Acronym ...
Name f v3o,
variation of triangular prism,
vertex figure of rectified great grand hecatonicosachoron
Circumradius sqrt[(21-sqrt(5))/24] = 0.884212
Lace city
in approx. ASCII-art
o   o
v   v
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between v3o and f v:   90°
  • between f v and f v (at f):   60°
Confer
general prisms:
n-p   n/d-p  
uniform variant:
trip  
variations:
v x3o   q x3o   f x3o   u x3o   x q3o   x f3o   x u3o   v f3o  

Incidence matrix according to Dynkin symbol

f v3o

. . . | 6 | 1 2 | 2 1
------+---+-----+----
f . . | 2 | 3 * | 2 0
. v . | 2 | * 6 | 1 1
------+---+-----+----
f v . | 4 | 2 2 | 3 *
. v3o | 3 | 0 3 | * 2

vv3oo&#f   → height = (1+sqrt(5))/2 = 1.618034
({3} || {3})

o.3o.    | 3 * | 2 1 0 | 1 2 0
.o3.o    | * 3 | 0 1 2 | 0 2 1
---------+-----+-------+------
v. ..    | 2 0 | 3 * * | 1 1 0
oo3oo&#f | 1 1 | * 3 * | 0 2 0
.v ..    | 0 2 | * * 3 | 0 1 1
---------+-----+-------+------
v.3o.    | 3 0 | 3 0 0 | 1 * *
vv ..&#f | 2 2 | 1 2 1 | * 3 *
.v3.o    | 0 3 | 0 0 3 | * * 1

ff ox&#v   → height = (sqrt(5)-1) sqrt(3)/4 = 0.535233
(f-line || (f,x)-{4})

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

fff&#v   → all heights = (sqrt(5)-1)/2 = 0.618034
(f-line || (f-line || f-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
-------+-------+-------------+--------
f..    | 2 0 0 | 1 * * * * * | 1 1 0 0
oo.&#v | 1 1 0 | * 2 * * * * | 1 0 1 0
o.o&#v | 1 0 1 | * * 2 * * * | 0 1 1 0
.f.    | 0 2 0 | * * * 1 * * | 1 0 0 1
.oo&#v | 0 1 1 | * * * * 2 * | 0 0 1 1
..f    | 0 0 2 | * * * * * 1 | 0 1 0 1
-------+-------+-------------+--------
ff.&#v | 2 2 0 | 1 2 0 1 0 0 | 1 * * *
f.f&#v | 2 0 2 | 1 0 2 0 0 1 | * 1 * *
ooo&#v | 1 1 1 | 0 1 1 0 1 0 | * * 2 *
.ff&#v | 0 2 2 | 0 0 0 1 2 1 | * * * 1

© 2004-2019
top of page