hemiatedsquare - 2n-gon duoprism
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| Acronym | 2,n-dap |
| Name | digon - n-gon duoantiprism, hemiatedsquare - 2n-gon duoprism |
| Circumradius | sqrt[A2/2+B2/(4 sin2(π/2n))] |
| Face vector | 4n, 14n, 16n+4, 6n+4 |
| Especially | s2s2s3s s2s2s2s (hex) |
| Confer | |
| External links | |
These isogonal polychora are obtained by hemiation of the uniform4,2n-duoprism (with n>2).But because of lower degree of freedom the three edge sizes A*sqrt(2), B*x(2n), sqrt(A2+B2) cannot be made all alike.
The exceptional case n=2 could be considered similarily, but the incidence matrices below will be different because of degeneracy.Then it becomes the hemiatedtes (hex) and even happens to be regular.
Incidence matrix according toDynkin symbol
s2no2o4sdemi( . . . . ) |4n | 4 1 2 | 1 6 6 | 2 2 4-----------------+----+----------+---------+-------- s 2 . s | 2 | 8n * * | 0 2 2 | 1 1 2 . . o4s | 2 | * 2n * | 0 0 4 | 0 2 2sefa( s2no . . ) | 2 | * * 4n | 1 2 0 | 2 0 1-----------------+----+----------+---------+-------- s2no . . | n | 0 0 n | 4 * * | 2 0 0sefa( s2no 2 s ) | 3 | 2 0 1 | * 8n * | 1 0 1sefa( s 2 o4s ) | 3 | 2 1 0 | * * 8n | 0 1 1-----------------+----+----------+---------+-------- s2no 2 s♦ 2n | 2n 0 2n | 2 2n 0 | 4 * * n-ap s 2 o4s♦ 4 | 4 2 0 | 0 0 4 | * 2n * tetsefa( s2no2o4s )♦ 4 | 4 1 1 | 0 2 2 | * * 4n disphenoidstarting figure:x2no o4x
s4o2sns (n>2)demi( . . . . ) |4n | 1 4 2 | 1 6 6 | 2 2 4------------------+----+----------+---------+-------- s4o . . | 2 | 2n * * | 0 4 0 | 2 0 2 A*sqrt(2) s 2 s . & | 2 | * 8n * | 0 2 2 | 1 1 2 sqrt(A2+B2)sefa( . . sns ) | 2 | * * 4n | 1 0 2 | 0 2 1 B*x(2n)------------------+----+----------+---------+-------- . sns | n | 0 0 n | 4 * * | 0 2 0sefa( s4o2s . ) & | 3 | 1 2 0 | * 8n * | 1 0 1sefa( s 2 sns ) | 3 | 0 2 1 | * * 8n | 0 1 1------------------+----+----------+---------+-------- s4o2s . &♦ 4 | 2 4 0 | 0 4 0 | 2n * * tet s 2 sns♦ 2n | 0 2n 2n | 2 0 2n | * 4 * n-apsefa( s4o2sns )♦ 4 | 1 4 1 | 0 2 2 | * * 4n disphenoidstarting figure:x4o xnx
s2s2sns (n>2)demi( . . . . ) |4n | 1 4 2 | 6 6 1 | 2 4 2------------------+----+----------+---------+-------- s2s . . | 2 | 2n * * | 4 0 0 | 2 2 0 A*sqrt(2) . s2s . & | 2 | * 8n * | 2 2 0 | 1 2 1 sqrt(A2+B2)sefa( . . sns ) | 2 | * * 4n | 0 2 1 | 0 1 2 B*x(2n)------------------+----+----------+---------+--------sefa( s2s2s . ) & | 3 | 1 2 0 | 8n * * | 1 1 0sefa( . s2sns ) & | 3 | 0 2 1 | * 8n * | 0 1 1 . sns | n | 0 0 n | * * 4 | 0 0 2------------------+----+----------+---------+-------- s2s2s . &♦ 4 | 2 4 0 | 4 0 0 | 2n * * tetsefa( s2s2sns )♦ 4 | 1 4 1 | 2 2 0 | * 4n * disphenoid . s2sns &♦ 2n | 0 2n 2n | 0 2n 2 | * * 4 n-apstarting figure:x x xnx
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