Acronym | ... |
Name | outer pentadiminished 2/10-luna of hexacosachoron |
Circumradius | (1+sqrt(5))/2 = 1.618034 |
Lace city in approx. ASCII-art |
o5o o5x o5o f5o o5f o5x f5o x5x |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles |
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Face vector | 37, 116, 113, 34 |
Confer |
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The special edge with 5 incident mibdies of this polychoron (each being adjoined with their special wedge edge) also allows for a 3-fold counterpart: xfox2oxfo3ooox&#xt. (A 4-fold version does not exist, so.)
This polychoron happens to be just a diminishing of 2/10-luna of ex. In fact, the latter one is re-obtained when augmenting the mibdies by according pyramids.
Incidence matrix according to Dynkin symbol
xfoxo oxfox5ooofx&#xt → height(1,2) = sqrt[(5+sqrt(5))/40] = 0.425325 height(2,3) = sqrt[(5-sqrt(5))/40] = 0.262866 height(3,4) = sqrt[(5-2 sqrt(5))/20] = 0.162460 height(4,5) = sqrt[(5+2 sqrt(5))/20] = 0.688191 o.... o....5o.... | 2 * * * * | 1 5 0 0 0 0 0 0 0 0 0 | 5 5 0 0 0 0 0 0 0 0 0 0 | 5 1 0 0 0 0 .o... .o...5.o... | * 10 * * * | 0 1 2 1 2 0 0 0 0 0 0 | 1 2 1 2 1 2 0 0 0 0 0 0 | 2 1 1 1 0 0 ..o.. ..o..5..o.. | * * 5 * * | 0 0 0 2 0 4 2 0 0 0 0 | 1 0 0 0 0 4 2 4 1 0 0 0 | 2 0 0 2 2 0 ...o. ...o.5...o. | * * * 10 * | 0 0 0 0 2 2 0 1 2 0 0 | 0 0 0 1 2 2 2 2 0 2 1 0 | 1 0 1 2 2 1 ....o ....o5....o | * * * * 10 | 0 0 0 0 0 0 1 0 2 1 1 | 0 0 0 0 2 0 0 2 1 1 2 1 | 0 0 2 2 1 1 ----------------------+--------------+------------------------------+---------------------------------+-------------- x.... ..... ..... | 2 0 0 0 0 | 1 * * * * * * * * * * | 5 0 0 0 0 0 0 0 0 0 0 0 | 5 0 0 0 0 0 oo... oo...5oo...&#x | 1 1 0 0 0 | * 10 * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 0 0 | 2 1 0 0 0 0 ..... .x... ..... | 0 2 0 0 0 | * * 10 * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 .oo.. .oo..5.oo..&#x | 0 1 1 0 0 | * * * 10 * * * * * * * | 1 0 0 0 0 2 0 0 0 0 0 0 | 2 0 0 1 0 0 .o.o. .o.o.5.o.o.&#x | 0 1 0 1 0 | * * * * 20 * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 | 1 0 1 1 0 0 ..oo. ..oo.5..oo.&#x | 0 0 1 1 0 | * * * * * 20 * * * * * | 0 0 0 0 0 1 1 1 0 0 0 0 | 1 0 0 1 1 0 ..o.o ..o.o5..o.o&#x | 0 0 1 0 1 | * * * * * * 10 * * * * | 0 0 0 0 0 0 0 2 1 0 0 0 | 0 0 0 2 1 0 ...x. ..... ..... | 0 0 0 2 0 | * * * * * * * 5 * * * | 0 0 0 0 0 0 2 0 0 2 0 0 | 1 0 0 0 2 1 ...oo ...oo5...oo&#x | 0 0 0 1 1 | * * * * * * * * 20 * * | 0 0 0 0 1 0 0 1 0 1 1 0 | 0 0 1 1 1 1 ..... ....x ..... | 0 0 0 0 2 | * * * * * * * * * 5 * | 0 0 0 0 0 0 0 0 0 0 2 1 | 0 0 2 0 0 1 ..... ..... ....x | 0 0 0 0 2 | * * * * * * * * * * 5 | 0 0 0 0 2 0 0 0 1 0 0 1 | 0 0 2 2 0 0 ----------------------+--------------+------------------------------+---------------------------------+-------------- xfo.. ..... .....&#xt | 2 2 1 0 0 | 1 2 0 2 0 0 0 0 0 0 0 | 5 * * * * * * * * * * * | 2 0 0 0 0 0 ..... ox... .....&#x | 1 2 0 0 0 | 0 2 1 0 0 0 0 0 0 0 0 | * 10 * * * * * * * * * * | 1 1 0 0 0 0 ..... .x...5.o... | 0 5 0 0 0 | 0 0 5 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * | 0 1 1 0 0 0 ..... .x.o. .....&#x | 0 2 0 1 0 | 0 0 1 0 2 0 0 0 0 0 0 | * * * 10 * * * * * * * * | 1 0 1 0 0 0 ..... ..... .o.fx&#xt | 0 1 0 2 2 | 0 0 0 0 2 0 0 0 2 0 1 | * * * * 10 * * * * * * * | 0 0 1 1 0 0 .ooo. .ooo.5.ooo.&#x | 0 1 1 1 0 | 0 0 0 1 1 1 0 0 0 0 0 | * * * * * 20 * * * * * * | 1 0 0 1 0 0 ..ox. ..... .....&#x | 0 0 1 2 0 | 0 0 0 0 0 2 0 1 0 0 0 | * * * * * * 10 * * * * * | 1 0 0 0 1 0 ..ooo ..ooo5..ooo&#x | 0 0 1 1 1 | 0 0 0 0 0 1 1 0 1 0 0 | * * * * * * * 20 * * * * | 0 0 0 1 1 0 ..... ..... ..o.x&#x | 0 0 1 0 2 | 0 0 0 0 0 0 2 0 0 0 1 | * * * * * * * * 5 * * * | 0 0 0 2 0 0 ...xo ..... .....&#x | 0 0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 0 | * * * * * * * * * 10 * * | 0 0 0 0 1 1 ..... ...ox .....&#x | 0 0 0 1 2 | 0 0 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * 10 * | 0 0 1 0 0 1 ..... ....x5....x | 0 0 0 0 10 | 0 0 0 0 0 0 0 0 0 5 5 | * * * * * * * * * * * 1 | 0 0 2 0 0 0 wedge ----------------------+--------------+------------------------------+---------------------------------+-------------- xfox. oxfo. .....&#xt ♦ 2 4 2 2 0 | 1 4 2 4 4 4 0 1 0 0 0 | 2 2 0 2 0 4 2 0 0 0 0 0 | 5 * * * * * ..... ox...5oo...&#x ♦ 1 5 0 0 0 | 0 5 5 0 0 0 0 0 0 0 0 | 0 5 1 0 0 0 0 0 0 0 0 0 | * 2 * * * * ..... .x.ox5.o.fx&#xt ♦ 0 5 0 5 10 | 0 0 5 0 10 0 0 0 10 5 5 | 0 0 1 5 5 0 0 0 0 0 5 1 | * * 2 * * * ..... ..... .oofx&#xr ♦ 0 1 1 2 2 | 0 0 0 1 2 2 2 0 2 0 1 | 0 0 0 0 1 2 0 2 1 0 0 0 | * * * 10 * * cycle: (BCFE) ..oxo ..... .....&#x ♦ 0 0 1 2 1 | 0 0 0 0 0 2 1 1 2 0 0 | 0 0 0 0 0 0 1 2 0 1 0 0 | * * * * 10 * ...xo ...ox .....&#x ♦ 0 0 0 2 2 | 0 0 0 0 0 0 0 1 4 1 0 | 0 0 0 0 0 0 0 0 0 2 2 0 | * * * * * 5
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