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Acronym
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...
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Name
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bidodecateric heptacontadipeton,
pentacontitetrapeton dual,
convex hull of madek
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Circumradius
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sqrt(2/3) = 0.816497
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Lace city
in approx. ASCII-art
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p p
E O
p X X p
O E
p p
| | | | | +-- o3o3o *b3o3o (point)
| | | | +------- o3o3o *b3o3x (tac)
| | | +---------- x3o3o *b3o3o (hin)
| | +-------------- o3o3x *b3o3o (alt. hin)
| +----------------- o3o3o *b3o3x (tac)
+---------------------- o3o3o *b3o3o (point)
where:
p = o3o3o *b3o (point)
X = x3o3o *b3o ("normal" hex)
E = o3o3x *b3o ("even" hex)
O = o3o3o *b3x ("odd" hex)
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Coordinates
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(0, 0, 0, 0, 0; sqrt(2/3)) & all changes of sign
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(1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8); 1/sqrt(24)) & all even changes of sign in all but the last coord
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(-1/sqrt(8), -1/sqrt(8), -1/sqrt(8), -1/sqrt(8), -1/sqrt(8); -1/sqrt(24)) & all even changes of sign in all but the last coord
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(1/sqrt(2), 0, 0, 0, 0; 1/sqrt(6)) & all permutations in all but the last coord & all changes of sign
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Dual
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mo
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Face vector
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54, 702, 2160, 2160, 720, 72
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Confer
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- general polytopal classes:
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Catalan polypeta
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External
links
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This polyteron can be obtained as the convex hull of the 2 jak compound
(madek).
Here all the edges of the former remain as long ones, while the short ones come in as interconnections of the 2 vertex set members.
In the compound the hixes all did form (subdimensional) compounds (stade) in turn.
Thus here the hull of those (bidot) is to be used for facets.
Note that this fattening to (subdimensional) hulls already fills out everything, i.e. no further facets have to be added here.
Incidence matrix according to Dynkin symbol
xo3oo3oo3oo3ox *c3oo&#zy → height = 1
y = R = sqrt(2/3) = sqrt(6)/3 = 0.816497
(tegum sum of 2 inverted jaks)
o.3o.3o.3o.3o. *c3o. & | 54 | 16 10 | 120 | 160 | 80 | 16
---------------------------+----+---------+------+------+-----+---
x. .. .. .. .. .. & | 2 | 432 * ♦ 5 | 10 | 10 | 5 x
oo3oo3oo3oo3oo *c3oo&#y | 2 | * 270 ♦ 16 | 32 | 24 | 8 y
---------------------------+----+---------+------+------+-----+---
xo .. .. .. .. ..&#y & | 3 | 1 2 | 2160 ♦ 4 | 6 | 4
---------------------------+----+---------+------+------+-----+---
xo .. .. .. ox ..&#y ♦ 4 | 2 4 | 4 | 2160 | 3 | 3
---------------------------+----+---------+------+------+-----+---
xo3oo .. oo3ox ..&#zy ♦ 6 | 6 9 | 18 | 9 | 720 | 2
---------------------------+----+---------+------+------+-----+---
xo3oo3oo3oo3ox ..&#zy ♦ 12 | 30 30 | 120 | 90 | 20 | 72
ooxooo3oooooo3oooxoo *b3oooooo3oxooxo&#yt → height(1,2) = height(3,4) = height(5,6) = 1/sqrt(6) = 2/sqrt(24) = 0.408248
height(2,3) = height(4,5) = 1/sqrt(24) = 0.204124
y = R = sqrt(2/3) = 4/sqrt(24) = 0.816497
(pt || pseudo tac || pseudo hin || pseudo alt. hin || pseudo tac || pt)
o.....3o.....3o..... *b3o.....3o..... & | 2 * * | 10 16 0 0 0 0 0 0 | 40 80 0 0 0 0 0 | 160 0 0 0 0 | 80 0 0 | 16 0
.o....3.o....3.o.... *b3.o....3.o.... & | * 20 * | 1 0 8 8 8 1 0 0 | 8 8 24 32 32 16 0 | 32 48 48 32 0 | 24 32 24 | 8 8
..o...3..o...3..o... *b3..o...3..o... & | * * 32 | 0 1 0 5 5 0 10 5 | 0 5 30 10 40 5 30 | 10 30 90 20 10 | 10 40 30 | 6 10
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
oo....3oo....3oo.... *b3oo....3oo....&#y & | 1 1 0 | 20 * * * * * * * ♦ 8 8 0 0 0 0 0 | 32 0 0 0 0 | 24 0 0 | 8 0 y
o.o...3o.o...3o.o... *b3o.o...3o.o...&#x & | 1 0 1 | * 32 * * * * * * ♦ 0 5 0 0 0 0 0 | 10 0 0 0 0 | 10 0 0 | 5 0 x
...... ...... ...... ...... .x.... & | 0 2 0 | * * 80 * * * * * ♦ 1 0 0 4 0 0 0 | 4 6 0 0 0 | 6 4 0 | 4 1 x
.oo...3.oo...3.oo... *b3.oo...3.oo...&#y & | 0 1 1 | * * * 160 * * * * ♦ 0 1 6 4 4 1 0 | 4 12 12 4 0 | 6 12 6 | 4 4 y
.o.o..3.o.o..3.o.o.. *b3.o.o..3.o.o..&#x & | 0 1 1 | * * * * 160 * * * ♦ 0 0 0 0 4 1 0 | 0 0 6 4 0 | 0 4 6 | 1 4 x
.o..o.3.o..o.3.o..o. *b3.o..o.3.o..o.&#y | 0 2 0 | * * * * * 10 * * ♦ 0 0 0 0 0 16 0 | 0 0 0 32 0 | 0 0 24 | 0 8 y
..x... ...... ...... ...... ...... & | 0 0 2 | * * * * * * 160 * ♦ 0 0 3 0 0 0 2 | 0 3 6 0 1 | 1 6 3 | 2 3 x
..oo..3..oo..3..oo.. *b3..oo..3..oo..&#y | 0 0 2 | * * * * * * * 80 ♦ 0 0 0 0 8 0 8 | 0 0 24 4 4 | 0 12 12 | 2 6 y
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
...... ...... ...... ...... ox....&#y & | 1 2 0 | 2 0 1 0 0 0 0 0 | 80 * * * * * * ♦ 4 0 0 0 0 | 6 0 0 | 4 0
ooo...3ooo...3ooo... *b3ooo...3ooo...&#(xyy) & | 1 1 1 | 1 1 0 1 0 0 0 0 | * 160 * * * * * ♦ 4 0 0 0 0 | 6 0 0 | 4 0
.ox... ...... ...... ...... ...... & | 0 1 2 | 0 0 0 2 0 0 1 0 | * * 480 * * * * ♦ 0 2 2 0 0 | 1 4 1 | 2 2
...... ...... ...... ...... .xo...&#y & | 0 2 1 | 0 0 1 2 0 0 0 0 | * * * 320 * * * ♦ 1 3 0 0 0 | 3 3 0 | 3 1
.ooo..3.ooo..3.ooo.. *b3.ooo..3.ooo..&#(xyy) & | 0 1 2 | 0 0 0 1 1 0 0 1 | * * * * 640 * * ♦ 0 0 3 1 0 | 0 3 3 | 1 3
.oo.o.3.oo.o.3.oo.o. *b3.oo.o.3.oo.o.&#(xyy) & | 0 2 1 | 0 0 0 1 1 1 0 0 | * * * * * 160 * ♦ 0 0 0 4 0 | 0 0 6 | 0 4
..xo.. ...... ...... ...... ...... & | 0 0 3 | 0 0 0 0 0 0 1 2 | * * * * * * 320 ♦ 0 0 3 0 1 | 0 3 3 | 1 3
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
...... ...... ...... ...... oxo...&#(xy) & ♦ 1 2 1 | 2 1 1 2 0 0 0 0 | 1 2 0 1 0 0 0 | 320 * * * * | 3 0 0 | 3 0
.ox... ...... ...... ...... .xo...&#y & ♦ 0 2 2 | 0 0 1 4 0 0 1 0 | 0 0 2 2 0 0 0 | * 480 * * * | 1 2 0 | 2 1
.oxo.. ...... ...... ...... ......&#(xy) & ♦ 0 1 3 | 0 0 0 2 1 0 1 2 | 0 0 1 0 2 0 1 | * * 960 * * | 0 2 1 | 1 2
.oooo.3.oooo.3.oooo. *b3.oooo.3.oooo.&#(xy) ♦ 0 2 2 | 0 0 0 2 2 1 0 1 | 0 0 0 0 2 2 0 | * * * 320 * | 0 0 3 | 0 3
..xo.. ...... ..ox.. ...... ......&#y ♦ 0 0 4 | 0 0 0 0 0 0 2 4 | 0 0 0 0 0 0 4 | * * * * 80 | 0 0 3 | 0 3
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
oox... ...... ...... ooo...3oxo...&#yt & ♦ 1 3 2 | 3 2 3 6 0 0 1 0 | 3 6 3 6 0 0 0 | 6 3 0 0 0 | 160 * * | 2 0
.oxo..3.ooo.. ...... ...... .xoo..&#yt & ♦ 0 2 4 | 0 0 1 6 2 0 3 3 | 0 0 6 3 6 0 3 | 0 3 6 0 0 | * 320 * | 1 1
.oxoo. ...... .ooxo. ...... ......&#(xy) ♦ 0 2 4 | 0 0 0 4 4 1 2 4 | 0 0 2 0 8 4 4 | 0 0 4 4 1 | * * 240 | 0 2
-----------------------------------------------+---------+----------------------------+----------------------------+--------------------+-------------+------
ooxo..3oooo.. ...... *b3oooo..3oxoo..&#yt & ♦ 1 5 6 | 5 5 10 20 5 0 10 5 | 10 20 30 30 20 0 10 | 30 30 30 0 0 | 10 10 0 | 32 *
.oxoo.3.oooo.3.ooxo. ...... .xoox.&#yt ♦ 0 4 8 | 0 0 2 16 16 2 12 12 | 0 0 24 8 48 16 24 | 0 12 48 24 6 | 0 8 12 | * 40