Acronym histodip
Name hexagon - octagram duoprism
 
Circumradius sqrt[2-1/sqrt(2)] = 1.137055
Dihedral angles
  • at {8/3} between stop and stop:   120°
  • at {4} between hip and stop:   90°
  • at {6} between hip and hip:   45°
Confer
general duoprisms:
n/d,m/b-dip  
External
links
hedrondude

As abstract polytope histodip is isomorph to hodip, thereby replacing octagrams by octagons, resp. stop by op.


Incidence matrix according to Dynkin symbol

x6o x8/3o

. . .   . | 48 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 48  * | 1  2 0 | 2 1
. . x   . |  2 |  * 48 | 0  2 1 | 1 2
----------+----+-------+--------+----
x6o .   . |  6 |  6  0 | 8  * * | 2 0
x . x   . |  4 |  2  2 | * 48 * | 1 1
. . x8/3o |  8 |  0  8 | *  * 6 | 0 2
----------+----+-------+--------+----
x6o x   .  12 | 12  6 | 2  6 0 | 8 *
x . x8/3o  16 |  8 16 | 0  8 2 | * 6

x6o x8/5o

. . .   . | 48 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 48  * | 1  2 0 | 2 1
. . x   . |  2 |  * 48 | 0  2 1 | 1 2
----------+----+-------+--------+----
x6o .   . |  6 |  6  0 | 8  * * | 2 0
x . x   . |  4 |  2  2 | * 48 * | 1 1
. . x8/5o |  8 |  0  8 | *  * 6 | 0 2
----------+----+-------+--------+----
x6o x   .  12 | 12  6 | 2  6 0 | 8 *
x . x8/5o  16 |  8 16 | 0  8 2 | * 6

x6/5o x8/3o

.   . .   . | 48 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 48  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 48 | 0  2 1 | 1 2
------------+----+-------+--------+----
x6/5o .   . |  6 |  6  0 | 8  * * | 2 0
x   . x   . |  4 |  2  2 | * 48 * | 1 1
.   . x8/3o |  8 |  0  8 | *  * 6 | 0 2
------------+----+-------+--------+----
x6/5o x   .  12 | 12  6 | 2  6 0 | 8 *
x   . x8/3o  16 |  8 16 | 0  8 2 | * 6

x6/5o x8/5o

.   . .   . | 48 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 48  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 48 | 0  2 1 | 1 2
------------+----+-------+--------+----
x6/5o .   . |  6 |  6  0 | 8  * * | 2 0
x   . x   . |  4 |  2  2 | * 48 * | 1 1
.   . x8/5o |  8 |  0  8 | *  * 6 | 0 2
------------+----+-------+--------+----
x6/5o x   .  12 | 12  6 | 2  6 0 | 8 *
x   . x8/5o  16 |  8 16 | 0  8 2 | * 6

x3x x8/3o

. . .   . | 48 |  1  1  2 | 1  2  2 1 | 2 1 1
----------+----+----------+-----------+------
x . .   . |  2 | 24  *  * | 1  2  0 0 | 2 1 0
. x .   . |  2 |  * 24  * | 1  0  2 0 | 2 0 1
. . x   . |  2 |  *  * 48 | 0  1  1 1 | 1 1 1
----------+----+----------+-----------+------
x3x .   . |  6 |  3  3  0 | 8  *  * * | 2 0 0
x . x   . |  4 |  2  0  2 | * 24  * * | 1 1 0
. x x   . |  4 |  0  2  2 | *  * 24 * | 1 0 1
. . x8/3o |  8 |  0  0  8 | *  *  * 6 | 0 1 1
----------+----+----------+-----------+------
x3x x   .  12 |  6  6  6 | 2  3  3 0 | 8 * *
x . x8/3o  16 |  8  0 16 | 0  8  0 2 | * 3 *
. x x8/3o  16 |  0  8 16 | 0  0  8 2 | * * 3

x3x x8/5o

. . .   . | 48 |  1  1  2 | 1  2  2 1 | 2 1 1
----------+----+----------+-----------+------
x . .   . |  2 | 24  *  * | 1  2  0 0 | 2 1 0
. x .   . |  2 |  * 24  * | 1  0  2 0 | 2 0 1
. . x   . |  2 |  *  * 48 | 0  1  1 1 | 1 1 1
----------+----+----------+-----------+------
x3x .   . |  6 |  3  3  0 | 8  *  * * | 2 0 0
x . x   . |  4 |  2  0  2 | * 24  * * | 1 1 0
. x x   . |  4 |  0  2  2 | *  * 24 * | 1 0 1
. . x8/5o |  8 |  0  0  8 | *  *  * 6 | 0 1 1
----------+----+----------+-----------+------
x3x x   .  12 |  6  6  6 | 2  3  3 0 | 8 * *
x . x8/5o  16 |  8  0 16 | 0  8  0 2 | * 3 *
. x x8/5o  16 |  0  8 16 | 0  0  8 2 | * * 3

x4/3x x6o

.   . . . | 48 |  1  1  2 | 1  2  2 1 | 2 1 1
----------+----+----------+-----------+------
x   . . . |  2 | 24  *  * | 1  2  0 0 | 2 1 0
.   x . . |  2 |  * 24  * | 1  0  2 0 | 2 0 1
.   . x . |  2 |  *  * 48 | 0  1  1 1 | 1 1 1
----------+----+----------+-----------+------
x4/3x . . |  8 |  4  4  0 | 6  *  * * | 2 0 0
x   . x . |  4 |  2  0  2 | * 24  * * | 1 1 0
.   x x . |  4 |  0  2  2 | *  * 24 * | 1 0 1
.   . x6o |  6 |  0  0  6 | *  *  * 8 | 0 1 1
----------+----+----------+-----------+------
x4/3x x .  16 |  8  8  8 | 2  4  4 0 | 6 * *
x   . x6o  12 |  6  0 12 | 0  6  0 2 | * 4 *
.   x x6o  12 |  0  6 12 | 0  0  6 2 | * * 4

x4/3x x6/5o

.   . .   . | 48 |  1  1  2 | 1  2  2 1 | 2 1 1
------------+----+----------+-----------+------
x   . .   . |  2 | 24  *  * | 1  2  0 0 | 2 1 0
.   x .   . |  2 |  * 24  * | 1  0  2 0 | 2 0 1
.   . x   . |  2 |  *  * 48 | 0  1  1 1 | 1 1 1
------------+----+----------+-----------+------
x4/3x .   . |  8 |  4  4  0 | 6  *  * * | 2 0 0
x   . x   . |  4 |  2  0  2 | * 24  * * | 1 1 0
.   x x   . |  4 |  0  2  2 | *  * 24 * | 1 0 1
.   . x6/5o |  6 |  0  0  6 | *  *  * 8 | 0 1 1
------------+----+----------+-----------+------
x4/3x x   .  16 |  8  8  8 | 2  4  4 0 | 6 * *
x   . x6/5o  12 |  6  0 12 | 0  6  0 2 | * 4 *
.   x x6/5o  12 |  0  6 12 | 0  0  6 2 | * * 4

x3x x4/3x

. . .   . | 48 |  1  1  1  1 | 1  1  1  1  1 1 | 1 1 1 1
----------+----+-------------+-----------------+--------
x . .   . |  2 | 24  *  *  * | 1  1  1  0  0 0 | 1 1 1 0
. x .   . |  2 |  * 24  *  * | 1  0  0  1  1 0 | 1 1 0 1
. . x   . |  2 |  *  * 24  * | 0  1  0  1  0 1 | 1 0 1 1
. . .   x |  2 |  *  *  * 24 | 0  0  1  0  1 1 | 0 1 1 1
----------+----+-------------+-----------------+--------
x3x .   . |  6 |  3  3  0  0 | 8  *  *  *  * * | 1 1 0 0
x . x   . |  4 |  2  0  2  0 | * 12  *  *  * * | 1 0 1 0
x . .   x |  4 |  2  0  0  2 | *  * 12  *  * * | 0 1 1 0
. x x   . |  4 |  0  2  2  0 | *  *  * 12  * * | 1 0 0 1
. x .   x |  4 |  0  2  0  2 | *  *  *  * 12 * | 0 1 0 1
. . x4/3x |  8 |  0  0  4  4 | *  *  *  *  * 6 | 0 0 1 1
----------+----+-------------+-----------------+--------
x3x x   .  12 |  6  6  6  0 | 2  3  0  3  0 0 | 4 * * *
x3x .   x  12 |  6  6  0  6 | 2  0  3  0  3 0 | * 4 * *
x . x4/3x  16 |  8  0  8  8 | 0  4  4  0  0 2 | * * 3 *
. x x4/3x  16 |  0  8  8  8 | 0  0  0  4  4 2 | * * * 3

xux xxx8/3ooo&#xt   → both heights = sqrt(3)/2 = 0.866025
(stop || pseudo (x,u)-stop || stop)

o.. o..8/3o..     | 16  *  * | 1  2  1  0  0 0  0 | 2 1  2 1 0  0 0 0 | 1 1 2 0 0
.o. .o.8/3.o.     |  * 16  * | 0  0  1  2  1 0  0 | 0 0  2 1 1  2 0 0 | 0 1 2 1 0
..o ..o8/3..o     |  *  * 16 | 0  0  0  0  1 1  2 | 0 0  0 1 0  2 2 1 | 0 0 2 1 1
------------------+----------+--------------------+-------------------+----------
x.. ...   ...     |  2  0  0 | 8  *  *  *  * *  * | 2 0  0 1 0  0 0 0 | 1 0 2 0 0
... x..   ...     |  2  0  0 | * 16  *  *  * *  * | 1 1  1 0 0  0 0 0 | 1 1 1 0 0
oo. oo.8/3oo.&#x  |  1  1  0 | *  * 16  *  * *  * | 0 0  2 1 0  0 0 0 | 0 1 2 0 0
... .x.   ...     |  0  2  0 | *  *  * 16  * *  * | 0 0  1 0 1  1 0 0 | 0 1 1 1 0
.oo .oo8/3.oo&#x  |  0  1  1 | *  *  *  * 16 *  * | 0 0  0 1 0  2 0 0 | 0 0 2 1 0
..x ...   ...     |  0  0  2 | *  *  *  *  * 8  * | 0 0  0 1 0  0 2 0 | 0 0 2 0 1
... ..x   ...     |  0  0  2 | *  *  *  *  * * 16 | 0 0  0 0 0  1 1 1 | 0 0 1 1 1
------------------+----------+--------------------+-------------------+----------
x.. x..   ...     |  4  0  0 | 2  2  0  0  0 0  0 | 8 *  * * *  * * * | 1 0 1 0 0
... x..8/3o..     |  8  0  0 | 0  8  0  0  0 0  0 | * 2  * * *  * * * | 1 1 0 0 0
... xx.   ...&#x  |  2  2  0 | 0  1  2  1  0 0  0 | * * 16 * *  * * * | 0 1 1 0 0
xux ...   ...&#xt |  2  2  2 | 1  0  2  0  2 1  0 | * *  * 8 *  * * * | 0 0 2 0 0
... .x.8/3.o.     |  0  8  0 | 0  0  0  8  0 0  0 | * *  * * 2  * * * | 0 1 0 1 0
... .xx   ...&#x  |  0  2  2 | 0  0  0  1  2 0  1 | * *  * * * 16 * * | 0 0 1 1 0
..x ..x   ...     |  0  0  4 | 0  0  0  0  0 2  2 | * *  * * *  * 8 * | 0 0 1 0 1
... ..x8/3..o     |  0  0  8 | 0  0  0  0  0 0  8 | * *  * * *  * * 2 | 0 0 0 1 1
------------------+----------+--------------------+-------------------+----------
x.. x..8/3o..      16  0  0 | 8 16  0  0  0 0  0 | 8 2  0 0 0  0 0 0 | 1 * * * *
... xx.8/3oo.&#x    8  8  0 | 0  8  8  8  0 0  0 | 0 1  8 0 1  0 0 0 | * 2 * * *
xux xxx   ...&#xt   4  4  4 | 2  2  4  2  4 2  2 | 1 0  2 2 0  2 1 0 | * * 8 * *
... .xx8/3.oo&#x    0  8  8 | 0  0  0  8  8 0  8 | 0 0  0 0 1  8 0 1 | * * * 2 *
..x ..x8/3..o       0  0 16 | 0  0  0  0  0 8 16 | 0 0  0 0 0  0 8 2 | * * * * 1
or
o.. o..8/3o..      & | 32  * |  1  2  1  0 |  2 1  2 1 0 | 1 1 2
.o. .o.8/3.o.        |  * 16 |  0  0  2  2 |  0 0  4 1 1 | 0 2 2
---------------------+-------+-------------+-------------+------
x.. ...   ...      & |  2  0 | 16  *  *  * |  2 0  0 1 0 | 1 0 2
... x..   ...      & |  2  0 |  * 32  *  * |  1 1  1 0 0 | 1 1 1
oo. oo.8/3oo.&#x   & |  1  1 |  *  * 32  * |  0 0  2 1 0 | 0 1 2
... .x.   ...        |  0  2 |  *  *  * 16 |  0 0  2 0 1 | 0 2 1
---------------------+-------+-------------+-------------+------
x.. x..   ...      & |  4  0 |  2  2  0  0 | 16 *  * * * | 1 0 1
... x..8/3o..      & |  8  0 |  0  8  0  0 |  * 4  * * * | 1 1 0
... xx.   ...&#x   & |  2  2 |  0  1  2  1 |  * * 32 * * | 0 1 1
xux ...   ...&#xt    |  4  2 |  2  0  4  0 |  * *  * n * | 0 0 2
... .x.8/3.o.        |  0  8 |  0  0  0  8 |  * *  * * 2 | 0 2 0
---------------------+-------+-------------+-------------+------
x.. x..8/3o..      &  16  0 |  8 16  0  0 |  8 2  0 0 0 | 2 * *
... xx.8/3oo.&#x   &   8  8 |  0  8  8  8 |  0 1  8 0 1 | * 4 *
xux xxx   ...&#xt      8  4 |  4  4  8  2 |  2 0  4 2 0 | * * 8

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