Acronym ...
Name w x4o,
variation of cube
Circumradius sqrt[5+2 sqrt(2)]/2 = 1.398966
Lace city
in approx. ASCII-art
x      x
x      x
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between x4o and w x:   90°
  • between w x and w x (at w):   90°
Confer
general prisms:
n-p  
uniform variant:
cube  
variations:
q x4o   f x4o   u x4o  

Incidence matrix according to Dynkin symbol

w x4o

. . . | 8 | 1 2 | 2 1
------+---+-----+----
w . . | 2 | 4 * | 2 0
. x . | 2 | * 8 | 1 1
------+---+-----+----
w x . | 4 | 2 2 | 4 *
. x4o | 4 | 0 4 | * 2

w x x

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

xx4oo&#w   → height = 1+sqrt(2) = 2.414214
({4} || {4})

o.4o.    | 4 * | 2 1 0 | 1 2 0
.o4.o    | * 4 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | 4 * * | 1 1 0
oo4oo&#w | 1 1 | * 4 * | 0 2 0
.x ..    | 0 2 | * * 4 | 0 1 1
---------+-----+-------+------
x.4o.    | 4 0 | 4 0 0 | 1 * *
xx ..&#w | 2 2 | 1 2 1 | * 4 *
.x4.o    | 0 4 | 0 0 4 | * * 1

xx xx&#w   → height = 1+sqrt(2) = 2.414214
({4} || {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
.. x.    | 2 0 | * 2 * * * | 1 0 1 0
oo oo&#w | 1 1 | * * 4 * * | 0 1 1 0
.x ..    | 0 2 | * * * 2 * | 0 1 0 1
.. .x    | 0 2 | * * * * 2 | 0 0 1 1
---------+-----+-----------+--------
x. x.    | 4 0 | 2 2 0 0 0 | 1 * * *
xx ..&#w | 2 2 | 1 0 2 1 0 | * 2 * *
.. xx&#w | 2 2 | 0 1 2 0 1 | * * 2 *
.x .x    | 0 4 | 0 0 0 2 2 | * * * 1

ww xx&#x   → height = 1
((w,x)-{4} || (w,x)-{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
---------+-----+-----------+--------
w. ..    | 2 0 | 2 * * * * | 1 1 0 0
.. x.    | 2 0 | * 2 * * * | 1 0 1 0
oo oo&#x | 1 1 | * * 4 * * | 0 1 1 0
.w ..    | 0 2 | * * * 2 * | 0 1 0 1
.. .x    | 0 2 | * * * * 2 | 0 0 1 1
---------+-----+-----------+--------
w. x.    | 4 0 | 2 2 0 0 0 | 1 * * *
ww ..&#x | 2 2 | 1 0 2 1 0 | * 2 * *
.. xx&#x | 2 2 | 0 1 2 0 1 | * * 2 *
.w .x    | 0 4 | 0 0 0 2 2 | * * * 1

www oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
(w-line || pseudo (w,q)-{4} || w-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
------------+-------+-----------+------
w.. ...     | 2 0 0 | 1 * * * * | 2 0 0
oo. oo.&#x  | 1 1 0 | * 4 * * * | 1 1 0
.w. ...     | 0 2 0 | * * 2 * * | 1 0 1
.oo .oo&#x  | 0 1 1 | * * * 4 * | 0 1 1
..w ...     | 0 0 2 | * * * * 1 | 0 0 2
------------+-------+-----------+------
ww. ...&#x  | 2 2 0 | 1 2 1 0 0 | 2 * *
... oqo&#xt | 1 2 1 | 0 2 0 2 0 | * 2 *
.ww ...&#x  | 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
---------------+-----+-------+----
w.. ...      & | 2 0 | 2 * * | 2 0
oo. oo.&#x   & | 1 1 | * 8 * | 1 1
.w. ...        | 0 2 | * * 2 | 2 0
---------------+-----+-------+----
ww. ...&#x   & | 2 2 | 1 2 1 | 4 *
... oqo&#xt    | 2 2 | 0 4 0 | * 2

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