Acronym	dygytpuf, K-4.13
Name	dyadic gyrotegmipucofastegium, 3-prism atop reflected ortho 3-prism
Segmentochoron display
Circumradius	sqrt(3/4) = 0.866025
Lace city in approx. ASCII-art	x x x o o x x x
Coordinates	(1/2, 1/2, 1/2, 0)         & all changes of sign (equatorial pseudo cube) (1/2, 0, 0, 1/sqrt(2))    & all changes of sign in all but last coordinates (0, 1/2, 0, -1/sqrt(2))   & all changes of sign in all but last coordinates
Face vector	12, 30, 30, 12
Confer	related segmentochora: squippyp   general gyrotegmipucofastegia: n-gytcuf   general polytopal classes: segmentochora
External links

The lace city display shows that this polychoron can be dissected vertically into 2 squippyps, thereby adding one cube as further facet each, which here occurs as internal pseudo facet only. In fact, the other way round, this polychoron well can be considered as an external blend of those 2 components.

Incidence matrix according to Dynkin symbol

xxo oxx oxo&#xt   → both heights = sqrt(1/2) = 0.707107
(line || pseudo cube || ortho line)

o.. o.. o..    | 2 * * | 1 4 0 0 0 0 0 | 4 2 2 0 0 0 0 0 0 | 2 2 1 0 0 0
.o. .o. .o.    | * 8 * | 0 1 1 1 1 1 0 | 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1
..o ..o ..o    | * * 2 | 0 0 0 0 0 4 1 | 0 0 0 0 0 0 2 4 2 | 0 0 0 2 1 2
---------------+-------+---------------+-------------------+------------
x.. ... ...    | 2 0 0 | 1 * * * * * * | 4 0 0 0 0 0 0 0 0 | 2 2 0 0 0 0
oo. oo. oo.&#x | 1 1 0 | * 8 * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 0
.x. ... ...    | 0 2 0 | * * 4 * * * * | 1 0 0 1 1 0 1 0 0 | 1 1 0 1 1 0
... .x. ...    | 0 2 0 | * * * 4 * * * | 0 1 0 1 0 1 0 1 0 | 1 0 1 1 0 1
... ... .x.    | 0 2 0 | * * * * 4 * * | 0 0 1 0 1 1 0 0 1 | 0 1 1 0 1 1
.oo .oo .oo&#x | 0 1 1 | * * * * * 8 * | 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1
... ..x ...    | 0 0 2 | * * * * * * 1 | 0 0 0 0 0 0 0 4 0 | 0 0 0 2 0 2
---------------+-------+---------------+-------------------+------------
xx. ... ...&#x | 2 2 0 | 1 2 1 0 0 0 0 | 4 * * * * * * * * | 1 1 0 0 0 0
... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 0 | * 4 * * * * * * * | 1 0 1 0 0 0
... ... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * 4 * * * * * * | 0 1 1 0 0 0
.x. .x. ...    | 0 4 0 | 0 0 2 2 0 0 0 | * * * 2 * * * * * | 1 0 0 1 0 0
.x. ... .x.    | 0 4 0 | 0 0 2 0 2 0 0 | * * * * 2 * * * * | 0 1 0 0 1 0
... .x. .x.    | 0 4 0 | 0 0 0 2 2 0 0 | * * * * * 2 * * * | 0 0 1 0 0 1
.xo ... ...&#x | 0 2 1 | 0 0 1 0 0 2 0 | * * * * * * 4 * * | 0 0 0 1 1 0
... .xx ...&#x | 0 2 2 | 0 0 0 1 0 2 1 | * * * * * * * 4 * | 0 0 0 1 0 1
... ... .xo&#x | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * * * 4 | 0 0 0 0 1 1
---------------+-------+---------------+-------------------+------------
xx. ox. ...&#x ♦ 2 4 0 | 1 4 2 2 0 0 0 | 2 2 0 1 0 0 0 0 0 | 2 * * * * *
xx. ... ox.&#x ♦ 2 4 0 | 1 4 2 0 2 0 0 | 2 0 2 0 1 0 0 0 0 | * 2 * * * *
... ox. ox.&#x ♦ 1 4 0 | 0 4 0 2 2 0 0 | 0 2 2 0 0 1 0 0 0 | * * 2 * * *
.xo .xx ...&#x ♦ 0 4 2 | 0 0 2 2 0 4 1 | 0 0 0 1 0 0 2 2 0 | * * * 2 * *
.xo ... .xo&#x ♦ 0 4 1 | 0 0 2 0 2 4 0 | 0 0 0 0 1 0 2 0 2 | * * * * 2 *
... .xx .xo&#x ♦ 0 4 2 | 0 0 0 2 2 4 1 | 0 0 0 0 0 1 0 2 2 | * * * * * 2

or
o.. o.. o..     & | 4 * | 1  4 0 0 | 4 2 2 0 0 | 2 2 1
.o. .o. .o.       | * 8 | 0  2 2 1 | 2 2 2 1 2 | 2 2 2
------------------+-----+----------+-----------+------
x.. ... ...     & | 2 0 | 2  * * * | 4 0 0 0 0 | 2 2 0
oo. oo. oo.&#x  & | 1 1 | * 16 * * | 1 1 1 0 0 | 1 1 1
.x. ... ...     & | 0 2 | *  * 8 * | 1 1 0 1 1 | 2 1 1
... ... .x.       | 0 2 | *  * * 4 | 0 0 2 0 2 | 0 2 2
------------------+-----+----------+-----------+------
xx. ... ...&#x  & | 2 2 | 1  2 1 0 | 8 * * * * | 1 1 0
... ox. ...&#x  & | 1 2 | 0  2 1 0 | * 8 * * * | 1 0 1
... ... ox.&#x  & | 1 2 | 0  2 0 1 | * * 8 * * | 0 1 1
.x. .x. ...       | 0 4 | 0  0 4 0 | * * * 2 * | 2 0 0
.x. ... .x.     & | 0 4 | 0  0 2 2 | * * * * 4 | 0 1 1
------------------+-----+----------+-----------+------
xx. ox. ...&#x  & ♦ 2 4 | 1  4 4 0 | 2 2 0 1 0 | 4 * *
xx. ... ox.&#x  & ♦ 2 4 | 1  4 2 2 | 2 0 2 0 1 | * 4 *
... ox. ox.&#x  & ♦ 1 4 | 0  4 2 2 | 0 2 2 0 1 | * * 4

ox xx&#x || xx xo&#x   → height = sqrt(2/3) = 0.816497
(trip || refl ortho trip)

o. o.      .. ..    | 2 * * * | 1 2 2 0 0 0 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 0 0 0 0 0 | 1 1 1 2 0 0 0 0
.o .o      .. ..    | * 4 * * | 0 1 0 1 1 1 1 0 0 0 0 | 1 1 0 0 1 1 1 1 1 1 1 0 0 0 | 1 0 1 1 1 1 1 0
.. ..      o. o.    | * * 4 * | 0 0 1 0 0 1 0 1 1 1 0 | 0 0 1 1 1 0 1 1 1 0 0 1 1 1 | 0 1 1 1 0 1 1 1
.. ..      .o .o    | * * * 2 | 0 0 0 0 0 0 2 0 0 2 1 | 0 0 0 0 0 0 0 0 2 2 1 0 2 1 | 0 0 0 0 1 2 1 1
--------------------+---------+-----------------------+-----------------------------+----------------
.. x.      .. ..    | 2 0 0 0 | 1 * * * * * * * * * * | 0 2 0 2 0 0 0 0 0 0 0 0 0 0 | 1 1 0 2 0 0 0 0
oo oo&#x   .. ..    | 1 1 0 0 | * 4 * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0 0
o. o.    || o. o.    | 1 0 1 0 | * * 4 * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
.x ..      .. ..    | 0 2 0 0 | * * * 2 * * * * * * * | 1 0 0 0 0 1 1 0 0 1 0 0 0 0 | 1 0 1 0 1 1 0 0
.. .x      .. ..    | 0 2 0 0 | * * * * 2 * * * * * * | 0 1 0 0 0 1 0 1 0 0 1 0 0 0 | 1 0 0 1 1 0 1 0
.o .o    || o. o.    | 0 1 1 0 | * * * * * 4 * * * * * | 0 0 0 0 1 0 1 1 1 0 0 0 0 0 | 0 0 1 1 0 1 1 0
.o .o    || .o .o    | 0 1 0 1 | * * * * * * 4 * * * * | 0 0 0 0 0 0 0 0 1 1 1 0 0 0 | 0 0 0 0 1 1 1 0
.. ..      x. ..    | 0 0 2 0 | * * * * * * * 2 * * * | 0 0 1 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 0 1 0 1
.. ..      .. x.    | 0 0 2 0 | * * * * * * * * 2 * * | 0 0 0 1 0 0 0 1 0 0 0 1 0 1 | 0 1 0 1 0 0 1 1
.. ..      oo oo&#x | 0 0 1 1 | * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 0 0 1 1 1
.. ..      .x ..    | 0 0 0 2 | * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 2 0 0 2 0 | 0 0 0 0 1 2 0 1
--------------------+---------+-----------------------+-----------------------------+----------------
ox ..&#x   .. ..    | 1 2 0 0 | 0 2 0 1 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0
.. xx&#x   .. ..    | 2 2 0 0 | 1 2 0 0 1 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * | 1 0 0 1 0 0 0 0
o. o.    || x. ..    | 1 0 2 0 | 0 0 2 0 0 0 0 1 0 0 0 | * * 2 * * * * * * * * * * * | 0 1 1 0 0 0 0 0
.. x.    || .. x.    | 2 0 2 0 | 1 0 2 0 0 0 0 0 1 0 0 | * * * 2 * * * * * * * * * * | 0 1 0 1 0 0 0 0
oo oo&#x || o. o.    | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 0 0 | * * * * 4 * * * * * * * * * | 0 0 1 1 0 0 0 0
.x .x      .. ..    | 0 4 0 0 | 0 0 0 2 2 0 0 0 0 0 0 | * * * * * 1 * * * * * * * * | 1 0 0 0 1 0 0 0
.x ..    || x. ..    | 0 2 2 0 | 0 0 0 1 0 2 0 1 0 0 0 | * * * * * * 2 * * * * * * * | 0 0 1 0 0 1 0 0
.. .x    || .. x.    | 0 2 2 0 | 0 0 0 0 1 2 0 0 1 0 0 | * * * * * * * 2 * * * * * * | 0 0 0 1 0 0 1 0
.o .o    || oo oo&#x | 0 1 1 1 | 0 0 0 0 0 1 1 0 0 1 0 | * * * * * * * * 4 * * * * * | 0 0 0 0 0 1 1 0
.x ..    || .x ..    | 0 2 0 2 | 0 0 0 1 0 0 2 0 0 0 1 | * * * * * * * * * 2 * * * * | 0 0 0 0 1 1 0 0
.. .x    || .o .o    | 0 2 0 1 | 0 0 0 0 1 0 2 0 0 0 0 | * * * * * * * * * * 2 * * * | 0 0 0 0 1 0 1 0
.. ..      x. x.    | 0 0 4 0 | 0 0 0 0 0 0 0 2 2 0 0 | * * * * * * * * * * * 1 * * | 0 1 0 0 0 0 0 1
.. ..      xx ..&#x | 0 0 2 2 | 0 0 0 0 0 0 0 1 0 2 1 | * * * * * * * * * * * * 2 * | 0 0 0 0 0 1 0 1
.. ..      .. xo&#x | 0 0 2 1 | 0 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * 2 | 0 0 0 0 0 0 1 1
--------------------+---------+-----------------------+-----------------------------+----------------
ox xx&#x   .. ..    ♦ 2 4 0 0 | 1 4 0 2 2 0 0 0 0 0 0 | 2 2 0 0 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * * *
o. x.    || x. x.    ♦ 2 0 4 0 | 1 0 4 0 0 0 0 2 2 0 0 | 0 0 2 2 0 0 0 0 0 0 0 1 0 0 | * 1 * * * * * *
ox ..&#x || x. ..    ♦ 1 2 2 0 | 0 2 2 1 0 2 0 1 0 0 0 | 1 0 1 0 2 0 1 0 0 0 0 0 0 0 | * * 2 * * * * *
.. xx&#x || .. x.    ♦ 2 2 2 0 | 1 2 2 0 1 2 0 0 1 0 0 | 0 1 0 1 2 0 0 1 0 0 0 0 0 0 | * * * 2 * * * *
.x .x    || .x .o    ♦ 0 4 0 2 | 0 0 0 2 2 0 4 0 0 0 1 | 0 0 0 0 0 1 0 0 0 2 2 0 0 0 | * * * * 1 * * *
.x ..    || xx ..&#x ♦ 0 2 2 2 | 0 0 0 1 0 2 2 1 0 2 1 | 0 0 0 0 0 0 1 0 2 1 0 0 1 0 | * * * * * 2 * *
.. .x    || .. xo&#x ♦ 0 2 2 1 | 0 0 0 0 1 2 2 0 1 2 0 | 0 0 0 0 0 0 0 1 2 0 1 0 0 1 | * * * * * * 2 *
.. ..      xx xo&#x ♦ 0 0 4 2 | 0 0 0 0 0 0 0 2 2 4 1 | 0 0 0 0 0 0 0 0 0 0 0 1 2 2 | * * * * * * * 1