Acronym	2n,m-dip
Name	2n-gonal - m-gonal duoprism
Circumradius	sqrt[1/(4 sin2(π/2n))+1/(4 sin2(π/m))]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Face vector	2nm, 4nm, 2nm+2n+m, 2n+m
Especially	4,2m-dip (m=4)   4,m-dip (n=2)   6,m-dip (n=3)   8,m-dip (n=4)   10,m-dip (n=5)   12,m-dip (n=6)   2n,4-dip (m=4)   2 3 4 5 6 {2n} x {m} tisdip thiddip todip tradedip titwadip 3 tes shiddip sodip squadedip sitwadip 4 squipdip phiddip podip padedip pitwadip 5 shiddip hiddip hodip hadedip hitwadip 6 squahedip haheddip heodip hedadip hetwadip 7 sodip hodip odip odedip otwadip 8 sendip hendip oedip edidip etwadip 9 squadedip hadedip odedip dedip datwadip 10 sitwadip hitwadip otwadip datwadip twaddip 12
Confer	general duoprisms: n,m-dip   2n,2m-dip   n/d,m/b-dip   n/d,2n/d-dip   general polytopal classes: Wythoffian polychora
External links

Although in here n>1 is allowed, snubbing links require n>2 generally. Nonetheless, s4o2s4o well is possible too (it even becomes a regular polychoron), it just has a different incidence structure because of degeneracies.

Incidence matrix according to Dynkin symbol

x2no xmo (n>1,m>2)

.  . . . | 2nm |   2   2 | 1   4  1 | 2  2
---------+-----+---------+----------+-----
x  . . . |   2 | 2nm   * | 1   2  0 | 2  1
.  . x . |   2 |   * 2nm | 0   2  1 | 1  2
---------+-----+---------+----------+-----
x2no . . |  2n |  2n   0 | m   *  * | 2  0
x  . x . |   4 |   2   2 | * 2nm  * | 1  1
.  . xmo |   m |   0   m | *   * 2n | 0  2
---------+-----+---------+----------+-----
x2no x . ♦  4n |  4n  2n | 2  2n  0 | m  *
x  . xmo ♦  2m |   m  2m | 0   m  2 | * 2n

snubbed forms: s2no2smo (for n>2 and even m>2)

xnx xmo (n>1,m>2)

. . . . | 2nm |  1  1   2 | 1  2  2  1 | 2 1 1
--------+-----+-----------+------------+------
x . . . |   2 | nm  *   * | 1  2  0  0 | 2 1 0
. x . . |   2 |  * nm   * | 1  0  2  0 | 2 0 1
. . x . |   2 |  *  * 2nm | 0  1  1  1 | 1 1 1
--------+-----+-----------+------------+------
xnx . . |  2n |  n  n   0 | m  *  *  * | 2 0 0
x . x . |   4 |  2  0   2 | * nm  *  * | 1 1 0
. x x . |   4 |  0  2   2 | *  * nm  * | 1 0 1
. . xmo |   m |  0  0   m | *  *  * 2n | 0 1 1
--------+-----+-----------+------------+------
xnx x . ♦  4n | 2n 2n  2n | 2  n  n  0 | m * *
x . xmo ♦  2m |  m  0  2m | 0  m  0  2 | * n *
. x xmo ♦  2m |  0  m  2m | 0  0  m  2 | * * n

snubbed forms: snx2xmo (for even n>2 and m>2)