| Acronym | ... |
| Name | dodeca-diminished equatorial tetrastratic segment of rox |
| Circumradius | sqrt[5+2 sqrt(5)] = 3.077684 |
|
Lace city in approx. ASCII-art |
x5o x5o
o5f
x5x x5x
x5f F=ff=x+f=2x+v,
F5o F5o V=F+v=2f=2x+2v,
o5F o5F A=F+x=3x+v
f5f f5f
o5V o5V
x5F
F5x F5x
x5F x5F
oA5Ao
F5x F5x
x5F x5F
F5x
V5o V5o
f5f f5f
F5o F5o
o5F o5F
f5x
x5x x5x
f5o
o5x o5x
|
o3x o3F x3V F3F B3x V3F F3V x3B F3F V3x F3o x3o
f3x F3f B3o x3B fC3Bo Bo3fC B3x o3B f3F x3f
F=ff=x+f=2x+v,
V=F+v=2f=2x+2v,
x3o x3F o3B A3f F3V B3f f3B V3F f3A B3o F3x o3x A=F+x=3x+v,
B=fff=A+v=3x+2v,
C=B+x=4x+2v=2F
f3x F3f B3o x3B fC3Bo Bo3fC B3x o3B f3F x3f
o3x o3F x3V F3F B3x V3F F3V x3B F3F V3x F3o x3o
| |
| Face vector | 300, 1140, 1128, 288 |
| Confer |
By means of either the pair of segmentochora idati and tiatid or alternatively the bistratic id-cap of rahi this polychoron can independantly continued on either side, then resulting in oo|ofxfo|oo-3-xo|xxoxx|ox-5-of|xofox|fo-&#xt, ox|ofxfo|xo-3-xx|xxoxx|xx-5-oo|xofox|oo-&#xt, or ox|ofxfo|oo-3-xx|xxoxx|ox-5-oo|xofox|fo-&#xt. All 3 in turn are different EKFs derived from ex.
The relation to rox runs as follows: that one in ike-first axial orientation can be given as DCBAVFfxoo-2-xoxFofofVx-3-oxoofoxxoo-5-ooxooxxoof-&#zx or xoxFofof(Vx)fofoFxox-3-oxoofoxx(oo)xxofooxo-5-ooxooxxo(of)oxxooxoo-&#xt. When applying a hexastratic diminishing on either side, i.e. removing xoxFofo-3-oxoofox-5-ooxooxx-&#xt on either side, one results with the equatorial tetrastratic segment of(Vx)fo-3-xx(oo)xx-5-xo(of)ox-&#xt. This polychoron then is the dodecadiminishing therefrom, deleting the vertex set of an inscribed V-scaled ike.
Incidence matrix according to Dynkin symbol
fxo ofx3xxo5xof&#zx → all heights = 0 o.. o..3o..5o.. | 120 * * | 2 1 2 2 0 0 0 0 | 1 2 2 2 1 2 2 0 0 0 0 0 | 1 2 1 1 2 0 0 .o. .o.3.o.5.o. | * 120 * | 0 0 2 0 2 2 1 0 | 0 0 2 1 0 0 2 1 2 2 2 0 | 0 1 0 1 2 1 2 ..o ..o3..o5..o | * * 60 | 0 0 0 4 0 4 0 2 | 0 0 0 0 4 2 4 0 0 2 2 1 | 0 0 2 2 2 0 1 --------------------+------------+------------------------------+--------------------------------------------+--------------------- ... ... x.. ... | 2 0 0 | 120 * * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 0 | 1 1 1 0 1 0 0 ... ... ... x.. | 2 0 0 | * 60 * * * * * * | 0 2 0 2 0 0 0 0 0 0 0 0 | 1 2 0 1 0 0 0 oo. oo.3oo.5oo.&#x | 1 1 0 | * * 240 * * * * * | 0 0 1 1 0 0 1 0 0 0 0 0 | 0 1 0 1 1 0 0 o.o o.o3o.o5o.o&#x | 1 0 1 | * * * 240 * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 1 1 1 0 0 ... ... .x. ... | 0 2 0 | * * * * 120 * * * | 0 0 1 0 0 0 0 1 1 0 1 0 | 0 1 0 0 1 1 1 .oo .oo3.oo5.oo&#x | 0 1 1 | * * * * * 240 * * | 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 1 0 1 .x. ... ... ... | 0 2 0 | * * * * * * 60 * | 0 0 0 0 0 0 0 0 2 2 0 0 | 0 0 0 1 0 1 2 ... ..x .. .. | 0 0 2 | * * * * * * * 60 | 0 0 0 0 2 0 0 0 0 0 0 1 | 0 0 2 1 0 0 0 --------------------+------------+------------------------------+--------------------------------------------+--------------------- ... o..3x.. ... | 3 0 0 | 3 0 0 0 0 0 0 0 | 40 * * * * * * * * * * * | 1 0 1 0 0 0 0 ... ... x..5x.. | 10 0 0 | 5 5 0 0 0 0 0 0 | * 24 * * * * * * * * * * | 1 1 0 0 0 0 0 ... ... xx. ...&#x | 2 2 0 | 1 0 2 0 1 0 0 0 | * * 120 * * * * * * * * * | 0 1 0 0 1 0 0 ... ... ... xo.&#x | 2 1 0 | 0 1 2 0 0 0 0 0 | * * * 120 * * * * * * * * | 0 1 0 1 0 0 0 ... o.x ... ...&#x | 1 0 2 | 0 0 0 2 0 0 0 1 | * * * * 120 * * * * * * * | 0 0 1 1 0 0 0 ... ... x.o ...&#x | 2 0 1 | 1 0 0 2 0 0 0 0 | * * * * * 120 * * * * * * | 0 0 1 0 1 0 0 ooo ooo3ooo5ooo&#x | 1 1 1 | 0 0 1 1 0 1 0 0 | * * * * * * 240 * * * * * | 0 0 0 1 1 0 0 ... ... .x.5.o. | 0 5 0 | 0 0 0 0 5 0 0 0 | * * * * * * * 24 * * * * | 0 1 0 0 0 1 0 .x. ... .x. ... | 0 4 0 | 0 0 0 0 2 0 2 0 | * * * * * * * * 60 * * * | 0 0 0 0 0 1 1 .xo ... ... ...&#x | 0 2 1 | 0 0 0 0 0 2 1 0 | * * * * * * * * * 120 * * | 0 0 0 1 0 0 1 ... ... .xo ...&#x | 0 2 1 | 0 0 0 0 1 2 0 0 | * * * * * * * * * * 120 * | 0 0 0 0 1 0 1 ... ..x3..o ... | 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * * 20 | 0 0 2 0 0 0 0 --------------------+------------+------------------------------+--------------------------------------------+--------------------- ... o..3x..5x.. ♦ 60 0 0 | 60 30 0 0 0 0 0 0 | 20 12 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * ... ... xx.5xo.&#x ♦ 10 5 0 | 5 5 10 0 5 0 0 0 | 0 1 5 5 0 0 0 1 0 0 0 0 | * 24 * * * * * ... o.x3x.o ...&#x ♦ 3 0 3 | 3 0 0 6 0 0 0 3 | 1 0 0 0 3 3 0 0 0 0 0 1 | * * 40 * * * * fxo ofx ... xof&#zx ♦ 4 4 4 | 0 2 8 8 0 8 2 2 | 0 0 0 4 4 0 8 0 0 4 0 0 | * * * 30 * * * ... ... xxo ...&#x ♦ 2 2 1 | 1 0 2 2 1 2 0 0 | 0 0 1 0 0 1 2 0 0 0 1 0 | * * * * 120 * * .x. ... .x.5.o. ♦ 0 10 0 | 0 0 0 0 10 0 5 0 | 0 0 0 0 0 0 0 2 5 0 0 0 | * * * * * 12 * .xo ... .xo ...&#x ♦ 0 4 1 | 0 0 0 0 2 4 2 0 | 0 0 0 0 0 0 0 0 1 2 2 0 | * * * * * * 60
ofxfo3xxoxx5xofox&#xt → outer heights = (sqrt(5)-1)/4 = 0.309017
inner heights = 1/2
(tid || pseudo (f,x)-ti || pseudo (x,f)-srid || pseudo (f,x)-ti || tid)
o....3o....5o.... & | 120 * * | 2 1 2 2 0 0 0 0 | 1 2 2 2 1 2 2 0 0 0 0 0 | 1 2 1 1 2 0 0
.o...3.o...5.o... & | * 120 * | 0 0 2 0 2 2 1 0 | 0 0 2 1 0 0 2 1 2 2 2 0 | 0 1 0 1 2 1 2
..o..3..o..5..o.. | * * 60 | 0 0 0 4 0 4 0 2 | 0 0 0 0 4 2 4 0 2 0 2 1 | 0 0 2 2 2 0 1
------------------------+------------+------------------------------+--------------------------------------------+---------------------
..... x.... ..... & | 2 0 0 | 120 * * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 0 | 1 1 1 0 1 0 0
..... ..... x.... & | 2 0 0 | * 60 * * * * * * | 0 2 0 2 0 0 0 0 0 0 0 0 | 1 2 0 1 0 0 0
oo...3oo...5oo...&#x & | 1 1 0 | * * 240 * * * * * | 0 0 1 1 0 0 1 0 0 0 0 0 | 0 1 0 1 1 0 0
o.o..3o.o..5o.o..&#x & | 1 0 1 | * * * 240 * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 1 1 1 0 0
..... .x... ..... & | 0 2 0 | * * * * 120 * * * | 0 0 1 0 0 0 0 1 1 1 0 0 | 0 1 0 0 1 1 1
.oo..3.oo..5.oo..&#x & | 0 1 1 | * * * * * 240 * * | 0 0 0 0 0 0 1 0 1 0 1 0 | 0 0 0 1 1 0 1
.o.o.3.o.o.5.o.o.&#x | 0 2 0 | * * * * * * 60 * | 0 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 1 0 1 2
..x.. ..... ..... | 0 0 2 | * * * * * * * 60 | 0 0 0 0 2 0 0 0 0 0 0 1 | 0 0 2 1 0 0 0
------------------------+------------+------------------------------+--------------------------------------------+---------------------
o....3x.... ..... & | 3 0 0 | 3 0 0 0 0 0 0 0 | 40 * * * * * * * * * * * | 1 0 1 0 0 0 0
..... x....5x.... & | 10 0 0 | 5 5 0 0 0 0 0 0 | * 24 * * * * * * * * * * | 1 1 0 0 0 0 0
..... xx... .....&#x & | 2 2 0 | 1 0 2 0 1 0 0 0 | * * 120 * * * * * * * * * | 0 1 0 0 1 0 0
..... ..... xo...&#x & | 2 1 0 | 0 1 2 0 0 0 0 0 | * * * 120 * * * * * * * * | 0 1 0 1 0 0 0
o.x.. ..... .....&#x & | 1 0 2 | 0 0 0 2 0 0 0 1 | * * * * 120 * * * * * * * | 0 0 1 1 0 0 0
..... x.o.. .....&#x & | 2 0 1 | 1 0 0 2 0 0 0 0 | * * * * * 120 * * * * * * | 0 0 1 0 1 0 0
ooo..3ooo..5ooo..&#x & | 1 1 1 | 0 0 1 1 0 1 0 0 | * * * * * * 240 * * * * * | 0 0 0 1 1 0 0
..... .x...5.o... & | 0 5 0 | 0 0 0 0 5 0 0 0 | * * * * * * * 24 * * * * | 0 1 0 0 0 1 0
..... .xo.. .....&#x & | 0 2 1 | 0 0 0 0 1 2 0 0 | * * * * * * * * 120 * * * | 0 0 0 0 1 0 1
..... .x.x. .....&#x | 0 4 0 | 0 0 0 0 2 0 2 0 | * * * * * * * * * 60 * * | 0 0 0 0 0 1 1
.ooo.3.ooo.5.ooo.&#x | 0 2 1 | 0 0 0 0 0 2 1 0 | * * * * * * * * * * 120 * | 0 0 0 1 0 0 1
..x..3..o.. ..... | 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * * * 20 | 0 0 2 0 0 0 0
------------------------+------------+------------------------------+--------------------------------------------+---------------------
o....3x....5x.... & ♦ 60 0 0 | 60 30 0 0 0 0 0 0 | 20 12 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * *
..... xx...5xo...&#xt & ♦ 10 5 0 | 5 5 10 0 5 0 0 0 | 0 1 5 5 0 0 0 1 0 0 0 0 | * 24 * * * * *
o.x..3x.o.. .....&#x & ♦ 3 0 3 | 3 0 0 6 0 0 0 3 | 1 0 0 0 3 3 0 0 0 0 0 1 | * * 40 * * * *
ofxfo ..... xofox&#xt ♦ 4 4 4 | 0 2 8 8 0 8 2 2 | 0 0 0 4 4 0 8 0 0 0 4 0 | * * * 30 * * *
..... xxo.. .....&#x & ♦ 2 2 1 | 1 0 2 2 1 2 0 0 | 0 0 1 0 0 1 2 0 1 0 0 0 | * * * * 120 * *
..... .x.x.5.o.o.&#x ♦ 0 10 0 | 0 0 0 0 10 0 5 0 | 0 0 0 0 0 0 0 2 0 5 0 0 | * * * * * 12 *
..... .xox. .....&#x ♦ 0 4 1 | 0 0 0 0 2 4 2 0 | 0 0 0 0 0 0 0 0 2 1 2 0 | * * * * * * 60
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