Acronym ek
Name diacosipentacontahexazetton,
octacross (β8),
aeroyott(id),
octaexal antiprism,
vertex figure of vee,
(one of the) Delone cell(s) of lattice E8,
Gosset polytope 51,1
Circumradius 1/sqrt(2) = 0.707107
Inradius 1/4
Coordinates (1/sqrt(2), 0, 0, 0, 0, 0, 0, 0)   & all permutations, all changes of sign
Volume 1/2520 = 0.00039683
Surface 4/315 = 0.012698
Rel. Roundness 105 π4/65536 = 15.606620 %
Dual octo
Dihedral angles
  • at hop between oca and oca:   arccos(-3/4) = 138.590378°
Confer
related segmentozetta:
zeepy  
general polytopal classes:
orthoplex   noble polytopes   segmentozetta   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
External
links 		wikipedia  

Incidence matrix according to Dynkin symbol

x3o3o3o3o3o3o4o

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


o3o3o *b3o3o3o3o3x

. . .    . . . . . | 16 ♦  14 |  84 |  280 |  560 |  672 |  448 |  64  64
-------------------+----+-----+-----+------+------+------+------+--------
. . .    . . . . x |  2 | 112 ♦  12 |   60 |  160 |  240 |  192 |  32  32
-------------------+----+-----+-----+------+------+------+------+--------
. . .    . . . o3x |  3 |   3 | 448 ♦   10 |   40 |   80 |   80 |  16  16
-------------------+----+-----+-----+------+------+------+------+--------
. . .    . . o3o3x ♦  4 |   6 |   4 | 1120 ♦    8 |   24 |   32 |   8   8
-------------------+----+-----+-----+------+------+------+------+--------
. . .    . o3o3o3x ♦  5 |  10 |  10 |    5 | 1792 ♦    6 |   12 |   4   4
-------------------+----+-----+-----+------+------+------+------+--------
. . .    o3o3o3o3x ♦  6 |  15 |  20 |   15 |    6 | 1792 |    4 |   2   2
-------------------+----+-----+-----+------+------+------+------+--------
. o . *b3o3o3o3o3x ♦  7 |  21 |  35 |   35 |   21 |    7 | 1024 |   1   1
-------------------+----+-----+-----+------+------+------+------+--------
o3o . *b3o3o3o3o3x ♦  8 |  28 |  56 |   70 |   56 |   28 |    7 | 128   *
. o3o *b3o3o3o3o3x ♦  8 |  28 |  56 |   70 |   56 |   28 |    7 |   * 128


xo3oo3oo3oo3oo3oo3ox&#x   → height = 1/2
(oca || dual oca)

o.3o.3o.3o.3o.3o.3o.    & | 16 ♦  7  7 |  21  63 |  35 140 105 |  35 175  350 | 21 126 315 210 |  7  49 147 245 | 1  8 28  56 35
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x. .. .. .. .. .. ..    & |  2 | 56  * ♦   6   6 |  15  30  15 |  20  60   80 | 15  60 105  60 |  6  30  66  90 | 1  6 16  26 15
oo3oo3oo3oo3oo3oo3oo&#x   |  2 |  * 56 ♦   0  12 |   0  30  30 |   0  40  120 |  0  30 120  90 |  0  12  60 120 | 0  2 12  30 20
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o. .. .. .. .. ..    & |  3 |  3  0 | 112   * ♦   5   5   0 |  10  20   10 | 10  30  30  10 |  5  20  30  25 | 1  5 10  11  5
xo .. .. .. .. .. ..&#x & |  3 |  1  2 |   * 336 ♦   0   5   5 |   0  10   30 |  0  10  40  30 |  0   5  25  50 | 0  1  6  15 10
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o. .. .. .. ..    & ♦  4 |  6  0 |   4   0 | 140   *   * ♦   4   4    0 |  6  12   6   0 |  4  12  12   4 | 1  4  6   4  1
xo3oo .. .. .. .. ..&#x & ♦  4 |  3  3 |   1   3 |   * 560   * ♦   0   4    4 |  0   6  12   6 |  0   4  12  16 | 0  1  4   7  4
xo .. .. .. .. .. ox&#x   ♦  4 |  2  4 |   0   4 |   *   * 420 ♦   0   0    8 |  0   0  12  12 |  0   0   8  24 | 0  0  2   8  6
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o.3o. .. .. ..    & ♦  5 | 10  0 |  10   0 |   5   0   0 | 112   *    * ♦  3   3   0   0 |  3   6   3   0 | 1  3  3   1  0
xo3oo3oo .. .. .. ..&#x & ♦  5 |  6  4 |   4   6 |   1   4   0 |   * 560    * ♦  0   3   3   0 |  0   3   6   3 | 0  1  3   3  1
xo3oo .. .. .. .. ox&#x & ♦  5 |  4  6 |   1   9 |   0   2   3 |   *   * 1120 ♦  0   0   3   3 |  0   0   3   9 | 0  0  1   4  3
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o.3o.3o. .. ..    & ♦  6 | 15  0 |  20   0 |  15   0   0 |   6   0    0 | 56   *   *   * |  2   2   0   0 | 1  2  1   0  0
xo3oo3oo3oo .. .. ..&#x & ♦  6 | 10  5 |  10  10 |   5  10   0 |   1   5    0 |  * 336   *   * |  0   2   2   0 | 0  1  2   1  0
xo3oo3oo .. .. .. ox&#x & ♦  6 |  7  8 |   4  16 |   1   8   6 |   0   2    4 |  *   * 840   * |  0   0   2   2 | 0  0  1   2  1
xo3oo .. .. .. oo3ox&#x   ♦  6 |  6  9 |   2  18 |   0   6   9 |   0   0    6 |  *   *   * 560 |  0   0   0   4 | 0  0  0   2  2
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
x.3o.3o.3o.3o.3o. ..    & ♦  7 | 21  0 |  35   0 |  35   0   0 |  21   0    0 |  7   0   0   0 | 16   *   *   * | 1  1  0   0  0
xo3oo3oo3oo3oo .. ..&#x & ♦  7 | 15  6 |  20  15 |  15  20   0 |   6  15    0 |  1   6   0   0 |  * 112   *   * | 0  1  1   0  0
xo3oo3oo3oo .. .. ox&#x & ♦  7 | 11 10 |  10  25 |   5  20  10 |   1  10   10 |  0   2   5   0 |  *   * 336   * | 0  0  1   1  0
xo3oo3oo .. .. oo3ox&#x & ♦  7 |  9 12 |   5  30 |   1  16  18 |   0   3   18 |  0   0   3   4 |  *   *   * 560 | 0  0  0   1  1
--------------------------+----+-------+---------+-------------+--------------+----------------+----------------+---------------
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 | 2  *  *   *  *
xo3oo3oo3oo3oo3oo ..&#x & ♦  8 | 21  7 |  35  21 |  35  35   0 |  21  35    0 |  7  21   0   0 |  1   7   0   0 | * 16  *   *  *
xo3oo3oo3oo3oo .. ox&#x & ♦  8 | 16 12 |  20  36 |  15  40  15 |   6  30   20 |  1  12  15   0 |  0   2   6   0 | *  * 56   *  *
xo3oo3oo3oo .. oo3ox&#x & ♦  8 | 13 15 |  11  45 |   5  35  30 |   1  15   40 |  0   3  15  10 |  0   0   3   5 | *  *  * 112  *
xo3oo3oo .. oo3oo3ox&#x   ♦  8 | 12 16 |   8  48 |   2  32  36 |   0   8   48 |  0   0  12  16 |  0   0   0   8 | *  *  *   * 70


oqo xoo3ooo3ooo3ooo3ooo3oox&#xt   → both heights = 1/sqrt(14) = 0.267261
(hop || perp pseudo q-line || dual hop)

...

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