| Acronym | ... |
| Name | Fxo xfo3oox5xxx&#zxt |
|
Lace city in approx. ASCII-art |
o5x o5x
x5x
o5x o5x
o5F
f5x f5x
x5x x5x
f5f f5f
o5V
x5f x5f
V5o V5o
x5F
F5o F5o
o5F o5F
F5x
o5V o5V
f5x f5x
V5o
f5f f5f
x5x x5x
x5f x5f
F5o
x5o x5o
x5x
x5o x5o
| | | | +-- srid
| | | +-------------- (f,x)-srid
| | +--------------------- tid
| +---------------------------- (f,x)-srid
+---------------------------------------- srid
|
x3o x3f o3V f3F V3x x3V F3f V3o f3x o3x - srid
f3o f3f V3x o3B f3A B3x x3B A3f B3o x3V f3f o3f - (f,x)-srid
o3x o3F x3V F3F B3x V3f f3V x3B F3F V3x F3o x3o - tid
f3o f3f V3x o3B f3A B3x x3B A3f B3o x3V f3f o3f - (f,x)-srid
x3o x3f o3V f3F V3x x3V F3f V3o f3x o3x - srid
where:
F=ff=f+1, V=2f, A=f+2, B=fff
| |
| Face vector | 300, 840, 828, 258 |
| Confer |
|
The relation to ex runs as follows: ex in axial icosahedral subsymmetry can be given as VFfxo2oxofo3oooox5ooxoo&#zx = oxofofoxo3ooooxoooo5ooxoooxoo&#xt (F = ff = f+x, V = uf = f+f). That will be transformed into VFfxo2oxofo3oofox5oo(-x)oo&#zx. Then a Stott expansion wrt. the third node produces oxofofoxo3oofoxofoo5xxoxxxoxx. This polychoron then will be that diminishing therefrom, which deletes both the first and third layer from either end each.
It shall be noted that this CRF can well be dissected into 12 pecufs + 2 sridatidu. In fact, this is because sridatidu just is the around-symmetrical Stott expansion of the axial tower iku and the latter was a diminishing of ex, i.e. the latter could be adjoined with its reflection at the larger base, and that result, by filling in the according dimples with 12 pescs, then resulted still in a CRF. The same holds true here as well, provided the dimples in here get be filled by the accordingly expanded segmentochora, i.e. by 12 pecufs. (The latter become readily recognizable at the top and bottom each of the first lace city representation.)
Incidence matrix according to Dynkin symbol
xfofx3ooxoo5xxxxx&#xt → height(1,2) = height(4,5) = (1+sqrt(5))/4 = 0.809017
height(2,3) = height(3,4) = 1/2
(srid || pseudo (f,x)-srid || pseudo tid || pseudo (f,x)-srid || srid)
o....3o....5o.... & | 120 * * | 2 2 1 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 0 0 | 1 1 2 1 0 0 0
.o...3.o...5.o... & | * 120 * | 0 0 1 2 2 1 0 0 | 0 0 0 2 2 1 1 2 2 2 0 | 0 1 2 1 1 2 1
..o..3..o..5..o.. | * * 60 | 0 0 0 0 4 0 2 1 | 0 0 0 2 0 0 4 4 2 0 1 | 0 2 2 0 2 2 0
------------------------+------------+------------------------------+---------------------------------------+--------------------
x.... ..... ..... & | 2 0 0 | 120 * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0
..... ..... x.... & | 2 0 0 | * 120 * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0 0
oo...3oo...5oo...&#x & | 1 1 0 | * * 120 * * * * * | 0 0 0 2 2 0 0 0 0 0 0 | 0 1 2 1 0 0 0
..... ..... .x...&#x & | 0 2 0 | * * * 120 * * * * | 0 0 0 0 1 1 0 1 0 1 0 | 0 0 1 1 0 1 1
.oo..3.oo..5.oo..&#x & | 0 1 1 | * * * * 240 * * * | 0 0 0 1 0 0 1 1 1 0 0 | 0 1 1 0 1 1 0
.o.o.3.o.o.5.o.o.&#x | 0 2 0 | * * * * * 60 * * | 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 1 2 1
..... ..x.. ..... | 0 0 2 | * * * * * * 60 * | 0 0 0 0 0 0 2 0 0 0 1 | 0 2 0 0 1 0 0
..... ..... ..x.. | 0 0 2 | * * * * * * * 30 | 0 0 0 0 0 0 0 4 0 0 0 | 0 0 2 0 0 2 0
------------------------+------------+------------------------------+---------------------------------------+--------------------
x....3o.... ..... & | 3 0 0 | 3 0 0 0 0 0 0 0 | 40 * * * * * * * * * * | 1 1 0 0 0 0 0
x.... ..... x.... & | 4 0 0 | 2 2 0 0 0 0 0 0 | * 60 * * * * * * * * * | 1 0 1 0 0 0 0
..... o....5x.... & | 5 0 0 | 0 5 0 0 0 0 0 0 | * * 24 * * * * * * * * | 1 0 0 1 0 0 0
xfo.. ..... .....&#xt & | 2 2 1 | 1 0 2 0 2 0 0 0 | * * * 120 * * * * * * * | 0 1 1 0 0 0 0
..... ..... xx...&#x & | 2 2 0 | 0 1 2 1 0 0 0 0 | * * * * 120 * * * * * * | 0 0 1 1 0 0 0
..... .o...5.x... & | 0 5 0 | 0 0 0 5 0 0 0 0 | * * * * * 24 * * * * * | 0 0 0 1 0 0 1
..... .ox.. .....&#x & | 0 1 2 | 0 0 0 0 2 0 1 0 | * * * * * * 120 * * * * | 0 1 0 0 1 0 0
..... ..... .xx..&#x & | 0 2 2 | 0 0 0 1 2 0 0 1 | * * * * * * * 120 * * * | 0 0 1 0 0 1 0
.ooo.3.ooo.5.ooo.&#x | 0 2 1 | 0 0 0 0 2 1 0 0 | * * * * * * * * 120 * * | 0 0 0 0 1 1 0
..... ..... .x.x.&#x | 0 4 0 | 0 0 0 2 0 2 0 0 | * * * * * * * * * 60 * | 0 0 0 0 0 1 1
..o..3..x.. ..... | 0 0 3 | 0 0 0 0 0 0 3 0 | * * * * * * * * * * 20 | 0 2 0 0 0 0 0
------------------------+------------+------------------------------+---------------------------------------+--------------------
x....3o....5x.... & ♦ 60 0 0 | 60 60 0 0 0 0 0 0 | 20 30 12 0 0 0 0 0 0 0 0 | 2 * * * * * *
xfo..3oox.. .....&#xt & ♦ 3 3 3 | 3 0 3 0 6 0 3 0 | 1 0 0 3 0 0 3 0 0 0 1 | * 40 * * * * *
xfo.. ..... xxx..&#xt & ♦ 4 4 2 | 2 2 4 2 4 0 0 1 | 0 1 0 2 2 0 0 2 0 0 0 | * * 60 * * * *
..... oo...5xx...&#x & ♦ 5 5 0 | 0 5 5 5 0 0 0 0 | 0 0 1 0 5 1 0 0 0 0 0 | * * * 24 * * *
..... .oxo. .....&#x ♦ 0 2 2 | 0 0 0 0 4 1 1 0 | 0 0 0 0 0 0 2 0 2 0 0 | * * * * 60 * *
..... ..... .xxx.&#x ♦ 0 4 2 | 0 0 0 2 4 2 0 1 | 0 0 0 0 0 0 0 2 2 1 0 | * * * * * 60 *
..... .o.o.5.x.x.&#x ♦ 0 10 0 | 0 0 0 10 0 5 0 0 | 0 0 0 0 0 2 0 0 0 5 0 | * * * * * * 12
or Fxo xfo3oox5xxx&#zxt → all existing heights = 0 o.. o..3o..5o.. | 120 * * | 2 2 1 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 0 0 | 1 1 2 1 0 0 0 .o. .o.3.o.5.o. | * 120 * | 0 0 1 1 2 2 0 0 | 0 0 0 2 2 2 1 2 1 2 0 | 0 1 2 1 1 1 2 ..o ..o3..o5..o | * * 60 | 0 0 0 0 0 4 2 1 | 0 0 0 2 0 0 0 2 4 4 1 | 0 2 2 0 0 2 2 --------------------+------------+------------------------------+---------------------------------------+-------------------- ... x.. ... ... | 2 0 0 | 120 * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 ... ... ... x.. | 2 0 0 | * 120 * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0 0 oo. oo.3oo.5oo.&#x | 1 1 0 | * * 120 * * * * * | 0 0 0 2 2 0 0 0 0 0 0 | 0 1 2 1 0 0 0 .x. ... ... ... | 0 2 0 | * * * 60 * * * * | 0 0 0 0 0 2 0 2 0 0 0 | 0 0 0 0 1 1 2 ... ... ... .x. | 0 2 0 | * * * * 120 * * * | 0 0 0 0 1 1 1 0 0 1 0 | 0 0 1 1 1 0 1 .oo .oo3.oo5.oo&#x | 0 1 1 | * * * * * 240 * * | 0 0 0 1 0 0 0 1 1 1 0 | 0 1 1 0 0 1 1 ... ... ..x ... | 0 0 2 | * * * * * * 60 * | 0 0 0 0 0 0 0 0 2 0 1 | 0 2 0 0 0 1 0 ... ... ... ..x | 0 0 2 | * * * * * * * 30 | 0 0 0 0 0 0 0 0 0 4 0 | 0 0 2 0 0 0 2 --------------------+------------+------------------------------+---------------------------------------+-------------------- ... x..3o.. ... | 3 0 0 | 3 0 0 0 0 0 0 0 | 40 * * * * * * * * * * | 1 1 0 0 0 0 0 ... x.. ... x.. | 4 0 0 | 2 2 0 0 0 0 0 0 | * 60 * * * * * * * * * | 1 0 1 0 0 0 0 ... ... o..5x.. | 5 0 0 | 0 5 0 0 0 0 0 0 | * * 24 * * * * * * * * | 1 0 0 1 0 0 0 ... xfo ... ...&#xt | 2 2 1 | 1 0 2 0 0 2 0 0 | * * * 120 * * * * * * * | 0 1 1 0 0 0 0 ... ... ... xx.&#x | 2 2 0 | 0 1 2 0 1 0 0 0 | * * * * 120 * * * * * * | 0 0 1 1 0 0 0 .x. ... ... .x. | 0 4 0 | 0 0 0 2 2 0 0 0 | * * * * * 60 * * * * * | 0 0 0 0 1 0 1 ... ... .o.5.x. | 0 5 0 | 0 0 0 0 5 0 0 0 | * * * * * * 24 * * * * | 0 0 0 1 1 0 0 .xo ... ... ...&#x | 0 2 1 | 0 0 0 1 0 2 0 0 | * * * * * * * 120 * * * | 0 0 0 0 0 1 1 ... ... .ox ...&#x | 0 1 2 | 0 0 0 0 0 2 1 0 | * * * * * * * * 120 * * | 0 1 0 0 0 1 0 ... ... ... .xx&#x | 0 2 2 | 0 0 0 0 1 2 0 1 | * * * * * * * * * 120 * | 0 0 1 0 0 0 1 ... ..o3..x ... | 0 0 3 | 0 0 0 0 0 0 3 0 | * * * * * * * * * * 20 | 0 2 0 0 0 0 0 --------------------+------------+------------------------------+---------------------------------------+-------------------- ... x..3o..5x.. ♦ 60 0 0 | 60 60 0 0 0 0 0 0 | 20 30 12 0 0 0 0 0 0 0 0 | 2 * * * * * * ... xfo3oox ...&#xt ♦ 3 3 3 | 3 0 3 0 0 6 3 0 | 1 0 0 3 0 0 0 0 3 0 1 | * 40 * * * * * ... xfo ... xxx&#xt ♦ 4 4 2 | 2 2 4 0 2 4 0 1 | 0 1 0 2 2 0 0 0 0 2 0 | * * 60 * * * * ... ... oo.5xx.&#x ♦ 5 5 0 | 0 5 5 0 5 0 0 0 | 0 0 1 0 5 0 1 0 0 0 0 | * * * 24 * * * .x. ... .o.5.x. ♦ 0 10 0 | 0 0 0 5 10 0 0 0 | 0 0 0 0 0 5 2 0 0 0 0 | * * * * 12 * * .xo ... .ox ...&#x ♦ 0 2 2 | 0 0 0 1 0 4 1 0 | 0 0 0 0 0 0 0 2 2 0 0 | * * * * * 60 * .xo ... ... .xx&#x ♦ 0 4 2 | 0 0 0 2 2 4 0 1 | 0 0 0 0 0 1 0 2 0 2 0 | * * * * * * 60
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