Acronym	squaf, K-4.14
Name	square antifastegium, square - squap wedge, {4} || gyro cube, bidiminished octahedral antiprism
Segmentochoron display
Circumradius	sqrt[(4+sqrt(2))/7] = 0.879465
Face vector	12, 32, 31, 11
Confer	segmentochora family: n-af   n/d-af   related segmentochora: oct || cube general polytopal classes: segmentochora
External links

Incidence matrix according to Dynkin symbol

xoo4oxx&#x   → height(1,2) = height(1,3) = 1/sqrt(sqrt(2)) = 0.840896
               height(2,3) = 1
( {4} || (dual {4} || dual {4}) )

o.. o..    | 4 * * | 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o. .o.    | * 4 * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o ..o    | * * 4 | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
-----------+-------+-------------+-------------------+----------
x.. ...    | 2 0 0 | 4 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.4oo.&#x | 1 1 0 | * 8 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o4o.o&#x | 1 0 1 | * * 8 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x.    | 0 2 0 | * * * 4 * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo4.oo&#x | 0 1 1 | * * * * 4 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x    | 0 0 2 | * * * * * 4 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
-----------+-------+-------------+-------------------+----------
x..4o..    | 4 0 0 | 4 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 4 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 4 * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 4 * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 4 * * * * | 0 1 0 1 0
ooo4ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 8 * * * | 0 0 1 1 0
.o.4.x.    | 0 4 0 | 0 0 0 4 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 4 * | 0 0 0 1 1
..o4..x    | 0 0 4 | 0 0 0 0 0 4 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+-------------+-------------------+----------
xo.4ox.&#x ♦ 4 4 0 | 4 8 0 4 0 0 | 1 4 4 0 0 0 1 0 0 | 1 * * * *
x.o4o.x&#x ♦ 4 0 4 | 4 0 8 0 0 4 | 1 0 0 4 4 0 0 0 1 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 4 * *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * 4 *
.oo4.xx&#x ♦ 0 4 4 | 0 0 0 4 4 4 | 0 0 0 0 0 0 1 4 1 | * * * * 1

xo4ox ox&#x   → height = sqrt[2 sqrt(2)-1]/2 = 0.676097
({4} || gyro cube)

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

{4} || squap   → height = sqrt[4-sqrt(2)]/2 = 0.804019

o.. o..    | 4 * * | 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o. .o.    | * 4 * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o ..o    | * * 4 | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
-----------+-------+-------------+-------------------+----------
x.. ...    | 2 0 0 | 4 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.4oo.&#x | 1 1 0 | * 8 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o4o.o&#x | 1 0 1 | * * 8 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x.    | 0 2 0 | * * * 4 * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo4.oo&#x | 0 1 1 | * * * * 4 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x    | 0 0 2 | * * * * * 4 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
-----------+-------+-------------+-------------------+----------
x..4o..    | 4 0 0 | 4 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 4 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 4 * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 4 * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 4 * * * * | 0 1 0 1 0
ooo4ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 8 * * * | 0 0 1 1 0
.o.4.x.    | 0 4 0 | 0 0 0 4 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 4 * | 0 0 0 1 1
..o4..x    | 0 0 4 | 0 0 0 0 0 4 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+-------------+-------------------+----------
xo.4ox.&#x ♦ 4 4 0 | 4 8 0 4 0 0 | 1 4 4 0 0 0 1 0 0 | 1 * * * *
x.o4o.x&#x ♦ 4 0 4 | 4 0 8 0 0 4 | 1 0 0 4 4 0 0 0 1 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 4 * *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * 4 *
.oo4.xx&#x ♦ 0 4 4 | 0 0 0 4 4 4 | 0 0 0 0 0 0 1 4 1 | * * * * 1