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