Acronym  nap 
Name  ngonal antiprism 
© ©  
Circumradius  sqrt[(32 cos(π/n))/(88 cos(π/n))] 
Height  sqrt[(1+2 cos(π/n))/(2+2 cos(π/n))] 
Coordinates 
(cos(k π/n)/[2 sin(π/n)], sin(k π/n)/[2 sin(π/n)], (1)^{k} h/2) all k integral where h is the height given above 
Vertex figure  [3^{3},n] 
Snub derivation 

General of army  (is itself convex) 
Colonel of regiment  (is itself locally convex) 
Especially  tet (n=2)* oct (n=3) squap (n=4) pap (n=5) hap (n=6) oap (n=8) dap (n=10) azap (n=∞) 
Dihedral angles 

Confer 

External links 
* The case n=2 equally would be considerable here by concept, it just has a different incidence matrix as the ngons become degenerate.
The compound of 2 mutually gyrated ngonal antiprisms, one considered as xonox&#x, the other as oxnxo&#x, has for encasing convex hull a variant of the 2ngonal prism, in fact the variant a2no b, where a = 1/[2 cos(π/2n)] and b = sqrt[1  1/[2 cos(π/2n)]^{2}] = sqrt[(1+2 cos(π/n))/(2+2 cos(π/n))]. This is how the below mentioned semiation as a vertex alternation (snubbing) truely works (when resizing would be considered first).
Incidence matrix according to Dynkin symbol
s2sns (n>2) demi( . . . )  2n  1 1 2  1 3 +++ s2s .  2  n * *  0 2 s . s2*a  2  * n *  0 2 sefa( . sns )  2  * * 2n  1 1 +++ . sns ♦ n  0 0 n  2 * sefa( s2sns )  3  1 1 1  * 2n starting figure: x xnx
s2s2no (n>2) demi( . . . )  2n  2 2  1 3 +++ s2s .  2  2n *  0 2 sefa( . s2no )  2  * 2n  1 1 +++ . s2no ♦ n  0 n  2 * sefa( s2s2no )  3  2 1  * 2n starting figure: x x2no
xonox&#x (n>2) → height = sqrt[(1+2 cos(π/n))/(2+2 cos(π/n))]
({n}  dual {n})
o.no.  n *  2 2 0  1 2 1 0
.on.o  * n  0 2 2  0 1 2 1
+++
x. ..  2 0  n * *  1 1 0 0
oonoo&#x  1 1  * 2n *  0 1 1 0
.. .x  0 2  * * n  0 0 1 1
+++
x.no.  n 0  n 0 0  1 * * *
xo ..&#x  2 1  1 2 0  * n * *
.. ox&#x  1 2  0 2 1  * * n *
.on.x  0 n  0 0 n  * * * 1
© 20042020  top of page 