Acronym | 2n-p |
TOCID symbol | (2n)P, t(n)P |
Name | 2n-gonal prism |
Circumradius | sqrt[1/4+1/(4 sin2(π/2n))] |
Vertex figure | [42,2n] |
Snub derivation |
|
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Face vector | 4n, 6n, 2n+2 |
Especially | cube (n=2) hip (n=3) op (n=4) dip (n=5) twip (n=6) azip (n=∞) |
Confer |
|
External links |
Although in here n>1 is allowed, snubbing links require n>2 generally. Nonetheless, s2s4o well is possible too (it even becomes a regular polyhedron), it just has a different incidence structure because of degeneracies.
Incidence matrix according to Dynkin symbol
x x2no (n>1) . . . | 4n | 1 2 | 2 1 -------+----+-------+----- x . . | 2 | 2n * | 2 0 . x . | 2 | * 4n | 1 1 -------+----+-------+----- x x . | 4 | 2 2 | 2n * . x2no | 2n | 0 2n | * 2 snubbed forms: x2s2no (for n>2), x2s2no (for even n>2), s2s2no (for n>2)
x xnx (n>1) . . . | 4n | 1 1 1 | 1 1 1 ------+----+----------+------ x . . | 2 | 2n * * | 1 1 0 . x . | 2 | * 2n * | 1 0 1 . . x | 2 | * * 2n | 0 1 1 ------+----+----------+------ x x . | 4 | 2 2 0 | n * * x . x | 4 | 2 0 2 | * n * . xnx | 2n | 0 n n | * * 2 snubbed forms: x2βnx (for n>2), x2snx (for even n>2), β2βnx (for n>2), s2snx (for even n>2), x2sns (for n>2), x2sns (for even n>2), s2sns (for n>2)
s2s2nx (n>1) demi( . . . ) | 4n | 1 1 1 | 1 2 ---------------+----+----------+----- s2s | 2 | 2n * * | 0 2 demi( . . x ) | 2 | * 2n * | 1 1 sefa( . s2nx ) | 2 | * * 2n | 1 1 ---------------+----+----------+----- s2nx ♦ 2n | 0 n n | 2 * sefa( s2s2nx ) | 4 | 2 1 1 | * 2n starting figure: x x2nx
x2s2nx (n>1) demi( . . . ) | 4n | 1 1 1 | 1 1 1 ---------------+----+----------+------ demi( x . . ) | 2 | 2n * * | 0 1 1 demi( . . x ) | 2 | * 2n * | 1 1 0 sefa( . s2nx ) | 2 | * * 2n | 1 0 1 ---------------+----+----------+------ . s2nx ♦ 2n | 0 n n | 2 * * demi( x . x ) | 4 | 2 2 0 | * n * sefa( x2s2nx ) | 4 | 2 0 2 | * * n starting figure: x x2nx
x2s2ns (n>1) demi( . . . ) | 4n | 1 2 | 1 2 ---------------+----+-------+----- demi( x . . ) | 2 | 2n * | 0 2 sefa( . s2ns ) | 2 | * 4n | 1 1 ---------------+----+-------+----- . s2ns ♦ 2n | 0 2n | 2 * sefa( x2s2ns ) | 4 | 2 2 | * 2n starting figure: x x2nx
x2s4no (n>1) demi( . . . ) | 4n | 1 2 | 1 2 ---------------+----+-------+----- demi( x . . ) | 2 | 2n * | 0 2 sefa( . s4no ) | 2 | * 4n | 1 1 ---------------+----+-------+----- . s4no ♦ 2n | 0 2n | 2 * sefa( x2s4no ) | 4 | 2 2 | * 2n starting figure: x x4no
xx2noo&#x (n>1) → height = 1
({2n} || {2n})
o.2no. | 2n * | 2 1 0 | 1 2 0
.o2n.o | * 2n | 0 1 2 | 0 2 1
----------+-------+----------+-------
x. .. | 2 0 | 2n * * | 1 1 0
oo2noo&#x | 1 1 | * 2n * | 0 2 0
.x .. | 0 2 | * * 2n | 0 1 1
----------+-------+----------+-------
x.2no. | 2n 0 | 2n 0 0 | 1 * *
xx ..&#x | 2 2 | 1 2 1 | * 2n *
.x2n.o | 0 2n | 0 0 2n | * * 1
xxnxx&#x (n>1) → height = 1
({2n} || {2n})
o.no. | 2n * | 1 1 1 0 0 | 1 1 1 0
.on.o | * 2n | 0 0 1 1 1 | 0 1 1 1
---------+-------+------------+--------
x. .. | 2 0 | n * * * * | 1 1 0 0
.. x. | 2 0 | * n * * * | 1 0 1 0
oonoo&#x | 1 1 | * * 2n * * | 0 1 1 0
.x .. | 0 2 | * * * n * | 0 1 0 1
.. .x | 0 2 | * * * * n | 0 0 1 1
---------+-------+------------+--------
x.nx. | 2n 0 | n n 0 0 0 | 1 * * *
xx ..&#x | 2 2 | 1 0 2 1 0 | * n * *
.. xx&#x | 2 2 | 0 1 2 0 1 | * * n *
.xn.x | 0 2n | 0 0 0 n n | * * * 1
© 2004-2024 | top of page |