Acronym | N,pen-dip |
Name | N-gon - pentachoron duoprism |
Circumradius | sqrt[1/(4 sin2(π/N))+2/5] |
Confer |
|
Face vector | 5n, 15n, 20n+5, 15n+10, 6n+10, n+5 |
Especially | trapen (N=3) squapen (N=4) open (N=8) stopen (N=8/3) |
For non-convex cases use N = n/d.
Incidence matrix according to Dynkin symbol
xNo x3o3o3o (N>2) . . . . . . | 5n | 2 4 | 1 8 6 | 4 12 4 | 6 8 1 | 4 2 ------------+----+--------+-----------+-----------+---------+---- x . . . . . | 2 | 5n * | 1 4 0 | 4 6 0 | 6 4 0 | 4 1 . . x . . . | 2 | * 10n | 0 2 3 | 1 6 3 | 3 6 1 | 3 2 ------------+----+--------+-----------+-----------+---------+---- xNo . . . . | n | n 0 | 5 * * ♦ 4 0 0 | 6 0 0 | 4 0 x . x . . . | 4 | 2 2 | * 10n * | 1 3 0 | 3 3 0 | 3 1 . . x3o . . | 3 | 0 3 | * * 10n | 0 2 2 | 1 4 1 | 2 2 ------------+----+--------+-----------+-----------+---------+---- xNo x . . . ♦ 2n | 2n n | 2 n 0 | 10 * * | 3 0 0 | 3 0 x . x3o . . ♦ 6 | 3 6 | 0 3 2 | * 10n * | 1 2 0 | 2 1 . . x3o3o . ♦ 4 | 0 6 | 0 0 4 | * * 5n | 0 2 1 | 1 2 ------------+----+--------+-----------+-----------+---------+---- xNo x3o . . ♦ 3n | 3n 3n | 3 3n n | 3 n 0 | 10 * * | 2 0 x . x3o3o . ♦ 8 | 4 12 | 0 6 8 | 0 4 2 | * 5n * | 1 1 . . x3o3o3o ♦ 5 | 0 10 | 0 0 10 | 0 0 5 | * * n | 0 2 ------------+----+--------+-----------+-----------+---------+---- xNo x3o3o . ♦ 4n | 4n 6n | 4 6n 4n | 6 4n n | 4 n 0 | 5 * x . x3o3o3o ♦ 10 | 5 20 | 0 10 20 | 0 10 10 | 0 5 2 | * n
xxNoo ox3oo3oo&#x (N>2) → height = sqrt(5/8) = 0.790569
({N} || (N,tet)-dip)
o.No. o.3o.3o. | n * | 2 4 0 0 | 1 8 6 0 0 0 | 4 12 4 0 0 0 | 6 8 1 0 0 | 4 2 0
.oN.o .o3.o3.o | * 4n | 0 1 2 3 | 0 2 3 1 6 3 | 1 6 3 3 6 1 | 3 6 1 3 2 | 3 2 1
------------------+------+------------+-----------------+----------------+------------+------
x. .. .. .. .. | 2 0 | n * * * | 1 4 0 0 0 0 | 4 6 0 0 0 0 | 6 4 0 0 0 | 4 1 0
ooNoo oo3oo3oo&#x | 1 1 | * 4n * * | 0 2 3 0 0 0 | 1 6 3 0 0 0 | 3 6 1 0 0 | 3 2 0
.x .. .. .. .. | 0 2 | * * 4n * | 0 1 0 1 3 0 | 1 3 0 3 3 0 | 3 3 0 3 1 | 3 1 1
.. .. .x .. .. | 0 2 | * * * 6n | 0 0 1 0 2 2 | 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1
------------------+------+------------+-----------------+----------------+------------+------
x.No. .. .. .. | n 0 | n 0 0 0 | 1 * * * * * ♦ 4 0 0 0 0 0 | 6 0 0 0 0 | 4 0 0
xx .. .. .. ..&#x | 2 2 | 1 2 1 0 | * 4n * * * * | 1 3 0 0 0 0 | 3 3 0 0 0 | 3 1 0
.. .. ox .. ..&#x | 1 2 | 0 2 0 1 | * * 6n * * * | 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.xN.o .. .. .. | 0 n | 0 0 n 0 | * * * 4 * * ♦ 1 0 0 3 0 0 | 3 0 0 3 0 | 3 0 1
.x .. .x .. .. | 0 4 | 0 0 2 2 | * * * * 6n * | 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.. .. .x3.o .. | 0 3 | 0 0 0 3 | * * * * * 4n | 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
------------------+------+------------+-----------------+----------------+------------+------
xxNoo .. .. ..&#x ♦ n n | n n n 0 | 1 n 0 1 0 0 | 4 * * * * * | 3 0 0 0 0 | 3 0 0
xx .. ox .. ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 0 1 0 | * 6n * * * * | 1 2 0 0 0 | 1 2 0
.. .. ox3oo ..&#x ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 | * * 4n * * * | 0 2 1 0 0 | 1 2 0
.xN.o .x .. .. ♦ 0 2n | 0 0 2n n | 0 0 0 2 n 0 | * * * 6 * * | 1 0 0 2 0 | 2 0 1
.x .. .x3.o .. ♦ 0 6 | 0 0 3 6 | 0 0 0 0 3 2 | * * * * 4n * | 0 1 0 1 1 | 1 1 1
.. .. .x3.o3.o ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 4 | * * * * * n | 0 0 1 0 2 | 0 2 1
------------------+------+------------+-----------------+----------------+------------+------
xxNoo ox .. ..&#x ♦ n 2n | n 2n 2n n | 1 2n n 2 n 0 | 2 n 0 1 0 0 | 6 * * * * | 2 0 0
xx .. ox3oo ..&#x ♦ 2 6 | 1 6 3 6 | 0 3 6 0 3 2 | 0 3 2 0 1 0 | * 4n * * * | 1 1 0
.. .. ox3oo3oo&#x ♦ 1 4 | 0 4 0 6 | 0 0 6 0 0 4 | 0 0 4 0 0 1 | * * n * * | 0 2 0
.xN.o .x3.o .. ♦ 0 3n | 0 0 3n 3n | 0 0 0 3 3n n | 0 0 0 3 n 0 | * * * 4 * | 1 0 1
.x .. .x3.o3.o ♦ 0 8 | 0 0 4 12 | 0 0 0 0 6 8 | 0 0 0 0 4 2 | * * * * n | 0 1 1
------------------+------+------------+-----------------+----------------+------------+------
xxNoo ox3oo ..&#x ♦ n 3n | n 3n 3n 3n | 1 3n 3n 3 3n n | 3 3n n 3 n 0 | 3 n 0 1 0 | 4 * *
xx .. ox3oo3oo&#x ♦ 2 8 | 1 8 4 12 | 0 4 12 0 6 8 | 0 6 8 0 4 2 | 0 4 2 0 1 | * n *
.xN.o .x3.o3.o ♦ 0 4n | 0 0 4n 6n | 0 0 0 4 6n 4n | 0 0 0 6 4n n | 0 0 0 4 n | * * 1
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