Acronym ...
Name v x3o,
variation of triangular prism,
vertex figure of rectified great grand stellated hecatonicosachoron
Circumradius sqrt[(17-3 sqrt(5))/24] = 0.654847
Lace city
in approx. ASCII-art 
o  o
    
x  x
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between x3o and v x:   90°
  • between v x and v x (at v):   60°
Face vector 6, 9, 5
Confer
general prisms:
n-p   n/d-p  
uniform variant:
trip  
variations:
q x3o   f x3o   u x3o   x q3o   x f3o   x h3o   x u3o   v f3o   f v3o  

Incidence matrix according to Dynkin symbol

v x3o

. . . | 6 | 1 2 | 2 1
------+---+-----+----
v . . | 2 | 3 * | 2 0
. x . | 2 | * 6 | 1 1
------+---+-----+----
v x . | 4 | 2 2 | 3 *
. x3o | 3 | 0 3 | * 2


xx3oo&#v   → height = (sqrt(5)-1)/2 = 0.618034
({3} || {3})

o.3o.    | 3 * | 2 1 0 | 1 2 0
.o3.o    | * 3 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | 3 * * | 1 1 0
oo3oo&#v | 1 1 | * 3 * | 0 2 0
.x ..    | 0 2 | * * 3 | 0 1 1
---------+-----+-------+------
x.3o.    | 3 0 | 3 0 0 | 1 * *
xx ..&#v | 2 2 | 1 2 1 | * 3 *
.x3.o    | 0 3 | 0 0 3 | * * 1


vv ox&#x   → height = sqrt(3)/2 = 0.866025
(v-line || (v,x)-{4})

o. o.    | 2 * | 1 2 0 0 | 2 1 0
.o .o    | * 4 | 0 1 1 1 | 1 1 1
---------+-----+---------+------
v. ..    | 2 0 | 1 * * * | 2 0 0
oo oo&#x | 1 1 | * 4 * * | 1 1 0
.v ..    | 0 2 | * * 2 * | 1 0 1
.. .x    | 0 2 | * * * 2 | 0 1 1
---------+-----+---------+------
vv ..&#x | 2 2 | 1 2 1 0 | 2 * *
.. ox&#x | 1 2 | 0 2 0 1 | * 2 *
.v .x    | 0 4 | 0 0 2 2 | * * 1


vvv&#x   → all heights = 1
(v-line || (v-line || v-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
-------+-------+-------------+--------
v..    | 2 0 0 | 1 * * * * * | 1 1 0 0
oo.&#x | 1 1 0 | * 2 * * * * | 1 0 1 0
o.o&#x | 1 0 1 | * * 2 * * * | 0 1 1 0
.v.    | 0 2 0 | * * * 1 * * | 1 0 0 1
.oo&#x | 0 1 1 | * * * * 2 * | 0 0 1 1
..v    | 0 0 2 | * * * * * 1 | 0 1 0 1
-------+-------+-------------+--------
vv.&#x | 2 2 0 | 1 2 0 1 0 0 | 1 * * *
v.v&#x | 2 0 2 | 1 0 2 0 0 1 | * 1 * *
ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * 2 *
.vv&#x | 0 2 2 | 0 0 0 1 2 1 | * * * 1

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