Acronym pysnic
Name pyritosnub cube,
pyritohedral sirco variant,
edge-alternated girco
Circumradius sqrt[13+6 sqrt(2)]/2 = 2.317611
Snub derivation
Confer
uniform variant:
sirco  
variations:
xfF fFx Fxf&#zx  
general polytopal classes:
isogonal  
External
links
polytopewiki  

This polyhedron is being obtained as mere vertex alternation, i.e. as snubbing without subsequent resizement, when being applied to girco. Here the edge size ratios are x : h : w = 1 : sqrt(3) : 1+sqrt(2) The uniform variant of this polyhedron however is the sirco (then with ratios 1 : 1 : 1). Note that a further polyhedron with this same combinatoric topology, but again different edge ratios, occurs when the id would be diminished at the vertices of an inscribed oct. That one then (xfF fFx Fxf&#zx) would use edge ratios x : x : f = 1 : 1 : (1+sqrt(5))/2 instead.


Incidence matrix according to Dynkin symbol

xwX wXx Xxw&#zh   → height = 0
                    X = x+2q = q+w

o.. o.. o..    | 8 * * | 1 1 1 1 0 0 0 0 0 | 1 1 1 1 0 0 0
.o. .o. .o.    | * 8 * | 0 0 1 0 1 1 1 0 0 | 0 1 0 1 1 1 0
..o ..o ..o    | * * 8 | 0 0 0 1 0 0 1 1 1 | 0 0 1 1 0 1 1
---------------+-------+-------------------+--------------
x.. ... ...    | 2 0 0 | 4 * * * * * * * * | 1 1 0 0 0 0 0
... w.. ...    | 2 0 0 | * 4 * * * * * * * | 1 0 1 0 0 0 0
oo. oo. oo.&#h | 1 1 0 | * * 8 * * * * * * | 0 1 0 1 0 0 0
o.o o.o o.o&#h | 1 0 1 | * * * 8 * * * * * | 0 0 1 1 0 0 0
.w. ... ...    | 0 2 0 | * * * * 4 * * * * | 0 1 0 0 1 0 0
... ... .x.    | 0 2 0 | * * * * * 4 * * * | 0 0 0 0 1 1 0
.oo .oo .oo&#h | 0 1 1 | * * * * * * 8 * * | 0 0 0 1 0 1 0
... ..x ...    | 0 0 2 | * * * * * * * 4 * | 0 0 1 0 0 0 1
... ... ..w    | 0 0 2 | * * * * * * * * 4 | 0 0 0 0 0 1 1
---------------+-------+-------------------+--------------
x.. w.. ...    | 4 0 0 | 2 2 0 0 0 0 0 0 0 | 2 * * * * * *
xw. ... ...&#h | 2 2 0 | 1 0 2 0 1 0 0 0 0 | * 4 * * * * *
... w.x ...&#h | 2 0 2 | 0 1 0 2 0 0 0 1 0 | * * 4 * * * *
ooo ooo ooo&#h | 1 1 1 | 0 0 1 1 0 0 1 0 0 | * * * 8 * * *
.w. ... .x.    | 0 4 0 | 0 0 0 0 2 2 0 0 0 | * * * * 2 * *
... ... .xw&#h | 0 2 2 | 0 0 0 0 0 1 2 0 1 | * * * * * 4 *
... ..x ..w    | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * 2
or
o.. o.. o..    & | 24 |  1  1  2 | 1  2 1
-----------------+----+----------+-------
x.. ... ...    & |  2 | 12  *  * | 1  1 0
... w.. ...    & |  2 |  * 12  * | 1  1 0
oo. ... ...&#h & |  2 |  *  * 24 | 0  1 1
-----------------+----+----------+-------
x.. w.. ...    & |  4 |  2  2  0 | 6  * *
xw. ... ...&#h & |  4 |  1  1  2 | * 12 *
ooo ooo ooo&#h   |  3 |  0  0  3 | *  * 8

s3s4x

demi( . . . ) | 24 |  1  2  1 | 1 1  2
--------------+----+----------+-------
demi( . . x ) |  2 | 12  *  * | 0 1  1  x
sefa( s3s . ) |  2 |  * 24  * | 1 0  1  h
sefa( . s4x ) |  2 |  *  * 12 | 0 1  1  w
--------------+----+----------+-------
      s3s .     3 |  0  3  0 | 8 *  *  h3o
      . s4x     4 |  2  0  2 | * 6  *  x2w
sefa( s3s4x ) |  4 |  1  2  1 | * * 12  xw&#h

starting figure: x3x4x

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