Acronym | ... |
Name | vertex-first rotunda of hexacosachoron |
Circumradius | (1+sqrt(5))/2 = 1.618034 |
Lace city in approx. ASCII-art |
o5o o5x x5o o5o f5o o5f o5x f5o o5o x5x o5f x5o f5o o5f o5o o5x x5o o5o |
o3o x3o o3f f3o o3x (F=ff) o3o o3f f3x x3f f3o o3o f3o o3F F3o o3f o3x x3f F3o f3f o3F f3x x3o | |
Dihedral angles | |
Face vector | 75, 384, 592, 283 |
Confer |
The upper lace city above shows that this polychoron is not exactly half of ex: rather, if attaching its mirror image onto the right, it can be seen at the top and bottom that pentagonal scalene dimples in here got omitted, which elsewise would had got dissected midwise. In fact there would be 12 such pescs all around on that mirror hyper plane. Despite this lack this rotunda in here still is convex, as is proven by the given dihedral angles. Even more, this rotunda indeed gets obtained as the convex hull of the vertex set of half of ex.
Incidence matrix according to Dynkin symbol
oxofo3oooox5ooxoo&#xt → height(1,2) = height(3,4) = (sqrt(5)-1)/4 = 0.309017 height(2,3) = height(4,5) = 1/2 (pt || pseudo ike || pseudo doe || pseudo f-ike || id) o....3o....5o.... | 1 * * * * ♦ 12 0 0 0 0 0 0 0 0 | 30 0 0 0 0 0 0 0 0 0 0 0 | 20 0 0 0 0 0 0 0 0 .o...3.o...5.o... | * 12 * * * ♦ 1 5 5 1 0 0 0 0 0 | 5 5 10 5 5 0 0 0 0 0 0 0 | 5 5 5 5 0 0 0 0 0 ..o..3..o..5..o.. | * * 20 * * ♦ 0 0 3 0 3 3 3 0 0 | 0 0 3 6 3 6 3 3 6 0 0 0 | 0 1 3 6 1 3 6 0 0 ...o.3...o.5...o. | * * * 12 * ♦ 0 0 0 1 0 5 0 5 0 | 0 0 0 0 5 5 0 0 10 5 0 0 | 0 0 0 5 0 5 5 1 0 ....o3....o5....o | * * * * 30 | 0 0 0 0 0 0 2 2 4 | 0 0 0 0 0 0 4 1 4 4 2 2 | 0 0 0 0 2 4 2 2 1 ----------------------+---------------+----------------------------+--------------------------------------+-------------------------- oo...3oo...5oo...&#x | 1 1 0 0 0 | 12 * * * * * * * * | 5 0 0 0 0 0 0 0 0 0 0 0 | 5 0 0 0 0 0 0 0 0 .x... ..... ..... | 0 2 0 0 0 | * 30 * * * * * * * | 1 2 2 0 0 0 0 0 0 0 0 0 | 2 2 1 0 0 0 0 0 0 .oo..3.oo..5.oo..&#x | 0 1 1 0 0 | * * 60 * * * * * * | 0 0 2 2 1 0 0 0 0 0 0 0 | 0 1 2 2 0 0 0 0 0 .o.o.3.o.o.5.o.o.&#x | 0 1 0 1 0 | * * * 12 * * * * * | 0 0 0 0 5 0 0 0 0 0 0 0 | 0 0 0 5 0 0 0 0 0 ..... ..... ..x.. | 0 0 2 0 0 | * * * * 30 * * * * | 0 0 0 2 0 2 0 1 0 0 0 0 | 0 0 1 2 0 0 2 0 0 ..oo.3..oo.5..oo.&#x | 0 0 1 1 0 | * * * * * 60 * * * | 0 0 0 0 1 2 0 0 2 0 0 0 | 0 0 0 2 0 1 2 0 0 ..o.o3..o.o5..o.o&#x | 0 0 1 0 1 | * * * * * * 60 * * | 0 0 0 0 0 0 2 1 2 0 0 0 | 0 0 0 0 1 2 2 0 0 ...oo3...oo5...oo&#x | 0 0 0 1 1 | * * * * * * * 60 * | 0 0 0 0 0 0 0 0 2 2 0 0 | 0 0 0 0 0 2 1 1 0 ..... ....x ..... | 0 0 0 0 2 | * * * * * * * * 60 | 0 0 0 0 0 0 1 0 0 1 1 1 | 0 0 0 0 1 1 0 1 1 ----------------------+---------------+----------------------------+--------------------------------------+-------------------------- ox... ..... .....&#x | 1 2 0 0 0 | 2 1 0 0 0 0 0 0 0 | 30 * * * * * * * * * * * | 2 0 0 0 0 0 0 0 0 .x...3.o... ..... | 0 3 0 0 0 | 0 3 0 0 0 0 0 0 0 | * 20 * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 .xo.. ..... .....&#x | 0 2 1 0 0 | 0 1 2 0 0 0 0 0 0 | * * 60 * * * * * * * * * | 0 1 1 0 0 0 0 0 0 ..... ..... .ox..&#x | 0 1 2 0 0 | 0 0 2 0 1 0 0 0 0 | * * * 60 * * * * * * * * | 0 0 1 1 0 0 0 0 0 .ooo.3.ooo.5.ooo.&#x | 0 1 1 1 0 | 0 0 1 1 0 1 0 0 0 | * * * * 60 * * * * * * * | 0 0 0 2 0 0 0 0 0 ..... ..... ..xo.&#x | 0 0 2 1 0 | 0 0 0 0 1 2 0 0 0 | * * * * * 60 * * * * * * | 0 0 0 1 0 0 1 0 0 ..... ..o.x .....&#x | 0 0 1 0 2 | 0 0 0 0 0 0 2 0 1 | * * * * * * 60 * * * * * | 0 0 0 0 1 1 0 0 0 ..... ..... ..x.o&#x | 0 0 2 0 1 | 0 0 0 0 1 0 2 0 0 | * * * * * * * 30 * * * * | 0 0 0 0 0 0 2 0 0 ..ooo3..ooo5..ooo&#x | 0 0 1 1 1 | 0 0 0 0 0 1 1 1 0 | * * * * * * * * 120 * * * | 0 0 0 0 0 1 1 0 0 ..... ...ox .....&#x | 0 0 0 1 2 | 0 0 0 0 0 0 0 2 1 | * * * * * * * * * 60 * * | 0 0 0 0 0 1 0 1 0 ....o3....x ..... | 0 0 0 0 3 | 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * 20 * | 0 0 0 0 1 0 0 0 1 ..... ....x5....o | 0 0 0 0 5 | 0 0 0 0 0 0 0 0 5 | * * * * * * * * * * * 12 | 0 0 0 0 0 0 0 1 1 ----------------------+---------------+----------------------------+--------------------------------------+-------------------------- ox...3oo... .....&#x ♦ 1 3 0 0 0 | 3 3 0 0 0 0 0 0 0 | 3 1 0 0 0 0 0 0 0 0 0 0 | 20 * * * * * * * * .xo..3.oo.. .....&#x ♦ 0 3 1 0 0 | 0 3 3 0 0 0 0 0 0 | 0 1 3 0 0 0 0 0 0 0 0 0 | * 20 * * * * * * * .xo.. ..... .ox..&#x ♦ 0 2 2 0 0 | 0 1 4 0 1 0 0 0 0 | 0 0 2 2 0 0 0 0 0 0 0 0 | * * 30 * * * * * * ..... ..... .oxo.&#xt ♦ 0 1 2 1 0 | 0 0 2 1 1 2 0 0 0 | 0 0 0 1 2 1 0 0 0 0 0 0 | * * * 60 * * * * * ..o.o3..o.x .....&#x ♦ 0 0 1 0 3 | 0 0 0 0 0 0 3 0 3 | 0 0 0 0 0 0 3 0 0 0 1 0 | * * * * 20 * * * * ..... ..oox .....&#xt ♦ 0 0 1 1 2 | 0 0 0 0 0 1 2 2 1 | 0 0 0 0 0 0 1 0 2 1 0 0 | * * * * * 60 * * * ..... ..... ..xoo&#xt ♦ 0 0 2 1 1 | 0 0 0 0 1 2 2 1 0 | 0 0 0 0 0 1 0 1 2 0 0 0 | * * * * * * 60 * * ..... ...ox5...oo&#x ♦ 0 0 0 1 5 | 0 0 0 0 0 0 0 5 5 | 0 0 0 0 0 0 0 0 0 5 0 1 | * * * * * * * 12 * ....o3....x5....o ♦ 0 0 0 0 30 | 0 0 0 0 0 0 0 0 60 | 0 0 0 0 0 0 0 0 0 0 20 12 | * * * * * * * * 1
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