Acronym ...
Name x f3o,
variation of triangular prism
Circumradius sqrt[(9+2 sqrt(5))/12] = 1.059565
Lace city
in approx. ASCII-art
o o
   
   
f f
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between f3o and x f:   90°
  • between x f and x f (at x):   60°
Confer
general prisms:
n-p   n/d-p  
uniform variant:
trip  
variations:
v x3o   q x3o   f x3o   u x3o   x q3o   x u3o   v f3o   f v3o  

Incidence matrix according to Dynkin symbol

x f3o

. . . | 6 | 1 2 | 2 1
------+---+-----+----
x . . | 2 | 3 * | 2 0
. f . | 2 | * 6 | 1 1
------+---+-----+----
x f . | 4 | 2 2 | 3 *
. f3o | 3 | 0 3 | * 2

ff3oo&#x   → height = 1
(f-{3} || f-{3})

o.3o.    | 3 * | 2 1 0 | 1 2 0
.o3.o    | * 3 | 0 1 2 | 0 2 1
---------+-----+-------+------
f. ..    | 2 0 | 3 * * | 1 1 0
oo3oo&#x | 1 1 | * 3 * | 0 2 0
.f ..    | 0 2 | * * 3 | 0 1 1
---------+-----+-------+------
f.3o.    | 3 0 | 3 0 0 | 1 * *
ff ..&#x | 2 2 | 1 2 1 | * 3 *
.f3.o    | 0 3 | 0 0 3 | * * 1

xx of&#f   → height = sqrt[(9+3 sqrt(5))/8] = 1.401259
(line || (x,f)-{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&#f | 1 1 | * 4 * * | 1 1 0
.x ..    | 0 2 | * * 2 * | 1 0 1
.. .f    | 0 2 | * * * 2 | 0 1 1
---------+-----+---------+------
xx ..&#f | 2 2 | 1 2 1 0 | 2 * *
.. of&#f | 1 2 | 0 2 0 1 | * 2 *
.x .f    | 0 4 | 0 0 2 2 | * * 1

xxx&#f   → all heights = (1+sqrt(5))/2 = 1.618034
(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.&#f | 1 1 0 | * 2 * * * * | 1 0 1 0
o.o&#f | 1 0 1 | * * 2 * * * | 0 1 1 0
.x.    | 0 2 0 | * * * 1 * * | 1 0 0 1
.oo&#f | 0 1 1 | * * * * 2 * | 0 0 1 1
..x    | 0 0 2 | * * * * * 1 | 0 1 0 1
-------+-------+-------------+--------
xx.&#f | 2 2 0 | 1 2 0 1 0 0 | 1 * * *
x.x&#f | 2 0 2 | 1 0 2 0 0 1 | * 1 * *
ooo&#f | 1 1 1 | 0 1 1 0 1 0 | * * 2 *
.xx&#f | 0 2 2 | 0 0 0 1 2 1 | * * * 1

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