Acronym | n/d-p | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
TOCID symbol | (n/d)P | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Name |
n/d-prism, n-prism with winding number d | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Circumradius | sqrt[1/4+1/(4 sin^{2}(π d/n))] | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Vertex figure | [4^{2},n/d] | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
General of army |
if d=1: is itself convex if gcd(n,d)=k: use a (stretched) m-p for its general (with integral m=n/k) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment | (is itself locally convex) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Especially |
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Confer |
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External links |
Note that for d odd the 2 n/d-gram layers are aligned in a gyrated way, which then effects that top and bottom vertices are situated on gap. While for d even the 2 n/d-gram layers are still aligned in a gyrated way, but this time it effects in a seeming ungyrated parallel alignment, just like in the mere n/d-p, but now with crossed lacings, so that the according height becomes lesser than 1 here.
Incidence matrix according to Dynkin symbol
x xn/do (n>2,n/2>d>1) . . . | 2n | 1 2 | 2 1 --------+----+------+---- x . . | 2 | n * | 2 0 . x . | 2 | * 2n | 1 1 --------+----+------+---- x x . | 4 | 2 2 | n * . xn/do | n | 0 n | * 2
x2sn/ds (n>2,n/2>d>1) demi( . . . ) | 2n | 1 2 | 1 2 ----------------+----+------+---- demi( x . . ) | 2 | n * | 0 2 sefa( . sn/ds ) | 2 | * 2n | 1 1 ----------------+----+------+---- . sn/ds ♦ n | 0 n | 2 * sefa( x2sn/ds ) | 4 | 2 2 | * n starting figure: x xn/dx
x2s2n/do (n>2,n/2>d>1) demi( . . . ) | 2n | 1 2 | 1 2 -----------------+----+------+---- demi( x . . ) | 2 | n * | 0 2 sefa( . s2n/do ) | 2 | * 2n | 1 1 -----------------+----+------+---- . s2n/do ♦ n | 0 n | 2 * sefa( x2s2n/do ) | 4 | 2 2 | * n starting figure: x x2n/do
xxn/doo&#x (n>2,n/2>d>1) → height = 1
({n/d} || {n/d})
o.n/do. | n * | 2 1 0 | 1 2 0
.on/d.o | * n | 0 1 2 | 0 2 1
-----------+-----+-------+------
x. .. | 2 0 | n * * | 1 1 0
oon/doo&#x | 1 1 | * n * | 0 2 0
.x .. | 0 2 | * * n | 0 1 1
-----------+-----+-------+------
x.n/do. | n 0 | n 0 0 | 1 * *
xx ..&#x | 2 2 | 1 2 1 | * n *
.xn/d.o | 0 n | 0 0 n | * * 1
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