Acronym n,m-dafup
Name (n,m)-duoantifastegiaprism,
(n,m)-duoantiwedge,
(n,m)-dip atop bidual (n,m)-dip
Circumradius sqrt([2+1/(1-cos(pi/n))+1/(1-cos(pi/m))]/8)
Face vector 2nm, 8nm, 10nm+2n+2m, 4nm+4n+4m, 2n+2m+2
Especially n-daf (m=2)*
3 4 5 6 7 8 9 10  
tridafup tisdafup tapdafup
(tipdafup)
thidafup thedafup todafup tedafup tridadafup
(tidadafup)
3
  squidafup squipdafup
(sipdafup)
shidafup shedafup sodafup sendafup
(sedafup)
squadadafup
(sidadafup)
4
    pedafup phidafup phedafup podafup peendafup padedafup
(pedadafup)
5
      hidafup hahedafup hodafup hendafup hadedafup
(hidadafup)
6
        hedafup heodafup heendafup hedadafup 7
          odafup oedafup odidafup 8
            edafup edidafup 9
              dedafup 10
Confer
general polytopal classes:
segmentotera   scaliform  
External
links
polytopewiki  

* The case m=2 (n-daf) would be included here by concept. But the m-gons – and thus also the base polytopes – then become degenerate. Therefore they would require for a different incidence matrix. This degeneracy of the second prism type of the duoprismatic bases then is what reduces there the prism suffix in the name too.


Incidence matrix according to Dynkin symbol

xo-n-ox xo-m-ox&#x   → height = sqrt([2-1/(1+cos(pi/n))-1/(1+cos(pi/m))]/2)
((n,m)-dip || bidual (n,m)-dip)

o.-n-o. o.-m-o.    | nm  * |  2  2   4  0  0 | 1  4 1   4   2   4   2 0  0 0 | 2 2  2  4  2  2  1  2 0 0 | 1 2 1 2 1 0
.o-n-.o .o-m-.o    |  * nm |  0  0   4  2  2 | 0  0 0   2   4   2   4 1  4 1 | 0 0  2  1  2  2  4  2 2 2 | 0 1 2 1 2 1
-------------------+-------+-----------------+-------------------------------+---------------------------+------------
x.   .. ..   ..    |  2  0 | nm  *   *  *  * | 1  2 0   2   0   0   0 0  0 0 | 2 1  2  2  1  0  0  0 0 0 | 1 2 1 1 0 0
..   .. x.   ..    |  2  0 |  * nm   *  *  * | 0  2 1   0   0   2   0 0  0 0 | 1 2  0  2  0  1  0  2 0 0 | 1 1 0 2 1 0
oo-n-oo oo-m-oo&#x |  1  1 |  *  * 4nm  *  * | 0  0 0   1   1   1   1 0  0 0 | 0 0  1  1  1  1  1  1 0 0 | 0 1 1 1 1 0
..   .x ..   ..    |  0  2 |  *  *   * nm  * | 0  0 0   0   2   0   0 1  2 0 | 0 0  2  0  0  1  2  0 2 1 | 0 1 2 0 1 1
..   .. ..   .x    |  0  2 |  *  *   *  * nm | 0  0 0   0   0   0   2 0  2 1 | 0 0  0  0  1  0  2  2 1 2 | 0 0 1 1 2 1
-------------------+-------+-----------------+-------------------------------+---------------------------+------------
x.-n-o. ..   ..    |  n  0 |  n  0   0  0  0 | m  * *   *   *   *   * *  * * | 2 0  2  0  0  0  0  0 0 0 | 1 2 1 0 0 0
x.   .. x.   ..    |  4  0 |  2  2   0  0  0 | * nm *   *   *   *   * *  * * | 1 1  0  1  0  0  0  0 0 0 | 1 1 0 1 0 0
..   .. x.-m-o.    |  m  0 |  0  m   0  0  0 | *  * n   *   *   *   * *  * * | 0 2  0  0  0  0  0  2 0 0 | 1 0 0 2 1 0
xo   .. ..   ..&#x |  2  1 |  1  0   2  0  0 | *  * * 2nm   *   *   * *  * * | 0 0  1  1  1  0  0  0 0 0 | 0 1 1 1 0 0
..   ox ..   ..&#x |  1  2 |  0  0   2  1  0 | *  * *   * 2nm   *   * *  * * | 0 0  1  0  0  1  1  0 0 0 | 0 1 1 0 1 0
..   .. xo   ..&#x |  2  1 |  0  1   2  0  0 | *  * *   *   * 2nm   * *  * * | 0 0  0  1  0  1  0  1 0 0 | 0 1 0 1 1 0
..   .. ..   ox&#x |  1  2 |  0  0   2  0  1 | *  * *   *   *   * 2nm *  * * | 0 0  0  0  1  0  1  1 0 0 | 0 0 1 1 1 0
.o-n-.x ..   ..    |  0  n |  0  0   0  n  0 | *  * *   *   *   *   * m  * * | 0 0  2  0  0  0  0  0 2 0 | 0 1 2 0 0 1
..   .x ..   .x    |  0  4 |  0  0   0  2  2 | *  * *   *   *   *   * * nm * | 0 0  0  0  0  0  1  0 1 1 | 0 0 1 0 1 1
..   .. .o-m-.x    |  0  m |  0  0   0  0  m | *  * *   *   *   *   * *  * n | 0 0  0  0  0  0  0  2 0 2 | 0 0 0 1 2 1
-------------------+-------+-----------------+-------------------------------+---------------------------+------------
x.-n-o. x.   ..     2n  0 | 2n  n   0  0  0 | 2  n 0   0   0   0   0 0  0 0 | m *  *  *  *  *  *  * * * | 1 1 0 0 0 0
x.   .. x.-m-o.     2m  0 |  m 2m   0  0  0 | 0  m 2   0   0   0   0 0  0 0 | * n  *  *  *  *  *  * * * | 1 0 0 1 0 0
xo-n-ox ..   ..&#x   n  n |  n  0  2n  n  0 | 1  0 0   n   n   0   0 1  0 0 | * * 2m  *  *  *  *  * * * | 0 1 1 0 0 0
xo   .. xo   ..&#x   4  1 |  2  2   4  0  0 | 0  1 0   2   0   2   0 0  0 0 | * *  * nm  *  *  *  * * * | 0 1 0 1 0 0
xo   .. ..   ox&#x   2  2 |  1  0   4  0  1 | 0  0 0   2   0   0   2 0  0 0 | * *  *  * nm  *  *  * * * | 0 0 1 1 0 0
..   ox xo   ..&#x   2  2 |  0  1   4  1  0 | 0  0 0   0   2   2   0 0  0 0 | * *  *  *  * nm  *  * * * | 0 1 0 0 1 0
..   ox ..   ox&#x   1  4 |  0  0   4  2  2 | 0  0 0   0   2   0   2 0  1 0 | * *  *  *  *  * nm  * * * | 0 0 1 0 1 0
..   .. xo-m-ox&#x   m  m |  0  m  2m  0  m | 0  0 1   0   0   m   m 0  0 1 | * *  *  *  *  *  * 2n * * | 0 0 0 1 1 0
.o-n-.x ..   .x      0  6 |  0  0   0  6  3 | 0  0 0   0   0   0   0 2  3 0 | * *  *  *  *  *  *  * m * | 0 0 1 0 0 1
..   .x .o-m-.x      0  6 |  0  0   0  3  6 | 0  0 0   0   0   0   0 0  3 2 | * *  *  *  *  *  *  * * n | 0 0 0 0 1 1
-------------------+-------+-----------------+-------------------------------+---------------------------+------------
x.-n-o. x.-m-o.     nm  0 | nm nm   0  0  0 | m nm n   0   0   0   0 0  0 0 | m n  0  0  0  0  0  0 0 0 | 1 * * * * *
xo-n-ox xo   ..&#x  2n  n | 2n  n  4n  n  0 | 2  n 0  2n  2n  2n   0 1  0 0 | 1 0  2  n  0  n  0  0 0 0 | * m * * * *
xo-n-ox ..   ox&#x   n 2n |  n  0  4n 2n  n | 1  0 0  2n  2n   0  2n 2  n 0 | 0 0  2  0  n  0  n  0 1 0 | * * m * * *
xo   .. xo-m-ox&#x  2m  m |  m 2m  4m  0  m | 0  m 2  2m   0  2m  2m 0  0 1 | 0 1  0  m  m  0  0  2 0 0 | * * * n * *
..   ox xo-m-ox&#x   m 2m |  0  m  4m  m 2m | 0  0 1   0  2m  2m  2m 0  m 2 | 0 0  0  0  0  m  m  2 0 1 | * * * * n *
.o-n-.x .o-m-.x      0 nm |  0  0   0 nm nm | 0  0 0   0   0   0   0 m nm n | 0 0  0  0  0  0  0  0 m n | * * * * * 1
or
o.-n-o. o.-m-o.    & | 2nm |   2   2   4 |  1   4  1   6   6 |  2  2  2   5   4  2 | 1  3  3
---------------------+-----+-------------+-------------------+---------------------+--------
x.   .. ..   ..    & |   2 | 2nm   *   * |  1   2  0   2   0 |  2  1  2   2   1  0 | 1  3  1
..   .. x.   ..    & |   2 |   * 2nm   * |  0   2  1   0   2 |  1  2  0   2   1  2 | 1  1  3
oo-n-oo oo-m-oo&#x   |   2 |   *   * 4nm |  0   0  0   2   2 |  0  0  1   2   2  1 | 0  2  2
---------------------+-----+-------------+-------------------+---------------------+--------
x.-n-o. ..   ..    & |   n |   n   0   0 | 2m   *  *   *   * |  2  0  2   0   0  0 | 1  3  0
x.   .. x.   ..    & |   4 |   2   2   0 |  * 2nm  *   *   * |  1  1  0   1   0  0 | 1  1  1
..   .. x.-m-o.    & |   m |   0   m   0 |  *   * 2n   *   * |  0  2  0   0   0  2 | 1  0  3
xo   .. ..   ..&#x & |   3 |   1   0   2 |  *   *  * 4nm   * |  0  0  1   1   1  0 | 0  2  1
..   .. xo   ..&#x & |   3 |   0   1   2 |  *   *  *   * 4nm |  0  0  0   1   1  1 | 0  1  2
---------------------+-----+-------------+-------------------+---------------------+--------
x.-n-o. x.   ..    &   2n |  2n   n   0 |  2   n  0   0   0 | 2m  *  *   *   *  * | 1  1  0
x.   .. x.-m-o.    &   2m |   m  2m   0 |  0   m  2   0   0 |  * 2n  *   *   *  * | 1  0  1
xo-n-ox ..   ..&#x     2n |  2n   0  2n |  2   0  0  2n   0 |  *  * 2m   *   *  * | 0  2  0
xo   .. xo   ..&#x &    5 |   2   2   4 |  0   1  0   2   2 |  *  *  * 2nm   *  * | 0  1  1
xo   .. ..   ox&#x &    4 |   1   1   4 |  0   0  0   2   2 |  *  *  *   * 2nm  * | 0  1  1
..   .. xo-m-ox&#x     2m |   0  2m  2m |  0   0  2   0  2m |  *  *  *   *   * 2n | 0  0  2
---------------------+-----+-------------+-------------------+---------------------+--------
x.-n-o. x.-m-o.    &   nm |  nm  nm   0 |  m  nm  n   0   0 |  m  n  0   0   0  0 | 2  *  *
xo-n-ox xo   ..&#x &   3n |  3n   n  4n |  3   n  0  4n  2n |  1  0  2   n   n  0 | * 2m  *
xo   .. xo-m-ox&#x &   3m |   m  3m  4m |  0   m  3  2m  4m |  0  1  0   m   m  2 | *  * 2n

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