Acronym | ... |
Name |
triacontapenta-diminished hexacosachoron, fooo5ofxo xofx5oxox&#zx |
Circumradius | (1+sqrt(5))/2 = 1.618034 |
Lace city in approx. ASCII-art |
o5o o5o o5x D C o5o o5o f5o o5f A o5f B o5x o5x f5o f5o o5o o5o o5f o5f f5o f5o o5f o5o o5o o5x o5x o5o o5o |
x5o A o5x o5x B f5o f5o C x5o x5o x5x D f5o f5o o5x o5x f5o x5o x5o o5x | |
Face vector | 85, 335, 360, 110 |
Confer |
|
This orbiform CRF polychoron can be derived as a triacontapenta-diminishing of ex: In fact ex wrt. its pedipic subsymmetry I2(5)×I2(5) is given as xfooxo5xofxoo oxofox5ooxofx&#zx. While gap was derived therefrom by deleting the first and last layer this one is obtained by deleting the first and the fifth layer instead. Thus, depending on the chosen respective projection, there are 2 different according lace cities here.
Note that the deletion of first and fourth layer would result in the same figure. And that the deletion of the first and second and (alike again) the first and third layer would result in non-CRF polychora. Thence the naming as the triacontapenta-diminished hexacosachoron seems to be appropriate.
A diminishing in solely the fifth layer would result in xfooo5xofxo oxofx5ooxox&#zx.
This polychoron also allows for a Stott expansion wrt. the first node, then resulting in Fxxx5ofxo xofx5oxox&#zx.
Incidence matrix according to Dynkin symbol
fooo5ofxo xofx5oxox&#zx → height = 0 o...5o... o...5o... | 25 * * * | 2 4 2 0 0 0 0 0 0 | 1 4 2 4 1 0 0 0 0 0 | 2 2 2 0 A .o..5.o.. .o..5.o.. | * 25 * * | 0 4 0 2 2 0 0 0 0 | 0 2 4 4 0 1 2 1 0 0 | 2 4 2 0 B ..o.5..o. ..o.5..o. | * * 25 * | 0 0 2 0 2 2 2 0 0 | 0 0 0 4 2 0 1 2 4 1 | 0 2 4 2 C ...o5...o ...o5...o | * * * 10 | 0 0 0 0 0 0 5 1 1 | 0 0 0 0 0 0 0 5 5 5 | 0 0 5 5 D ------------------------+-------------+---------------------------+------------------------------+------------ .... .... x... .... | 2 0 0 0 | 25 * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 | 2 0 1 0 oo..5oo.. oo..5oo..&#x | 1 1 0 0 | * 100 * * * * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 o.o.5o.o. o.o.5o.o.&#x | 1 0 1 0 | * * 50 * * * * * * | 0 0 0 2 1 0 0 0 0 0 | 0 1 2 0 .... .... .... .x.. | 0 2 0 0 | * * * 25 * * * * * | 0 0 2 0 0 1 1 0 0 0 | 2 2 0 0 .oo.5.oo. .oo.5.oo.&#x | 0 1 1 0 | * * * * 50 * * * * | 0 0 0 2 0 0 1 1 0 0 | 0 2 2 0 .... ..x. .... .... | 0 0 2 0 | * * * * * 25 * * * | 0 0 0 0 1 0 0 0 2 0 | 0 0 2 1 ..oo5..oo ..oo5..oo&#x | 0 0 1 1 | * * * * * * 50 * * | 0 0 0 0 0 0 0 1 2 1 | 0 0 2 2 .... .... ...x .... | 0 0 0 2 | * * * * * * * 5 * | 0 0 0 0 0 0 0 5 0 0 | 0 0 5 0 .... .... .... ...x | 0 0 0 2 | * * * * * * * * 5 | 0 0 0 0 0 0 0 0 0 5 | 0 0 0 5 ------------------------+-------------+---------------------------+------------------------------+------------ .... .... x...5o... | 5 0 0 0 | 5 0 0 0 0 0 0 0 0 | 5 * * * * * * * * * | 2 0 0 0 .... .... xo.. ....&#x | 2 1 0 0 | 1 2 0 0 0 0 0 0 0 | * 50 * * * * * * * * | 1 0 1 0 .... .... .... ox..&#x | 1 2 0 0 | 0 2 0 1 0 0 0 0 0 | * * 50 * * * * * * * | 1 1 0 0 ooo.5ooo. ooo.5ooo.&#x | 1 1 1 0 | 0 1 1 0 1 0 0 0 0 | * * * 100 * * * * * * | 0 1 1 0 .... o.x. .... ....&#x | 1 0 2 0 | 0 0 2 0 0 1 0 0 0 | * * * * 25 * * * * * | 0 0 2 0 .... .... .o..5.x.. | 0 5 0 0 | 0 0 0 5 0 0 0 0 0 | * * * * * 5 * * * * | 2 0 0 0 .... .... .... .xo.&#x | 0 2 1 0 | 0 0 0 1 2 0 0 0 0 | * * * * * * 25 * * * | 0 2 0 0 .... .... .ofx ....&#xt | 0 1 2 2 | 0 0 0 0 2 0 2 1 0 | * * * * * * * 25 * * | 0 0 2 0 .... ..xo .... ....&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 0 | * * * * * * * * 50 * | 0 0 1 1 .... .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 2 0 1 | * * * * * * * * * 25 | 0 0 0 2 ------------------------+-------------+---------------------------+------------------------------+------------ .... .... xo..5ox..&#x ♦ 5 5 0 0 | 5 10 0 5 0 0 0 0 0 | 1 5 5 0 0 1 0 0 0 0 | 10 * * * .... .... .... oxo.&#x ♦ 1 2 1 0 | 0 2 1 1 2 0 0 0 0 | 0 0 1 2 0 0 1 0 0 0 | * 50 * * .... ofxo xofx ....&#xt ♦ 2 2 4 2 | 1 4 4 0 4 2 4 1 0 | 0 2 0 4 2 0 0 2 2 0 | * * 25 * .... ..xo .... ..ox&#x ♦ 0 0 2 2 | 0 0 0 0 0 1 4 0 1 | 0 0 0 0 0 0 0 0 2 2 | * * * 25
© 2004-2024 | top of page |