Acronym sodip, K-4.70
Name square - octagon duoprism
 
Circumradius sqrt[(3+sqrt(2))/2] = 1.485633
Coordinates ((1+sqrt(2))/2, 1/2, 1/2, 1/2)   & permutations in first 2 coordinates, all changes of sign
Volume 2[1+sqrt(2)] = 4.828427
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {4} between cube and cube:   135°
  • at {4} between cube and op:   90°
  • at {8} between op and op:   90°
Face vector 32, 64, 44, 12
Confer
general duoprisms:
4,n-dip   4,2n-dip   8,n-dip   n,m-dip   2n,m-dip   2n,2m-dip  
compounds:
sople  
related CRFs:
bicyte ausodip  
general polytopal classes:
Wythoffian polychora   segmentochora   bistratic lace towers  
External
links 		hedrondude   wikipedia   polytopewiki

As abstract polychoron sodip is isomorphic to sistodip, thereby replacing the octagons by octagrams, resp. replacing op by stop.


Incidence matrix according to Dynkin symbol

x4o x8o

. . . . | 32 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 32  * | 1  2 0 | 2 1
. . x . |  2 |  * 32 | 0  2 1 | 1 2
--------+----+-------+--------+----
x4o . . |  4 |  4  0 | 8  * * | 2 0
x . x . |  4 |  2  2 | * 32 * | 1 1
. . x8o |  8 |  0  8 | *  * 4 | 0 2
--------+----+-------+--------+----
x4o x . ♦  8 |  8  4 | 2  4 0 | 8 *
x . x8o ♦ 16 |  8 16 | 0  8 2 | * 4


x4o x8/7o

. . .   . | 32 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 32  * | 1  2 0 | 2 1
. . x   . |  2 |  * 32 | 0  2 1 | 1 2
----------+----+-------+--------+----
x4o .   . |  4 |  4  0 | 8  * * | 2 0
x . x   . |  4 |  2  2 | * 32 * | 1 1
. . x8/7o |  8 |  0  8 | *  * 4 | 0 2
----------+----+-------+--------+----
x4o x   . ♦  8 |  8  4 | 2  4 0 | 8 *
x . x8/7o ♦ 16 |  8 16 | 0  8 2 | * 4


x4/3o x8o

.   . . . | 32 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x   . . . |  2 | 32  * | 1  2 0 | 2 1
.   . x . |  2 |  * 32 | 0  2 1 | 1 2
----------+----+-------+--------+----
x4/3o . . |  4 |  4  0 | 8  * * | 2 0
x   . x . |  4 |  2  2 | * 32 * | 1 1
.   . x8o |  8 |  0  8 | *  * 4 | 0 2
----------+----+-------+--------+----
x4/3o x . ♦  8 |  8  4 | 2  4 0 | 8 *
x   . x8o ♦ 16 |  8 16 | 0  8 2 | * 4


x4/3o x8/7o

.   . .   . | 32 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 32  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 32 | 0  2 1 | 1 2
------------+----+-------+--------+----
x4/3o .   . |  4 |  4  0 | 8  * * | 2 0
x   . x   . |  4 |  2  2 | * 32 * | 1 1
.   . x8/7o |  8 |  0  8 | *  * 4 | 0 2
------------+----+-------+--------+----
x4/3o x   . ♦  8 |  8  4 | 2  4 0 | 8 *
x   . x8/7o ♦ 16 |  8 16 | 0  8 2 | * 4


x x x8o

. . . . | 32 |  1  1  2 | 1  2  2 1 | 2 1 1
--------+----+----------+-----------+------
x . . . |  2 | 16  *  * | 1  2  0 0 | 2 1 0
. x . . |  2 |  * 16  * | 1  0  2 0 | 2 0 1
. . x . |  2 |  *  * 32 | 0  1  1 1 | 1 1 1
--------+----+----------+-----------+------
x x . . |  4 |  2  2  0 | 8  *  * * | 2 0 0
x . x . |  4 |  2  0  2 | * 16  * * | 1 1 0
. x x . |  4 |  0  2  2 | *  * 16 * | 1 0 1
. . x8o |  8 |  0  0  8 | *  *  * 4 | 0 1 1
--------+----+----------+-----------+------
x x x . ♦  8 |  4  4  4 | 2  2  2 0 | 8 * *
x . x8o ♦ 16 |  8  0 16 | 0  8  0 2 | * 2 *
. x x8o ♦ 16 |  0  8 16 | 0  0  8 2 | * * 2


x4o x4x

. . . . | 32 |  2  1  1 | 1  2  2 1 | 1 1 2
--------+----+----------+-----------+------
x . . . |  2 | 32  *  * | 1  1  1 0 | 1 1 1
. . x . |  2 |  * 16  * | 0  2  0 1 | 1 0 2
. . . x |  2 |  *  * 16 | 0  0  2 1 | 0 1 2
--------+----+----------+-----------+------
x4o . . |  4 |  4  0  0 | 8  *  * * | 1 1 0
x . x . |  4 |  2  2  0 | * 16  * * | 1 0 1
x . . x |  4 |  2  0  2 | *  * 16 * | 0 1 1
. . x4x |  8 |  0  4  4 | *  *  * 4 | 0 0 2
--------+----+----------+-----------+------
x4o x . ♦  8 |  8  4  0 | 2  4  0 0 | 4 * *
x4o . x ♦  8 |  8  0  4 | 2  0  4 0 | * 4 *
x . x4x ♦ 16 |  8  8  8 | 0  4  4 2 | * * 4

snubbed forms: s4o2s4x


x x x4x

. . . . | 32 |  1  1  1  1 | 1 1 1 1 1 1 | 1 1 1 1
--------+----+-------------+-------------+--------
x . . . |  2 | 16  *  *  * | 1 1 1 0 0 0 | 1 1 1 0
. x . . |  2 |  * 16  *  * | 1 0 0 1 1 0 | 1 1 0 1
. . x . |  2 |  *  * 16  * | 0 1 0 1 0 1 | 1 0 1 1
. . . x |  2 |  *  *  * 16 | 0 0 1 0 1 1 | 0 1 1 1
--------+----+-------------+-------------+--------
x x . . |  4 |  2  2  0  0 | 8 * * * * * | 1 1 0 0
x . x . |  4 |  2  0  2  0 | * 8 * * * * | 1 0 1 0
x . . x |  4 |  2  0  0  2 | * * 8 * * * | 0 1 1 0
. x x . |  4 |  0  2  2  0 | * * * 8 * * | 1 0 0 1
. x . x |  4 |  0  2  0  2 | * * * * 8 * | 0 1 0 1
. . x4x |  8 |  0  0  4  4 | * * * * * 4 | 0 0 1 1
--------+----+-------------+-------------+--------
x x x . ♦  8 |  4  4  4  0 | 2 2 0 2 0 0 | 4 * * *
x x . x ♦  8 |  4  4  0  4 | 2 0 2 0 2 0 | * 4 * *
x . x4x ♦ 16 |  8  0  8  8 | 0 4 4 0 0 2 | * * 2 *
. x x4x ♦ 16 |  0  8  8  8 | 0 0 0 4 4 2 | * * * 2

snubbed forms: s2s2s4x, s2x2s4x


xx xx8oo&#x   → height = 1
(op || op)

o. o. o.    | 16  * | 1  2  1 0  0 | 2 1 1  2 0 0 | 1 2 1 0
.o .o .o    |  * 16 | 0  0  1 1  2 | 0 0 1  2 2 1 | 0 2 1 1
------------+-------+--------------+--------------+--------
x. .. ..    |  2  0 | 8  *  * *  * | 2 0 1  0 0 0 | 1 2 0 0
.. x. ..    |  2  0 | * 16  * *  * | 1 1 0  1 0 0 | 1 1 1 0
oo oo8oo&#x |  1  1 | *  * 16 *  * | 0 0 1  2 0 0 | 0 2 1 0
.x .. ..    |  0  2 | *  *  * 8  * | 0 0 1  0 2 0 | 0 2 0 1
.. .x ..    |  0  2 | *  *  * * 16 | 0 0 0  1 1 1 | 0 1 1 1
------------+-------+--------------+--------------+--------
x. x. ..    |  4  0 | 2  2  0 0  0 | 8 * *  * * * | 1 1 0 0
.. x.8o.    |  8  0 | 0  8  0 0  0 | * 2 *  * * * | 1 0 1 0
xx .. ..&#x |  2  2 | 1  0  2 1  0 | * * 8  * * * | 0 2 0 0
.. xx ..&#x |  2  2 | 0  1  2 0  1 | * * * 16 * * | 0 1 1 0
.x .x ..    |  0  4 | 0  0  0 2  2 | * * *  * 8 * | 0 1 0 1
.. .x8.o    |  0  8 | 0  0  0 0  8 | * * *  * * 2 | 0 0 1 1
------------+-------+--------------+--------------+--------
x. x.8o.    ♦ 16  0 | 8 16  0 0  0 | 8 2 0  0 0 0 | 1 * * *
xx xx ..&#x ♦  4  4 | 2  2  4 2  2 | 1 0 2  2 1 0 | * 8 * *
.. xx8oo&#x ♦  n  8 | 0  8  8 0  8 | 0 1 0  8 0 1 | * * 2 *
.x .x8.o    ♦  0 16 | 0  0  0 8 16 | 0 0 0  0 8 2 | * * * 1


xxx8ooo oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
({8} || pseudo (x,q)-op || {8})

o..8o.. o..     | 8  * * | 2  2  0  0 0 | 1  4 1 0  0 0 | 2 2 0
.o.8.o. .o.     | * 16 * | 0  1  2  1 0 | 0  2 1 1  2 0 | 1 2 1
..o8..o ..o     | *  * 8 | 0  0  0  2 2 | 0  0 1 0  4 1 | 0 2 2
----------------+--------+--------------+---------------+------
x.. ... ...     | 2  0 0 | 8  *  *  * * | 1  2 0 0  0 0 | 2 1 0
oo.8oo. oo.&#x  | 1  1 0 | * 16  *  * * | 0  2 1 0  0 0 | 1 2 0
.x. ... ...     | 0  2 0 | *  * 16 *  * | 0  1 0 1  1 0 | 1 1 1
.oo8.oo .oo&#x  | 0  1 1 | *  *  * 16 * | 0  0 1 0  2 0 | 0 2 1
..x ... ...     | 0  0 2 | *  *  *  * 8 | 0  0 0 0  2 1 | 0 1 2
----------------+--------+--------------+---------------+------
x..8o.. ...     | 8  0 0 | 8  0  0  0 0 | 1  * * *  * * | 2 0 0
xx. ... ...&#x  | 2  2 0 | 1  2  1  0 0 | * 16 * *  * * | 1 1 0
... ... oqo&#xt | 1  2 1 | 0  2  0  2 0 | *  * 8 *  * * | 0 2 0
.x.8.o. ...     | 0  8 0 | 0  0  8  0 0 | *  * * 2  * * | 1 0 1
.xx ... ...&#x  | 0  2 2 | 0  0  1  2 1 | *  * * * 16 * | 0 1 1
..x8..o ...     | 0  0 8 | 0  0  0  0 8 | *  * * *  * 1 | 0 0 2
----------------+--------+--------------+---------------+------
xx.8oo. ...&#x  ♦ 8  8 0 | 8  8  8  0 0 | 1  8 0 1  0 0 | 2 * *
xxx ... oqo&#xt ♦ 2  4 2 | 1  4  2  4 1 | 0  2 2 0  2 0 | * 8 *
.xx8.oo ...&#x  ♦ 0  8 8 | 0  0  8  8 8 | 0  0 0 1  8 1 | * * 2


xxx4xxx oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
({8} || pseudo (x,x,q)-op || {8})

o..4o.. o..     | 8  * * | 1 1  2 0 0  0 0 0 | 1 2 2 1 0 0 0 0 | 2 1 1 0
.o.4.o. .o.     | * 16 * | 0 0  1 1 1  1 0 0 | 0 1 1 1 1 1 1 0 | 1 1 1 1
..o4..o ..o     | *  * 8 | 0 0  0 0 0  2 1 1 | 0 0 0 1 0 2 2 1 | 0 1 1 2
----------------+--------+-------------------+-----------------+--------
x.. ... ...     | 2  0 0 | 4 *  * * *  * * * | 1 2 0 0 0 0 0 0 | 2 1 0 0
... x.. ...     | 2  0 0 | * 4  * * *  * * * | 1 0 2 0 0 0 0 0 | 2 0 1 0
oo.4oo. oo.&#x  | 1  1 0 | * * 16 * *  * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
.x. ... ...     | 0  2 0 | * *  * 8 *  * * * | 0 1 0 0 1 1 0 0 | 1 1 0 1
... .x. ...     | 0  2 0 | * *  * * 8  * * * | 0 0 1 0 1 0 1 0 | 1 0 1 1
.oo4.oo .oo&#x  | 0  1 1 | * *  * * * 16 * * | 0 0 0 1 0 1 1 0 | 0 1 1 1
..x ... ...     | 0  0 2 | * *  * * *  * 4 * | 0 0 0 0 0 2 0 1 | 0 1 0 2
... ..x ...     | 0  0 2 | * *  * * *  * * 4 | 0 0 0 0 0 0 2 1 | 0 0 1 2
----------------+--------+-------------------+-----------------+--------
x..4x.. ...     | 8  0 0 | 4 4  0 0 0  0 0 0 | 1 * * * * * * * | 2 0 0 0
xx. ... ...&#x  | 2  2 0 | 1 0  2 1 0  0 0 0 | * 8 * * * * * * | 1 1 0 0
... xx. ...&#x  | 2  2 0 | 0 1  2 0 1  0 0 0 | * * 8 * * * * * | 1 0 1 0
... ... oqo&#xt | 1  2 1 | 0 0  2 0 0  2 0 0 | * * * 8 * * * * | 0 1 1 0
.x.4.x. ...     | 0  8 0 | 0 0  0 4 4  0 0 0 | * * * * 2 * * * | 1 0 0 1
.xx ... ...&#x  | 0  2 2 | 0 0  0 1 0  2 1 0 | * * * * * 8 * * | 0 1 0 1
... .xx ...&#x  | 0  2 2 | 0 0  0 0 1  2 0 1 | * * * * * * 8 * | 0 0 1 1
..x4..x ...     | 0  0 8 | 0 0  0 0 0  0 4 4 | * * * * * * * 1 | 0 0 0 2
----------------+--------+-------------------+-----------------+--------
xx.4xx. ...&#x  ♦ 8  8 0 | 4 4  8 4 4  0 0 0 | 1 4 4 0 1 0 0 0 | 2 * * *
xxx ... oqo&#xt ♦ 2  4 2 | 1 0  4 2 0  4 1 0 | 0 2 0 2 0 2 0 0 | * 4 * *
... xxx oqo&#xt ♦ 2  4 2 | 0 1  4 0 2  4 0 1 | 0 0 2 2 0 0 2 0 | * * 4 *
.xx3.xx ...&#x  ♦ 0  8 8 | 0 0  0 4 4  8 4 4 | 0 0 0 0 1 4 4 1 | * * * 2

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