Acronym n,m-dafup
Name (n,m)-duoantifastegiaprism,
(n,m)-dip atop bidual (n,m)-dip
Circumradius sqrt([2+1/(1-cos(pi/n))+1/(1-cos(pi/m))]/8)
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  

* 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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