vee

Acronym

vee

Name

pentacosidodecayotton,
enneacross (β₉),
aeroxenn(id),
enneazettal antiprism,
vertex figure of ka,
Gosset polytope 6_1,1,
lattice C₉ contact polytope (span of its small roots),
equatorial cross-section of vertex-first ka

Circumradius

1/sqrt(2) = 0.707107

Inradius

1/sqrt(18) = 0.235702

Lace city
in approx. ASCII-art

©	o -- o3o3o3o3o3o3o4o (point) o z o -- x3o3o3o3o3o3o4o (ek) o -- o3o3o3o3o3o3o4o (point) where: o = o3o3o3o3o3o4o (point) z = x3o3o3o3o3o4o (zee)

Coordinates

(1/sqrt(2), 0, 0, 0, 0, 0, 0, 0, 0) & all permutations, all changes of sign

Volume

sqrt(2)/22680 = 0.000062355

Surface

1/420 = 0.0023810

Dual

enne

Dihedral angles
(at margins)

at oca between ene and ene: arccos(-7/9) = 141.057559°

Face vector

18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512

Confer

more general:: xPo3o...o3o4o
general polytopal classes:: Wythoffian polyyotta orthoplex noble polytopes segmentoyotta fundamental lace prisms Coxeter-Elte-Gosset polytopes
analogs:: regular orthoplex O_n

External
links

Incidence matrix according to Dynkin symbol

x3o3o3o3o3o3o3o4o

. . . . . . . . . | 18 ♦  16 | 112 |  448 | 1120 | 1792 | 1792 | 1024 | 256
------------------+----+-----+-----+------+------+------+------+------+----
x . . . . . . . . |  2 | 144 ♦  14 |   84 |  280 |  560 |  672 |  448 | 128
------------------+----+-----+-----+------+------+------+------+------+----
x3o . . . . . . . |  3 |   3 | 672 ♦   12 |   60 |  160 |  240 |  192 |  64
------------------+----+-----+-----+------+------+------+------+------+----
x3o3o . . . . . . ♦  4 |   6 |   4 | 2016 ♦   10 |   40 |   80 |   80 |  32
------------------+----+-----+-----+------+------+------+------+------+----
x3o3o3o . . . . . ♦  5 |  10 |  10 |    5 | 4032 ♦    8 |   24 |   32 |  16
------------------+----+-----+-----+------+------+------+------+------+----
x3o3o3o3o . . . . ♦  6 |  15 |  20 |   15 |    6 | 5376 ♦    6 |   12 |   8
------------------+----+-----+-----+------+------+------+------+------+----
x3o3o3o3o3o . . . ♦  7 |  21 |  35 |   35 |   21 |    7 | 4608 |    4 |   4
------------------+----+-----+-----+------+------+------+------+------+----
x3o3o3o3o3o3o . . ♦  8 |  28 |  56 |   70 |   56 |   28 |    8 | 2304 |   2
------------------+----+-----+-----+------+------+------+------+------+----
x3o3o3o3o3o3o3o . ♦  9 |  36 |  84 |  126 |  126 |   84 |   36 |    9 | 512

o3o3o *b3o3o3o3o3o3x

. . .    . . . . . . | 18 ♦  16 | 112 |  448 | 1120 | 1792 | 1792 | 1024 | 128 128
---------------------+----+-----+-----+------+------+------+------+------+--------
. . .    . . . . . x |  2 | 144 ♦  14 |   84 |  280 |  560 |  672 |  448 |  64  64
---------------------+----+-----+-----+------+------+------+------+------+--------
. . .    . . . . o3x |  3 |   3 | 672 ♦   12 |   60 |  160 |  240 |  192 |  32  32
---------------------+----+-----+-----+------+------+------+------+------+--------
. . .    . . . o3o3x ♦  4 |   6 |   4 | 2016 ♦   10 |   40 |   80 |   80 |  16  16
---------------------+----+-----+-----+------+------+------+------+------+--------
. . .    . . o3o3o3x ♦  5 |  10 |  10 |    5 | 4032 ♦    8 |   24 |   32 |   8   8
---------------------+----+-----+-----+------+------+------+------+------+--------
. . .    . o3o3o3o3x ♦  6 |  15 |  20 |   15 |    6 | 5376 ♦    6 |   12 |   4   4
---------------------+----+-----+-----+------+------+------+------+------+--------
. . .    o3o3o3o3o3x ♦  7 |  21 |  35 |   35 |   21 |    7 | 4608 |    4 |   2   2
---------------------+----+-----+-----+------+------+------+------+------+--------
. o . *b3o3o3o3o3o3x ♦  8 |  28 |  56 |   70 |   56 |   28 |    8 | 2304 |   1   1
---------------------+----+-----+-----+------+------+------+------+------+--------
o3o . *b3o3o3o3o3o3x ♦  9 |  36 |  84 |  126 |  126 |   84 |   36 |    9 | 256   *
. o3o *b3o3o3o3o3o3x ♦  9 |  36 |  84 |  126 |  126 |   84 |   36 |    9 |   * 256

xo3oo3oo3oo3oo3oo3oo3ox&#x   → height = sqrt(2)/3 = 0.471405
(ene || inv ene)

o.3o.3o.3o.3o.3o.3o.3o.    & | 18 ♦  8  8 |  28  84 |  56  224 168 |  70  350  700 |  56  336  840  560 | 28 196  588  980 |  8  64 224  448 280 | 1  9 36  84 126
-----------------------------+----+-------+---------+--------------+---------------+--------------------+------------------+---------------------+----------------
x. .. .. .. .. .. .. ..    & |  2 | 72  * ♦   7   7 |  21   42  21 |  35  105  140 |  35  140  245  140 | 21 105  231  315 |  7  42 112  182 105 | 1  7 22  42  56
oo3oo3oo3oo3oo3oo3oo3oo&#x   |  2 |  * 72 ♦   0  14 |   0   42  42 |   0   70  210 |   0   70  280  210 |  0  42  210  420 |  0  14  84  210 140 | 0  2 14  42  70
-----------------------------+----+-------+---------+--------------+---------------+--------------------+------------------+---------------------+----------------
x.3o. .. .. .. .. .. ..    & |  3 |  3  0 | 168   * ♦   6    6   0 |  15   30   15 |  20   60   60   20 | 15  60   90   75 |  6  30  60   66  30 | 1  6 15  21  21
xo .. .. .. .. .. .. ..&#x & |  3 |  1  2 |   * 504 ♦   0    6   6 |   0   15   45 |   0   20   80   60 |  0  15   75  150 |  0   6  36   90  60 | 0  1  7  21  35
-----------------------------+----+-------+---------+--------------+---------------+--------------------+------------------+---------------------+----------------
x.3o.3o. .. .. .. .. ..    & ♦  4 |  6  0 |   4   0 | 252    *   * ♦   5    5    0 |  10   20   10    0 | 10  30   30   10 |  5  20  30   20   5 | 1  5 10  10   6
xo3oo .. .. .. .. .. ..&#x & ♦  4 |  3  3 |   1   3 |   * 1008   * ♦   0    5    5 |   0   10   20   10 |  0  10   30   40 |  0   5  20   35  20 | 0  1  5  11  15
xo .. .. .. .. .. .. ox&#x   ♦  4 |  2  4 |   0   4 |   *    * 756 ♦   0    0   10 |   0    0   20   20 |  0   0   20   60 |  0   0  10   40  30 | 0  0  2  10  20
-----------------------------+----+-------+---------+--------------+---------------+--------------------+------------------+---------------------+----------------
x.3o.3o.3o. .. .. .. ..    & ♦  5 | 10  0 |  10   0 |   5    0   0 | 252    *    * ♦   4    4    0    0 |  6  12    6    0 |  4  12  12    4   0 | 1  4  6   4   1
xo3oo3oo .. .. .. .. ..&#x & ♦  5 |  6  4 |   4   6 |   1    4   0 |   * 1260    * ♦   0    4    4    0 |  0   6   12    6 |  0   4  12   12   4 | 0  1  4   6   5
xo3oo .. .. .. .. .. ox&#x & ♦  5 |  4  6 |   1   9 |   0    2   3 |   *    * 2520 ♦   0    0    4    4 |  0   0    6   18 |  0   0   4   16  12 | 0  0  1   5  10
-----------------------------+----+-------+---------+--------------+---------------+--------------------+------------------+---------------------+----------------
x.3o.3o.3o.3o. .. .. ..    & ♦  6 | 15  0 |  20   0 |  15    0   0 |   6    0    0 | 168    *    *    * ♦  3   3    0    0 |  3   6   3    0   0 | 1  3  3   1   0
xo3oo3oo3oo .. .. .. ..&#x & ♦  6 | 10  5 |  10  10 |   5   10   0 |   1    5    0 |   * 1008    *    * ♦  0   3    3    0 |  0   3   6    3   0 | 0  1  3   3   1
xo3oo3oo .. .. .. .. ox&#x & ♦  6 |  7  8 |   4  16 |   1    8   6 |   0    2    4 |   *    * 2520    * ♦  0   0    3    3 |  0   0   3    6   3 | 0  0  1   3   4
xo3oo .. .. .. .. oo3ox&#x   ♦  6 |  6  9 |   2  18 |   0    6   9 |   0    0    6 |   *    *    * 1680 ♦  0   0    0    6 |  0   0   0    6   6 | 0  0  0   2   6
-----------------------------+----+-------+---------+--------------+---------------+--------------------+------------------+---------------------+----------------
x.3o.3o.3o.3o.3o. .. ..    & ♦  7 | 21  0 |  35   0 |  35    0   0 |  21    0    0 |   7    0    0    0 | 72   *    *    * |  2   2   0    0   0 | 1  2  1   0   0
xo3oo3oo3oo3oo .. .. ..&#x & ♦  7 | 15  6 |  20  15 |  15   20   0 |   6   15    0 |   1    6    0    0 |  * 504    *    * |  0   2   2    0   0 | 0  1  2   1   0
xo3oo3oo3oo .. .. .. ox&#x & ♦  7 | 11 10 |  10  25 |   5   20  10 |   1   10   10 |   0    2    5    0 |  *   * 1512    * |  0   0   2    2   0 | 0  0  1   2   1
xo3oo3oo .. .. .. oo3ox&#x & ♦  7 |  9 12 |   5  30 |   1   16  18 |   0    3   18 |   0    0    3    4 |  *   *    * 2520 |  0   0   0    2   2 | 0  0  0   1   3
-----------------------------+----+-------+---------+--------------+---------------+--------------------+------------------+---------------------+----------------
x.3o.3o.3o.3o.3o.3o. ..    & ♦  8 | 28  0 |  56   0 |  70    0   0 |  56    0    0 |  28    0    0    0 |  8   0    0    0 | 18   *   *    *   * | 1  1  0   0   0
xo3oo3oo3oo3oo3oo .. ..&#x & ♦  8 | 21  7 |  35  21 |  35   35   0 |  21   35    0 |   7   21    0    0 |  1   7    0    0 |  * 144   *    *   * | 0  1  1   0   0
xo3oo3oo3oo3oo .. .. ox&#x & ♦  8 | 16 12 |  20  36 |  15   40  15 |   6   30   20 |   1   12   15    0 |  0   2    6    0 |  *   * 504    *   * | 0  0  1   1   0
xo3oo3oo3oo .. .. oo3ox&#x & ♦  8 | 13 15 |  11  45 |   5   35  30 |   1   15   40 |   0    3   15   10 |  0   0    3    5 |  *   *   * 1008   * | 0  0  0   1   1
xo3oo3oo .. .. oo3oo3ox&#x   ♦  8 | 12 16 |   8  48 |   2   32  36 |   0    8   48 |   0    0   12   16 |  0   0    0    8 |  *   *   *    * 630 | 0  0  0   0   2
-----------------------------+----+-------+---------+--------------+---------------+--------------------+------------------+---------------------+----------------
x.3o.3o.3o.3o.3o.3o.3o.    & ♦  9 | 36  0 |  84   0 | 126    0   0 | 126    0    0 |  84    0    0    0 | 36   0    0    0 |  9   0   0    0   0 | 2  *  *   *   *
xo3oo3oo3oo3oo3oo3oo ..&#x & ♦  9 | 28  8 |  56  28 |  70   56   0 |  56   70    0 |  28   56    0    0 |  8  28    0    0 |  1   8   0    0   0 | * 18  *   *   *
xo3oo3oo3oo3oo3oo .. ox&#x & ♦  9 | 22 14 |  35  49 |  35   70  21 |  21   70   35 |   7   42   35    0 |  1  14   21    0 |  0   2   7    0   0 | *  * 72   *   *
xo3oo3oo3oo3oo .. oo3ox&#x & ♦  9 | 18 18 |  21  63 |  15   66  45 |   6   45   75 |   1   18   45   20 |  0   3   18   15 |  0   0   3    6   0 | *  *  * 168   *
xo3oo3oo3oo .. oo3oo3ox&#x & ♦  9 | 16 20 |  14  70 |   6   60  60 |   1   25  100 |   0    4   40   40 |  0   0    6   30 |  0   0   0    4   5 | *  *  *   * 252

top of page