 | * *  *  *  *  * * 2 | 0 0 0 0 0 0 2 1 | 0 0 1 2
---------------+-----+------------+---------------------+-----------------+--------
x. .. x.4o.    ♦ 8 0 | 4 8  0 0 0 | 4 2  0  0  0  0 0 0 | 1 * * * * * * * | 0 0 2 0
xo ox .. ..&#x ♦ 2 2 | 1 0  4 1 0 | 0 0  2  2  0  0 0 0 | * 8 * * * * * * | 1 1 0 0
xo .. xo ..&#x ♦ 4 1 | 2 2  4 0 0 | 1 0  2  0  2  0 0 0 | * * 8 * * * * * | 1 0 1 0
xo .. .. ox&#x ♦ 2 2 | 1 0  4 0 1 | 0 0  2  0  0  2 0 0 | * * * 8 * * * * | 0 1 1 0
.. ox xo ..&#x ♦ 2 2 | 0 1  4 1 0 | 0 0  0  2  2  0 0 0 | * * * * 8 * * * | 1 0 0 1
.. ox .. ox&#x ♦ 1 4 | 0 0  4 2 2 | 0 0  0  2  0  2 1 0 | * * * * * 8 * * | 0 1 0 1
.. .. xo4ox&#x ♦ 4 4 | 0 4  8 0 4 | 0 1  0  0  4  4 0 1 | * * * * * * 4 * | 0 0 1 1
.. .x .o4.x    ♦ 0 8 | 0 0  0 4 8 | 0 0  0  0  0  0 4 2 | * * * * * * * 1 | 0 0 0 2
---------------+-----+------------+---------------------+-----------------+--------
xo ox xo ..&#x ♦ 4 2 | 2 2  8 1 0 | 1 0  4  4  4  0 0 0 | 0 2 2 0 2 0 0 0 | 4 * * *
xo ox .. ox&#x ♦ 2 4 | 1 0  8 2 2 | 0 0  4  4  0  4 1 0 | 0 2 0 2 0 2 0 0 | * 4 * *
xo .. xo4ox&#x ♦ 8 4 | 4 8 16 0 4 | 4 2  8  0  8  8 0 1 | 1 0 4 4 0 0 2 0 | * * 2 *
.. ox xo4ox&#x ♦ 4 8 | 0 4 16 4 8 | 0 1  0  8  8  8 4 2 | 0 0 0 0 4 4 2 1 | * * * 2

or
o. o. o.4o.    & | 16 |  1  2  4 |  2 1  6  6 | 1  2  5  4 2 |  3 3
-----------------+----+----------+------------+--------------+-----
x. .. .. ..    & |  2 |  8  *  * |  2 0  4  0 | 1  2  4  2 0 |  3 2
.. .. x. ..    & |  2 |  * 16  * |  1 1  0  2 | 1  0  2  1 2 |  1 3
oo oo oo4oo&#x   |  2 |  *  * 32 |  0 0  2  2 | 0  1  2  2 1 |  2 2
-----------------+----+----------+------------+--------------+-----
x. .. x. ..    & |  4 |  2  2  0 |  8 *  *  * | 1  0  2  0 0 |  1 2
.. .. x.4o.    & |  4 |  0  4  0 |  * 4  *  * | 1  0  0  0 2 |  0 3
xo .. .. ..&#x & |  3 |  1  0  2 |  * * 32  * | 0  1  1  1 0 |  2 1
.. .. xo ..&#x & |  3 |  0  1  2 |  * *  * 32 | 0  0  1  1 1 |  1 2
-----------------+----+----------+------------+--------------+-----
x. .. x.4o.    & ♦  8 |  4  8  0 |  4 2  0  0 | 2  *  *  * * |  0 2
xo ox .. ..&#x   ♦  4 |  2  0  4 |  0 0  4  0 | *  8  *  * * |  2 0
xo .. xo ..&#x & ♦  5 |  2  2  4 |  1 0  2  2 | *  * 16  * * |  1 1
xo .. .. ox&#x & ♦  4 |  1  1  4 |  0 0  2  2 | *  *  * 16 * |  1 1
.. .. xo4ox&#x   ♦  8 |  0  8  8 |  0 2  0  8 | *  *  *  * 4 |  0 2
-----------------+----+----------+------------+--------------+-----
xo ox xo ..&#x & ♦  6 |  3  2  8 |  1 0  8  4 | 0  2  2  2 0 |  8 *
xo .. xo4ox&#x & ♦ 12 |  4 12 16 |  4 4  8 16 | 1  0  4  4 2 |  * 4