in approx. ASCII-art
xNo xNo -- x xNo (N-p) oNx oNx -- x oNx (gyro N-p) | | | +-- s2sNs (N-ap) +-------- s2sNs (N-ap)
- general antiprism-prisms:
- n/d-appip
- general polytopal classes:
- segmentochora
links
| Acronym | n-appip, K-4.176 |
| Name | n-antiprism prism |
| Segmentochoron display |
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| Circumradius | sqrt[(5-4 cos(π/n))/(8-8 cos(π/n))] |
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Lace city in approx. ASCII-art |
xNo xNo -- x xNo (N-p) oNx oNx -- x oNx (gyro N-p) | | | +-- s2sNs (N-ap) +-------- s2sNs (N-ap) |
| Face vector | 4n, 10n, 8n+4, 2n+4 |
| Especially | ope (n=3) squappip (n=4) pappip (n=5) happip (n=6) heappip (n=7) oappip (n=8) eappip (n=9) dappip (n=10) |
| Confer |
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External links |
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n=2 would result in the tepe. But for sure the top resp. bottom face prisms then become degenerate and hence that one needs a different incidence matrix.
Incidence matrix according to Dynkin symbol
x s2sns (n>2) . demi( . . . ) | 4n | 1 1 1 2 | 1 1 1 2 3 | 1 1 3 ------------------+----+-------------+-------------+------- . s2s . | 2 | 2n * * * | 1 0 0 0 2 | 0 1 2 . s . s2*b | 2 | * 2n * * | 0 1 0 0 2 | 0 1 2 x demi( . . . ) | 2 | * * 2n * | 1 1 0 2 0 | 1 0 3 . sefa( . sns ) | 2 | * * * 4n | 0 0 1 1 1 | 1 1 1 ------------------+----+-------------+-------------+------- x s2s . | 4 | 2 0 2 0 | n * * * * | 0 0 2 x s . s2*b | 4 | 0 2 2 0 | * n * * * | 0 0 2 . . sns ♦ n | 0 0 0 n | * * 4 * * | 1 1 0 x sefa( . sns ) | 4 | 0 0 2 2 | * * * 2n * | 1 0 1 . sefa( s2sns ) | 3 | 1 1 0 1 | * * * * 4n | 0 1 1 ------------------+----+-------------+-------------+------- x . sns ♦ 2n | 0 0 n 2n | 0 0 2 n 0 | 2 * * . s2sns ♦ 2n | n n 0 2n | 0 0 2 0 2n | * 2 * x sefa( s2sns ) ♦ 6 | 2 2 3 2 | 1 1 0 1 2 | * * 2n
x s2s2no (n>2) . demi( . . . ) | 4n | 2 1 2 | 2 1 2 3 | 1 1 3 -----------------+----+----------+------------+------- . s2s . | 2 | 4n * * | 1 0 0 2 | 0 1 2 x demi( . . . ) | 2 | * 2n * | 2 0 2 0 | 1 0 3 . sefa( . s2no ) | 2 | * * 4n | 0 1 1 1 | 1 1 1 -----------------+----+----------+------------+------- x s2s . | 4 | 2 2 0 | 2n * * * | 0 0 2 . . s2no ♦ n | 0 0 n | * 4 * * | 1 1 0 x sefa( . s2no ) | 4 | 0 2 2 | * * 2n * | 1 0 1 . sefa( s2s2no ) | 3 | 2 0 1 | * * * 4n | 0 1 1 -----------------+----+----------+------------+------- x . s2no ♦ 2n | 0 n 2n | 0 2 n 0 | 2 * * . s2s2no ♦ 2n | 2n 0 2n | 0 2 0 2n | * 2 * x sefa( s2s2no ) ♦ 6 | 4 3 2 | 2 0 1 2 | * * 2n
xx xonox&#x (n>2) → height = sqrt[(1+2*cos(π/n))/(2+2*cos(π/n))]
({n}-p || gyro {n}-p)
o. o.no. | 2n * | 1 2 2 0 0 | 2 1 2 2 1 0 0 | 1 2 1 1 0
.o .on.o | * 2n | 0 0 2 1 2 | 0 0 2 1 2 2 1 | 0 1 2 1 1
------------+-------+--------------+------------------+----------
x. .. .. | 2 0 | n * * * * | 2 0 2 0 0 0 0 | 1 2 1 0 0
.. x. .. | 2 0 | * 2n * * * | 1 1 0 1 0 0 0 | 1 1 0 1 0
oo oonoo&#x | 1 1 | * * 4n * * | 0 0 1 1 1 0 0 | 0 1 1 1 0
.x .. .. | 0 2 | * * * n * | 0 0 2 0 0 2 0 | 0 1 2 0 1
.. .. .x | 0 2 | * * * * 2n | 0 0 0 0 1 1 1 | 0 0 1 1 1
------------+-------+--------------+------------------+----------
x. x. .. | 4 0 | 2 2 0 0 0 | n * * * * * * | 1 1 0 0 0
.. x.no. | n 0 | 0 n 0 0 0 | * 2 * * * * * | 1 0 0 1 0
xx .. ..&#x | 2 2 | 1 0 2 1 0 | * * 2n * * * * | 0 1 1 0 0
.. xo ..&#x | 2 1 | 0 1 2 0 0 | * * * 2n * * * | 0 1 0 1 0
.. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * * 2n * * | 0 0 1 1 0
.x .. .x | 0 4 | 0 0 0 2 2 | * * * * * n * | 0 0 1 0 1
.. .on.x | 0 n | 0 0 0 0 n | * * * * * * 2 | 0 0 0 1 1
------------+-------+--------------+------------------+----------
x. x.no. ♦ 2n 0 | n 2n 0 0 0 | n 2 0 0 0 0 0 | 1 * * * *
xx xo ..&#x ♦ 4 2 | 2 2 4 1 0 | 1 0 2 2 0 0 0 | * n * * *
xx .. ox&#x ♦ 2 4 | 1 0 4 2 2 | 0 0 2 0 2 1 0 | * * n * *
.. xonox&#x ♦ n n | 0 n 2n 0 n | 0 1 0 n n 0 1 | * * * 2 *
.x .on.x ♦ 0 2n | 0 0 0 n 2n | 0 0 0 0 0 n 2 | * * * * 1
s2sns || s2sns (n>2) → height = 1 ({n}-ap || {n}-ap) demi( . . . ) | 2n * | 1 1 2 1 0 0 0 | 1 3 1 1 2 0 0 | 1 1 3 0 demi( . . . ) | * 2n | 0 0 0 1 1 1 2 | 0 0 1 1 2 1 3 | 0 1 3 1 ------------------------------+-------+------------------+------------------+--------- s2s . | 2 0 | n * * * * * * | 0 2 1 0 0 0 0 | 1 0 1 0 s 2 s | 2 0 | * n * * * * * | 0 2 0 1 0 0 0 | 1 0 1 0 sefa( . sns ) | 2 0 | * * 2n * * * * | 1 1 0 0 1 0 0 | 1 1 1 0 demi( . . . ) || demi( . . . ) | 1 1 | * * * 2n * * * | 0 0 1 1 2 0 0 | 0 1 3 0 s2s . | 0 2 | * * * * n * * | 0 0 1 0 0 0 2 | 0 0 2 1 s 2 s | 0 2 | * * * * * n * | 0 0 0 1 0 0 2 | 0 0 2 1 sefa( . sns ) | 0 2 | * * * * * * 2n | 0 0 0 0 1 1 1 | 0 1 1 1 ------------------------------+-------+------------------+------------------+--------- . sns ♦ n 0 | 0 0 n 0 0 0 0 | 2 * * * * * * | 1 1 0 0 sefa( s2sns ) | 3 0 | 1 1 1 0 0 0 0 | * 2n * * * * * | 1 0 1 0 s2s . || s2s . | 2 2 | 1 0 0 2 1 0 0 | * * n * * * * | 0 0 2 0 s 2 s || s 2 s | 2 2 | 0 1 0 2 0 1 0 | * * * n * * * | 0 0 2 0 sefa( . sns ) || sefa( . sns ) | 2 2 | 0 0 1 2 0 0 1 | * * * * 2n * * | 0 1 1 0 . sns ♦ 0 n | 0 0 0 0 0 0 n | * * * * * 2 * | 0 1 0 1 sefa( s2sns ) | 0 3 | 0 0 0 0 1 1 1 | * * * * * * 2n | 0 0 1 1 ------------------------------+-------+------------------+------------------+--------- s2sns ♦ 2n 0 | n n 2n 0 0 0 0 | 2 2n 0 0 0 0 0 | 1 * * * . sns || . sns ♦ n n | 0 0 n n 0 0 n | 1 0 0 0 n 1 0 | * 2 * * sefa( s2sns ) || sefa( s2sns ) ♦ 3 3 | 1 1 1 3 1 1 1 | 0 1 1 1 1 0 1 | * * 2n * s2sns ♦ 0 2n | 0 0 0 0 n n 2n | 0 0 0 0 0 2 2n | * * * 1
s2s2no || s2s2no (n>2) → height = 1 ({n}-ap || {n}-ap) demi( . . . ) | 2n * | 2 2 1 0 0 | 1 3 2 2 0 0 | 1 1 3 0 demi( . . . ) | * 2n | 0 0 1 2 2 | 0 0 2 2 1 3 | 0 1 3 1 --------------------------------+-------+----------------+-----------------+--------- s2s . | 2 0 | 2n * * * * | 0 2 1 0 0 0 | 1 0 2 0 sefa( . s2no ) | 2 0 | * 2n * * * | 1 1 0 1 0 0 | 1 1 1 0 demi( . . . ) || demi( . . . ) | 1 1 | * * 2n * * | 0 0 2 2 0 0 | 0 1 3 0 s2s . ) | 0 2 | * * * 2n * | 0 0 1 0 0 2 | 0 0 2 1 sefa( . s2no ) | 0 2 | * * * * 2n | 0 0 0 1 1 1 | 0 1 1 1 --------------------------------+-------+----------------+-----------------+--------- . s2no ♦ n 0 | 0 n 0 0 0 | 2 * * * * * | 1 1 0 0 sefa( s2s2no ) | 3 0 | 2 1 0 0 0 | * 2n * * * * | 1 0 1 0 s2s . ) || s2s . ) | 2 2 | 1 0 2 1 0 | * * 2n * * * | 0 0 2 0 sefa( . s2no ) || sefa( . s2no ) | 2 2 | 0 1 2 0 1 | * * * 2n * * | 0 1 1 0 . s2no ♦ 0 n | 0 0 0 0 n | * * * * 2 * | 0 1 0 1 sefa( s2s2no ) | 0 3 | 0 0 0 2 1 | * * * * * 2n | 0 0 1 1 --------------------------------+-------+----------------+-----------------+--------- s2s2no ♦ 2n 0 | 2n 2n 0 0 0 | 2 2n 0 0 0 0 | 1 * * * . s2no || . s2no ♦ n n | 0 n n 0 n | 1 0 0 n 1 0 | * 2 * * sefa( s2s2no ) || sefa( s2s2no ) ♦ 3 3 | 2 1 3 2 1 | 0 1 2 1 0 1 | * * 2n * s2s2no ♦ 0 2n | 0 0 0 2n 2n | 0 0 0 0 2 2n | * * * 1
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