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if gcd(n,d)=1: then d=1 provides a topological variant of its general
| Acronym | n/d-py |
| Name | n/d-gonal pyramid |
| |
| Circumradius | 1/sqrt[4-1/sin2(πd/n)] |
| Vertex figures | [3n]/d, [3,3,n/d] |
| General of army |
if d=1: is itself convex if gcd(n,d)=1: then d=1 provides a topological variant of its general |
| Colonel of regiment | (is itself locally convex) |
| Dual | (topologically selfdual, in different orientation) |
| Face vector | n+1, 2n, n+1 |
| Especially | tet (n=3, d=1) squippy (n=4, d=1) peppy (n=5, d=1) stappy (n=5, d=2) hippy (n=6, d=1) shappy (n=7, d=2) ogpy (n=8, d=3) degpy (n=10, d=3) |
The height formula given below shows that only 2 < n/d < 6 is possible. The maximal height would be obtained at n/d = 2 with upright latteral triangles, the other extremal value n/d = 6 would generate a height of zero.
Incidence matrix according to Dynkin symbol
oxn/doo&#x (2<n/d<6) → height = sqrt(1-1/[4 sin2(π d/n)])
(pt || {n/d})
tip o. o. | 1 * | 4 0 | 4 0
base .o .o | * n | 1 2 | 2 1
----------------+-----+-----+----
lace oon/doo&#x | 1 1 | n * | 2 0
base .x .. | 0 2 | * n | 1 1
----------------+-----+-----+----
coat ox ..&#x | 1 2 | 2 1 | n *
base .xn/d.o | 0 n | 0 n | * 1
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