Acronym ...
Name x q3o,
variation of triangular prism,
vertex figure of rectified icositetrachoron
Circumradius sqrt(11/12) = 0.957427
Lace city
in approx. ASCII-art
o o
   
q q
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between q3o and x q:   90°
  • between x q and x q (at x):   60°
Confer
general prisms:
n-p   n/d-p  
uniform variant:
trip  
variations:
v x3o   q x3o   f x3o   u x3o   x f3o   x u3o   v f3o   f v3o  

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


Incidence matrix according to Dynkin symbol

x q3o

. . . | 6 | 1 2 | 2 1
------+---+-----+----
x . . | 2 | 3 * | 2 0
. q . | 2 | * 6 | 1 1
------+---+-----+----
x q . | 4 | 2 2 | 3 *
. q3o | 3 | 0 3 | * 2

qq3oo&#x   → height = 1
(q-{3} || q-{3})

o.3o.    | 3 * | 2 1 0 | 1 2 0
.o3.o    | * 3 | 0 1 2 | 0 2 1
---------+-----+-------+------
q. ..    | 2 0 | 3 * * | 1 1 0
oo3oo&#x | 1 1 | * 3 * | 0 2 0
.q ..    | 0 2 | * * 3 | 0 1 1
---------+-----+-------+------
q.3o.    | 3 0 | 3 0 0 | 1 * *
qq ..&#x | 2 2 | 1 2 1 | * 3 *
.q3.o    | 0 3 | 0 0 3 | * * 1

xx oq&#q   → height = sqrt(3/2) = 1.224745
(line || (x,q)-{4})

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

xxx&#q   → all heights = sqrt(2) = 1.414214
(line || (line || line))

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

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