Acronym ek
Name diacosipentacontahexazetton,
octacross8),
aeroyott(id),
octaexal antiprism,
vertex figure of vee,
(one of the) Delone cell(s) of lattice E8,
Gosset polytope 51,1,
lattice C8 contact polytope (span of its small roots)
Circumradius 1/sqrt(2) = 0.707107
Inradius 1/4 = 0.25
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  
analogs:
regular orthoplex On  
External
links
wikipedia   polytopewiki  

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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