Acronym ...
Name x q4o,
variation of cube
Circumradius sqrt(5)/2 = 1.118034
Lace city
in approx. ASCII-art
q   q
q   q
x   x
     
x   x
o  u  o
       
o  u  o
Volume 2
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between q4o and q x:   90°
  • between q x and q x (at x):   90°
Confer
general prisms:
n-p  
uniform variant:
cube  
variations:
q x4o   f x4o   u x4o   w x4o  

using edge sizes x = 1 and q = sqrt(2) = 1.414214


Incidence matrix according to Dynkin symbol

x q4o

. . . | 8 | 1 2 | 2 1
------+---+-----+----
x . . | 2 | 4 * | 2 0
. q . | 2 | * 8 | 1 1
------+---+-----+----
x q . | 4 | 2 2 | 4 *
. q4o | 4 | 0 4 | * 2

x q q

. . . | 8 | 1 1 1 | 1 1 1
------+---+-------+------
x . . | 2 | 4 * * | 1 1 0
. q . | 2 | * 4 * | 1 0 1
. . q | 2 | * * 4 | 0 1 1
------+---+-------+------
x q . | 4 | 2 2 0 | 2 * *
x . q | 4 | 2 0 2 | * 2 *
. q q | 4 | 0 2 2 | * * 2

qq4oo&#x   → height = 1
(q-{4} || q-{4})

o.4o.    | 4 * | 2 1 0 | 1 2 0
.o4.o    | * 4 | 0 1 2 | 0 2 1
---------+-----+-------+------
q. ..    | 2 0 | 4 * * | 1 1 0
oo4oo&#x | 1 1 | * 4 * | 0 2 0
.q ..    | 0 2 | * * 4 | 0 1 1
---------+-----+-------+------
q.4o.    | 4 0 | 4 0 0 | 1 * *
qq ..&#x | 2 2 | 1 2 1 | * 4 *
.q4.o    | 0 4 | 0 0 4 | * * 1

qq qq&#x   → height = 1
(q-{4} || q-{4})

o. o.    | 4 * | 1 1 1 0 0 | 1 1 1 0
.o .o    | * 4 | 0 0 1 1 1 | 0 1 1 1
---------+-----+-----------+--------
q. ..    | 2 0 | 2 * * * * | 1 1 0 0
.. q.    | 2 0 | * 2 * * * | 1 0 1 0
oo oo&#x | 1 1 | * * 4 * * | 0 1 1 0
.q ..    | 0 2 | * * * 2 * | 0 1 0 1
.. .q    | 0 2 | * * * * 2 | 0 0 1 1
---------+-----+-----------+--------
q. q.    | 4 0 | 2 2 0 0 0 | 1 * * *
qq ..&#x | 2 2 | 1 0 2 1 0 | * 2 * *
.. qq&#x | 2 2 | 0 1 2 0 1 | * * 2 *
.q .q    | 0 4 | 0 0 0 2 2 | * * * 1

xx qq&#q   → height = sqrt(2) = 1.41214
((x,q)-{4} || (x,q)-{4})

o. o.    | 4 * | 1 1 1 0 0 | 1 1 1 0
.o .o    | * 4 | 0 0 1 1 1 | 0 1 1 1
---------+-----+-----------+--------
x. ..    | 2 0 | 2 * * * * | 1 1 0 0
.. q.    | 2 0 | * 2 * * * | 1 0 1 0
oo oo&#q | 1 1 | * * 4 * * | 0 1 1 0
.x ..    | 0 2 | * * * 2 * | 0 1 0 1
.. .q    | 0 2 | * * * * 2 | 0 0 1 1
---------+-----+-----------+--------
x. q.    | 4 0 | 2 2 0 0 0 | 1 * * *
xx ..&#q | 2 2 | 1 0 2 1 0 | * 2 * *
.. qq&#q | 2 2 | 0 1 2 0 1 | * * 2 *
.x .q    | 0 4 | 0 0 0 2 2 | * * * 1

xxx ouo&#qt   → both heights = 1
(line || pseudo (x,q)-{4} || line)

o.. o..     | 2 * * | 1 2 0 0 0 | 2 1 0
.o. .o.     | * 4 * | 0 1 1 1 0 | 1 1 1
..o ..o     | * * 2 | 0 0 0 2 1 | 0 1 2
------------+-------+-----------+------
x.. ...     | 2 0 0 | 1 * * * * | 2 0 0
oo. oo.&#q  | 1 1 0 | * 4 * * * | 1 1 0
.x. ...     | 0 2 0 | * * 2 * * | 1 0 1
.oo .oo&#q  | 0 1 1 | * * * 4 * | 0 1 1
..x ...     | 0 0 2 | * * * * 1 | 0 0 2
------------+-------+-----------+------
xx. ...&#q  | 2 2 0 | 1 2 1 0 0 | 2 * *
... ouo&#qt | 1 2 1 | 0 2 0 2 0 | * 2 *
.xx ...&#q  | 0 2 2 | 0 0 1 2 1 | * * 2
or
o.. o..      & | 4 * | 1 2 0 | 2 1
.o. .o.        | * 4 | 0 2 1 | 2 1
---------------+-----+-------+----
x.. ...      & | 2 0 | 2 * * | 2 0
oo. oo.&#q   & | 1 1 | * 8 * | 1 1
.x. ...        | 0 2 | * * 2 | 2 0
---------------+-----+-------+----
xx. ...&#q   & | 2 2 | 1 2 1 | 4 *
... ouo&#qt    | 2 2 | 0 4 0 | * 2

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