Acronym | telex |
Name | vertex first tele-elongated hexacosachoron |
Lace city in approx. ASCII-art |
o2o o2o o2x x2f f2o x2f o2x x2o f2f F2x o2F F2x f2f x2o o2f F2o f2F f2F F2o o2f o2o f2x x2F Vo2oV F2f Vo2oV x2F f2x o2o o2f F2o f2F f2F F2o o2f x2o f2f F2x o2F F2x f2f x2o o2x x2f f2o x2f o2x o2o o2o |
x2o x2x F2o o2f F2o x2x where B = 2f+x = fff o2o F2f x2F A2x x2F F2f o2o A = f+2x V = 2f x2f A2o F2F A2o x2f F = f+x = ff x2o F2x o2F A2f Bx2oV A2f o2F F2x x2o x2f A2o F2F A2o x2f o2o F2f x2F A2x x2F F2f o2o x2x F2o o2f F2o x2x x2o | |
Face vector | 138, 654, 800, 284 |
Confer |
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This polychoron is obtained from ex = oxofofoxo-3-ooooxoooo-5-ooxoooxoo-&#xt = VFfxo-2-oxofo-3-oooox-5-ooxoo-&#zx. There an edge flip is applied to the first node of the 4th layer, providing the vertex coincident faceting VFf(-x)o-2-oxofo-3-oooox-5-ooxoo-&#zx. Then a partial (here: axial) Stott expansion wrt. the first node each yields this polychoron: BAFox-2-oxofo-3-oooox-5-ooxoo-&#zx = oxoofooxo-3-oooxoxooo-5-ooxoooxoo-&#xt. (B = 2f+x = fff, A = f+2x, V = 2f, F = f+x = ff)
In fact, the upper lace city picture displays what is being done here. One starts with the lace city of ex. But instead of a normal elongation, i.e cutting ex into 2 halves and putting prisms in between, here kind a telescopical elongation (tele-elongation for short) is being applied. The layers, neighbouring to the equatorial one, each remain attached to the opposite half! The pull then is applied until those formerly different layers become coincident. This is what is meant by first getting some edges (x) inversed ((-x)): asignment to the opposite half, and then applying the Stott expansion to that. Here the operation "x +" results in x + (-x) = o. Tele-elongation therefore is nothing but the axial subcase of the more general kaleido expansion (cf. expanded kaleido-facetings).
This polychoron not only allows several interesting diminishings according to the below provided vertex figures with sections being ike, gyepip, teddi, or pip. The uppermost edge of the displayed lace cities too can be chopped off completely, then providing a bilbiro section. In fact, that cutted off first segment is nothing but the bilbiro wedge.
Incidence matrix according to Dynkin symbol
oxoofooxo3oooxoxooo5ooxoooxoo&#xt → height(1,2) = height(8,9) = (sqrt(5)-1)/4 = 0.309017 height(2,3) = height(4,5) = height(5,6) = height(7,8) = 1/2 height(3,4) = height(6,7) = (1+sqrt(5))/4 = 0.809017 (pt || pseudo ike || pseudo doe || pseudo id || pseudo f-ike || pseudo id || pseudo doe || pseudo ike || pt) o........3o........5o........ & | 2 * * * * ♦ 12 0 0 0 0 0 0 0 | 30 0 0 0 0 0 0 0 0 0 | 20 0 0 0 0 0 0 .o.......3.o.......5.o....... & | * 24 * * * ♦ 1 5 5 0 0 0 0 0 | 5 5 10 5 0 0 0 0 0 0 | 5 5 5 1 0 0 0 ..o......3..o......5..o...... & | * * 40 * * ♦ 0 0 3 3 3 0 0 0 | 0 0 3 6 3 3 0 0 0 0 | 0 1 3 3 1 0 0 ...o.....3...o.....5...o..... & | * * * 60 * | 0 0 0 0 2 4 2 1 | 0 0 0 0 4 1 2 4 4 2 | 0 0 0 2 2 2 4 ....o....3....o....5....o.... | * * * * 12 ♦ 0 0 0 0 0 0 10 0 | 0 0 0 0 0 0 0 10 0 5 | 0 0 0 2 0 0 5 ------------------------------------+---------------+-----------------------------+-----------------------------------+--------------------- oo.......3oo.......5oo.......&#x & | 1 1 0 0 0 | 24 * * * * * * * | 5 0 0 0 0 0 0 0 0 0 | 5 0 0 0 0 0 0 .x....... ......... ......... & | 0 2 0 0 0 | * 60 * * * * * * | 1 2 2 0 0 0 0 0 0 0 | 2 2 1 0 0 0 0 .oo......3.oo......5.oo......&#x & | 0 1 1 0 0 | * * 120 * * * * * | 0 0 2 2 0 0 0 0 0 0 | 0 1 2 1 0 0 0 ......... ......... ..x...... & | 0 0 2 0 0 | * * * 60 * * * * | 0 0 0 2 0 1 0 0 0 0 | 0 0 1 2 0 0 0 ..oo.....3..oo.....5..oo.....&#x & | 0 0 1 1 0 | * * * * 120 * * * | 0 0 0 0 2 1 0 0 0 0 | 0 0 0 2 1 0 0 ......... ...x..... ......... & | 0 0 0 2 0 | * * * * * 120 * * | 0 0 0 0 1 0 1 1 1 0 | 0 0 0 1 1 1 1 ...oo....3...oo....5...oo....&#x & | 0 0 0 1 1 | * * * * * * 120 * | 0 0 0 0 0 0 0 2 0 1 | 0 0 0 1 0 0 2 ...o.o...3...o.o...5...o.o...&#x | 0 0 0 2 0 | * * * * * * * 30 | 0 0 0 0 0 0 0 0 4 2 | 0 0 0 0 0 2 4 ------------------------------------+---------------+-----------------------------+-----------------------------------+--------------------- ox....... ......... .........&#x & | 1 2 0 0 0 | 2 1 0 0 0 0 0 0 | 60 * * * * * * * * * | 2 0 0 0 0 0 0 .x.......3.o....... ......... & | 0 3 0 0 0 | 0 3 0 0 0 0 0 0 | * 40 * * * * * * * * | 1 1 0 0 0 0 0 .xo...... ......... .........&#x & | 0 2 1 0 0 | 0 1 2 0 0 0 0 0 | * * 120 * * * * * * * | 0 1 1 0 0 0 0 ......... ......... .ox......&#x & | 0 1 2 0 0 | 0 0 2 1 0 0 0 0 | * * * 120 * * * * * * | 0 0 1 1 0 0 0 ......... ..ox..... .........&#x & | 0 0 1 2 0 | 0 0 0 0 2 1 0 0 | * * * * 120 * * * * * | 0 0 0 1 1 0 0 ......... ......... ..xo.....&#x & | 0 0 2 1 0 | 0 0 0 1 2 0 0 0 | * * * * * 60 * * * * | 0 0 0 2 0 0 0 ...o.....3...x..... ......... & | 0 0 0 3 0 | 0 0 0 0 0 3 0 0 | * * * * * * 40 * * * | 0 0 0 0 1 1 0 ......... ...xo.... .........&#x & | 0 0 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * 120 * * | 0 0 0 1 0 0 1 ......... ...x.x... .........&#x | 0 0 0 4 0 | 0 0 0 0 0 2 0 2 | * * * * * * * * 60 * | 0 0 0 0 0 1 1 ...ooo...3...ooo...5...ooo...&#x | 0 0 0 2 1 | 0 0 0 0 0 0 2 1 | * * * * * * * * * 60 | 0 0 0 0 0 0 2 ------------------------------------+---------------+-----------------------------+-----------------------------------+--------------------- ox.......3oo....... .........&#x & ♦ 1 3 0 0 0 | 3 3 0 0 0 0 0 0 | 3 1 0 0 0 0 0 0 0 0 | 40 * * * * * * .xo......3.oo...... .........&#x & ♦ 0 3 1 0 0 | 0 3 3 0 0 0 0 0 | 0 1 3 0 0 0 0 0 0 0 | * 40 * * * * * .xo...... ......... .ox......&#x & ♦ 0 2 2 0 0 | 0 1 4 1 0 0 0 0 | 0 0 2 2 0 0 0 0 0 0 | * * 60 * * * * ......... .ooxo....5.oxoo....&#x & ♦ 0 1 5 5 1 | 0 0 5 5 10 5 5 0 | 0 0 0 5 5 5 0 5 0 0 | * * * 24 * * * ..oo.....3..ox..... .........&#x & ♦ 0 0 1 3 0 | 0 0 0 0 3 3 0 0 | 0 0 0 0 3 0 1 0 0 0 | * * * * 40 * * ...o.o...3...x.x... .........&#x ♦ 0 0 0 6 0 | 0 0 0 0 0 6 0 3 | 0 0 0 0 0 0 2 0 3 0 | * * * * * 20 * ......... ...xox... .........&#x ♦ 0 0 0 4 1 | 0 0 0 0 0 2 4 2 | 0 0 0 0 0 0 0 2 1 2 | * * * * * * 60
xxxoooFFFAAABxxxF FxfoFfxFofxooVoof xfFFfoFoxxofooVof fFxfoFoxFofxoooVf&#zx → all existing heights = 0 o................ o................ o................ o................ | 16 * * * * * * * * * * * * * * * * | 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .o............... .o............... .o............... .o............... | * 16 * * * * * * * * * * * * * * * | 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ..o.............. ..o.............. ..o.............. ..o.............. | * * 16 * * * * * * * * * * * * * * | 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...o............. ...o............. ...o............. ...o............. | * * * 4 * * * * * * * * * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 2 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ....o............ ....o............ ....o............ ....o............ | * * * * 4 * * * * * * * * * * * * ♦ 0 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1 2 2 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 2 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 .........o....... .........o....... .........o....... .........o....... | * * * * * * * * * 8 * * * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 2 2 1 2 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 2 1 2 2 0 0 0 0 0 0 0 0 2 2 2 2 1 2 2 1 0 0 0 0 0 | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1 2 2 0 0 0 2 2 2 1 0 ..........o...... ..........o...... ..........o...... ..........o...... | * * * * * * * * * * 8 * * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 2 0 0 0 1 2 1 2 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 1 2 2 0 0 1 2 2 2 0 0 0 0 2 2 2 1 0 | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 2 2 1 2 2 0 2 ...........o..... ...........o..... ...........o..... ...........o..... | * * * * * * * * * * * 8 * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 2 0 0 1 1 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 2 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 0 0 2 2 2 0 1 2 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 1 2 0 2 2 2 1 ............o.... ............o.... ............o.... ............o.... | * * * * * * * * * * * * 2 * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 0 4 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 8 0 2 0 8 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 8 0 4 4 .............o... .............o... .............o... .............o... | * * * * * * * * * * * * * 4 * * * | 0 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----------------------------------------------------------------------------+---------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------- x................ ................. ................. ................. | 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ................. ................. 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