| Acronym | ..., doe || 6-dim-id || f-ike || doe |
| Name | axially-pyritohedral (2,24,12,6)-diminishing of ex |
central: top doe, brown: adjacent mibdies, light yellow: opposing mibdies, remainder: tets, missing: outermost/bottom doe and peppies | |
| 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 |
| Face vector | 76, 300, 356, 132 |
| Confer |
The relation to ex here is as follows: first apply a vertex-wise deep parabidiminishing to obtain the parallel does, then already omitting 1+12 vertices on either side. Thereby several dissected 5-tet-rosettes have to be replaced by mere peppies. Next omit the full neighbouring vertex layer (of further 12 vertices) on one side. Herewith each peppy increases into a gyepip. And finally erase within the equatorial vertex layer from that (pseudo) id facet 6 vertices in octahedral position. This now diminishes those gyepips into mibdies and further introduces 6 more mibdies.
It is this interplay of icosahedral and octahedral symmetries of the equatorial layer, which results here in the maximal common subsymmetry of ex, an (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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