Acronym n,m-dip
Name n-gon - m-gon duoprism
 
 ©
Circumradius sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))]
Volume nm/[16 tan(π/n) tan(π/m)]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Face vector nm, 2nm, nm+n+m, n+m
Especially n,n-dip   2n,m-dip   2n,2m-dip   3,m-dip (n=3)   4,m-dip (n=4)   4,2m-dip (n=4)   5,m-dip (n=5)   6,m-dip (n=6)   8,m-dip (n=8)   10,m-dip (n=10)   12,m-dip (n=12)   ∞,m-dip (n=∞)   squat (n=∞, m=∞)  
3 4 5 6 7 8 9 10 12 {n} x {m}
triddip tisdip trapedip thiddip theddip todip tedip tradedip titwadip 3
  tes (squadip) squipdip shiddip squahedip sodip sendip squadedip sitwadip 4
    pedip phiddip pheddip podip peendip padedip pitwadip 5
      hiddip haheddip hodip hendip hadedip hitwadip 6
        hedip heodip heendip hedadip hetwadip 7
          odip oedip odedip otwadip 8
            edip edidip etwadip 9
              dedip datwadip 10
                twaddip 12
Confer
general duoprisms:
n/d,m/b-dip  
general polytopal classes:
Wythoffian polychora   noble polytopes (for n = m only)  
External
links
hedrondude   wikipedia   quickfur

Incidence matrix according to Dynkin symbol

xno xmo   (n>2,m>2)

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

snubbed forms: sno2smo (for even n>2, even m>2)

© 2004-2024
top of page