Acronym	sodip, K-4.70
Name	square - octagon duoprism
Circumradius	sqrt[(3+sqrt(2))/2] = 1.485633
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Confer	general duoprisms: 4,n-dip   4,2n-dip   8,n-dip   n,m-dip   2n,m-dip   2n,2m-dip   compounds: odop
External links

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

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

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