Acronym ..., doe || 6-dim-id || f-ike || doe
Name axially-pyritohedral (2,12,6)-diminishing of ex
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
 A     B   C     D                 
x2o   f2f o2F   F2x   o2F f2f   x2o		-- doe
                                   
                                   
                                   
 E     F   G                       
f2x   x2F F2f         F2f x2F   f2x		-- id \ fq-oct
                                   
 H     I         J                 
o2f   F2o       f2F       F2o   o2f		-- f-ike
                                   
x2o   f2f o2F   F2x   o2F f2f   x2o		-- doe
 K     L   M     N                 
Confer
uniform relative:
ex  
related segmentochora:
doaid  
related CRFs:
twaudoaid  

The relation to ex here is as follows: first apply a vertex-wise deep parabidiminishing to obtain the parallel does. This already has to replace several dissected 5-tet-rosettes by mere peppies. Next omit the full neighbouring vertex layer on one side. This thereby increases tha corresponding set of peppies into gyepips. And finally erase in the equatorial vertex layer from that (pseudo) id facet 6 vertices in octahedral position. This now diminishes the gyepips into mibdies and further introduces 6 more mibdies. – It is this interplay of (axially) icosahedral and (axially) octahedral symmetries, which results in the maximal common subsymmetry, the (axially) pyritohedral one.


Incidence matrix according to Dynkin symbol

xoF|f-2-oFx|f-2-Fxo|f-&#zx || (pseudo) fxF-2-xFf-2-Ffx-&#zx || (pseudo) oFf-2-foF-2-Ffo-&#zx || xoF|f-2-oFx|f-2-Fxo|f-&#zx
ACD B                                  EFG                              HIJ                     KMN L                     
aaa b                                  ccc                              ddd                     eee f                     
where: height(1,2) = (1+sqrt(5))/4 = 0.809017
       height(2,3) = 1/2
       height(3,4) = (sqrt(5)-1)/4 = 0.309017
(doe || pseudo (id \ fq-oct || pseudo f-ike || doe)

12 *  *  *  * * | 1  2  2  0  0  0  0  0  0  0  0  0  0 0  0 |  3  2  2  1  0 0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  3 1 0 0  0  0  0  0  0 0  a=A+C+D
 * 8  *  *  * * | 0  3  0  3  0  0  0  0  0  0  0  0  0 0  0 |  3  0  3  0  3 0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  3 0 1 0  0  0  0  0  0 0  b=B
 * * 24  *  * * | 0  0  1  1  2  1  1  1  1  1  0  0  0 0  0 |  0  1  1  1  2 1  2  1  1  2  1  1  1  1  1  0  0  0  0 | 0  2 1 1 1  1  2  1  1  0 0  c=E+F+G
 * *  * 12  * * | 0  0  0  0  0  0  2  2  0  0  1  2  2 0  0 |  0  1  0  0  0 0  2  1  0  0  2  2  2  2  0  1  2  2  0 | 0  1 1 0 0  1  2  2  2  1 0  d=H+I+J
 * *  *  * 12 * | 0  0  0  0  0  0  0  0  2  0  1  2  0 1  2 |  0  0  0  0  0 0  0  0  1  0  2  2  0  0  2  2  2  2  3 | 0  0 1 0 0  1  0  2  2  3 1  e=K+M+N
 * *  *  *  * 8 | 0  0  0  0  0  0  0  0  0  3  0  0  3 0  3 |  0  0  0  0  0 0  0  0  0  3  0  0  3  3  3  0  3  3  3 | 0  0 0 0 1  0  3  3  3  3 1  f=L
----------------+--------------------------------------------+---------------------------------------------------------+----------------------------
 2 0  0  0  0 0 | 6  *  *  *  *  *  *  *  *  *  *  *  * *  * |  2  2  0  0  0 0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  2 1 0 0  0  0  0  0  0 0
 1 1  0  0  0 0 | * 24  *  *  *  *  *  *  *  *  *  *  * *  * |  2  0  1  0  0 0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  2 0 0 0  0  0  0  0  0 0
 1 0  1  0  0 0 | *  * 24  *  *  *  *  *  *  *  *  *  * *  * |  0  1  1  1  0 0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 0  2 1 0 0  0  0  0  0  0 0
 0 1  1  0  0 0 | *  *  * 24  *  *  *  *  *  *  *  *  * *  * |  0  0  1  0  2 0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 0  2 0 1 0  0  0  0  0  0 0
 0 0  2  0  0 0 | *  *  *  * 24  *  *  *  *  *  *  *  * *  * |  0  0  0  0  1 1  1  0  0  1  0  0  0  0  0  0  0  0  0 | 0  1 0 1 1  0  1  0  0  0 0  type (1), at full {3} of "id \ fq-oct" layer
 0 0  2  0  0 0 | *  *  *  *  * 12  *  *  *  *  *  *  * *  * |  0  0  0  1  0 0  0  1  1  0  0  0  0  0  0  0  0  0  0 | 0  1 1 0 0  1  0  0  0  0 0  type (2), isol. unit edges of "id \ fq-oct" layer
 0 0  1  1  0 0 | *  *  *  *  *  * 24  *  *  *  *  *  * *  * |  0  1  0  0  0 0  1  0  0  0  0  1  1  0  0  0  0  0  0 | 0  1 1 0 0  0  1  0  1  0 0  type (+), those at the opposing mibdis
 0 0  1  1  0 0 | *  *  *  *  *  *  * 24  *  *  *  *  * *  * |  0  0  0  0  0 0  1  1  0  0  1  0  0  1  0  0  0  0  0 | 0  1 0 0 0  1  1  1  0  0 0  type (-), the other ones of the adjacent mibdis
 0 0  1  0  1 0 | *  *  *  *  *  *  *  * 24  *  *  *  * *  * |  0  0  0  0  0 0  0  0  1  0  1  1  0  0  1  0  0  0  0 | 0  0 1 0 0  1  0  1  1  0 0
 0 0  1  0  0 1 | *  *  *  *  *  *  *  *  * 24  *  *  * *  * |  0  0  0  0  0 0  0  0  0  2  0  0  1  1  1  0  0  0  0 | 0  0 0 0 1  0  2  1  1  0 0
 0 0  0  1  1 0 | *  *  *  *  *  *  *  *  *  * 12  *  * *  * |  0  0  0  0  0 0  0  0  0  0  2  0  0  0  0  0  2  0  0 | 0  0 0 0 0  1  0  2  0  1 0  type (x), isolated peppy lacing
 0 0  0  1  1 0 | *  *  *  *  *  *  *  *  *  *  * 24  * *  * |  0  0  0  0  0 0  0  0  0  0  0  1  0  0  0  1  0  1  0 | 0  0 1 0 0  0  0  0  1  1 0  type (y), neighbouring peppy lacings
 0 0  0  1  0 1 | *  *  *  *  *  *  *  *  *  *  *  * 24 *  * |  0  0  0  0  0 0  0  0  0  0  0  0  1  1  0  0  1  1  0 | 0  0 0 0 0  0  1  1  1  1 0
 0 0  0  0  2 0 | *  *  *  *  *  *  *  *  *  *  *  *  * 6  * |  0  0  0  0  0 0  0  0  0  0  0  0  0  0  0  2  0  0  2 | 0  0 1 0 0  0  0  0  0  2 1
 0 0  0  0  1 1 | *  *  *  *  *  *  *  *  *  *  *  *  * * 24 |  0  0  0  0  0 0  0  0  0  0  0  0  0  0  1  0  1  1  2 | 0  0 0 0 0  0  0  1  1  2 1
----------------+--------------------------------------------+---------------------------------------------------------+----------------------------
 3 2  0  0  0 0 | 1  4  0  0  0  0  0  0  0  0  0  0  0 0  0 | 12  *  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  1 0 0 0  0  0  0  0  0 0
 2 0  2  1  0 0 | 1  0  2  0  0  0  2  0  0  0  0  0  0 0  0 |  * 12  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  1 1 0 0  0  0  0  0  0 0
 1 1  1  0  0 0 | 0  1  1  1  0  0  0  0  0  0  0  0  0 0  0 |  *  * 24  *  * *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  2 0 0 0  0  0  0  0  0 0
 1 0  2  0  0 0 | 0  0  2  0  0  1  0  0  0  0  0  0  0 0  0 |  *  *  * 12  * *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  1 1 0 0  0  0  0  0  0 0
 0 1  2  0  0 0 | 0  0  0  2  1  0  0  0  0  0  0  0  0 0  0 |  *  *  *  * 24 *  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  1 0 1 0  0  0  0  0  0 0
 0 0  3  0  0 0 | 0  0  0  0  3  0  0  0  0  0  0  0  0 0  0 |  *  *  *  *  * 8  *  *  *  *  *  *  *  *  *  *  *  *  * | 0  0 0 1 1  0  0  0  0  0 0
 0 0  2  1  0 0 | 0  0  0  0  1  0  1  1  0  0  0  0  0 0  0 |  *  *  *  *  * * 24  *  *  *  *  *  *  *  *  *  *  *  * | 0  1 0 0 0  0  1  0  0  0 0  - implementing (1,+-)
 0 0  2  1  0 0 | 0  0  0  0  0  1  0  2  0  0  0  0  0 0  0 |  *  *  *  *  * *  * 12  *  *  *  *  *  *  *  *  *  *  * | 0  1 0 0 0  1  0  0  0  0 0  - implementing (2,--)
 0 0  2  0  1 0 | 0  0  0  0  0  1  0  0  2  0  0  0  0 0  0 |  *  *  *  *  * *  *  * 12  *  *  *  *  *  *  *  *  *  * | 0  0 1 0 0  1  0  0  0  0 0
 0 0  2  0  0 1 | 0  0  0  0  1  0  0  0  0  2  0  0  0 0  0 |  *  *  *  *  * *  *  *  * 24  *  *  *  *  *  *  *  *  * | 0  0 0 0 1  0  1  0  0  0 0
 0 0  1  1  1 0 | 0  0  0  0  0  0  0  1  1  0  1  0  0 0  0 |  *  *  *  *  * *  *  *  *  * 24  *  *  *  *  *  *  *  * | 0  0 0 0 0  1  0  1  0  0 0  - implementing (x,-)
 0 0  1  1  1 0 | 0  0  0  0  0  0  1  0  1  0  0  1  0 0  0 |  *  *  *  *  * *  *  *  *  *  * 24  *  *  *  *  *  *  * | 0  0 1 0 0  0  0  0  1  0 0  - implementing (y,+)
 0 0  1  1  0 1 | 0  0  0  0  0  0  1  0  0  1  0  0  1 0  0 |  *  *  *  *  * *  *  *  *  *  *  * 24  *  *  *  *  *  * | 0  0 0 0 0  0  1  1  0  0 0  - implementing (+)
 0 0  1  1  0 1 | 0  0  0  0  0  0  0  1  0  1  0  0  1 0  0 |  *  *  *  *  * *  *  *  *  *  *  *  * 24  *  *  *  *  * | 0  0 0 0 0  0  1  0  1  0 0  - implementing (-)
 0 0  1  0  1 1 | 0  0  0  0  0  0  0  0  1  1  0  0  0 0  1 |  *  *  *  *  * *  *  *  *  *  *  *  *  * 24  *  *  *  * | 0  0 0 0 0  0  0  1  1  0 0
 0 0  0  1  2 0 | 0  0  0  0  0  0  0  0  0  0  0  2  0 1  0 |  *  *  *  *  * *  *  *  *  *  *  *  *  *  * 12  *  *  * | 0  0 1 0 0  0  0  0  0  1 0
 0 0  0  1  1 1 | 0  0  0  0  0  0  0  0  0  0  1  0  1 0  1 |  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  * 24  *  * | 0  0 0 0 0  0  0  1  0  1 0  - implementing (x)
 0 0  0  1  1 1 | 0  0  0  0  0  0  0  0  0  0  0  1  1 0  1 |  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  *  * 24  * | 0  0 0 0 0  0  0  0  1  1 0  - implementing (y)
 0 0  0  0  3 2 | 0  0  0  0  0  0  0  0  0  0  0  0  0 1  4 |  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  *  *  * 12 | 0  0 0 0 0  0  0  0  0  1 1
----------------+--------------------------------------------+---------------------------------------------------------+----------------------------
12 8  0  0  0 0 | 6 24  0  0  0  0  0  0  0  0  0  0  0 0  0 | 12  0  0  0  0 0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 1  * * * *  *  *  *  *  * *  doe
 3 2  4  1  0 0 | 1  4  4  4  2  1  2  2  0  0  0  0  0 0  0 |  1  1  4  1  2 0  2  1  0  0  0  0  0  0  0  0  0  0  0 | * 12 * * *  *  *  *  *  * *  mibdi (adjacent)
 2 0  4  2  2 0 | 1  0  4  0  0  2  4  0  4  0  0  4  0 1  0 |  0  2  0  2  0 0  0  0  2  0  0  4  0  0  0  2  0  0  0 | *  * 6 * *  *  *  *  *  * *  mibdi (opposing)
 0 1  3  0  0 0 | 0  0  0  3  3  0  0  0  0  0  0  0  0 0  0 |  0  0  0  0  3 1  0  0  0  0  0  0  0  0  0  0  0  0  0 | *  * * 8 *  *  *  *  *  * *  tet bccc(1)
 0 0  3  0  0 1 | 0  0  0  0  3  0  0  0  0  3  0  0  0 0  0 |  0  0  0  0  0 1  0  0  0  3  0  0  0  0  0  0  0  0  0 | *  * * * 8  *  *  *  *  * *  tet ccc(1)f
 0 0  2  1  1 0 | 0  0  0  0  0  1  0  2  2  0  1  0  0 0  0 |  0  0  0  0  0 0  0  1  1  0  2  0  0  0  0  0  0  0  0 | *  * * * * 12  *  *  *  * *  tet c(2)c(--)de
 0 0  2  1  0 1 | 0  0  0  0  1  0  1  1  0  2  0  0  1 0  0 |  0  0  0  0  0 0  1  0  0  1  0  0  1  1  0  0  0  0  0 | *  * * * *  * 24  *  *  * *  tet c(1)c(+-)df
 0 0  1  1  1 1 | 0  0  0  0  0  0  0  1  1  1  1  0  1 0  1 |  0  0  0  0  0 0  0  0  0  0  1  0  1  0  1  0  1  0  0 | *  * * * *  *  * 24  *  * *  tet c(-)d(x)ef
 0 0  1  1  1 1 | 0  0  0  0  0  0  1  0  1  1  0  1  1 0  1 |  0  0  0  0  0 0  0  0  0  0  0  1  0  1  1  0  0  1  0 | *  * * * *  *  *  * 24  * *  tet c(+)d(y)ef
 0 0  0  1  3 2 | 0  0  0  0  0  0  0  0  0  0  1  2  2 1  4 |  0  0  0  0  0 0  0  0  0  0  0  0  0  0  0  1  2  2  1 | *  * * * *  *  *  *  * 12 *  peppy
 0 0  0  0 12 8 | 0  0  0  0  0  0  0  0  0  0  0  0  0 6 24 |  0  0  0  0  0 0  0  0  0  0  0  0  0  0  0  0  0  0 12 | *  * * * *  *  *  *  *  * 1  doe
 
 a b  c  d  e f   a  a  a  b  c  c  c  c  c  c  d  d  d e  e    a  a  a  a  b c  c  c  c  c  c  c  c  c  c  d  d  d  e   
                  a  b  c  c  c  c  d  d  e  f  e  e  f e  f    a  a  b  c  c c  c  c  c  c  d  d  d  d  e  e  e  e  e   
                             (1)(2)(+)(-)      (x)(y)           b  c  c  c  c c  d  d  e  f  e  e  f  f  f  e  f  f  f   
                                                                a  d            (1)(2)      (x)(y)(+)(-)      (x)(y) e   
                                                                b  c                                                 f   

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