| Acronym | n,oct-dip |
| Name | n-gon - octahedron duoprism |
| Circumradius | sqrt[1/2+1/(4 sin2(π/n))] |
| Face vector | 6n, 18n, 20n+6, 9n+12, n+8 |
| Especially | troct (n=3) squoct (n=4) poct (n=5) stoct (n=5/2) hoct (n=6) owoct (n=8) stowoct (n=8/3) |
| Confer |
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Incidence matrix according to Dynkin symbol
xno x3o4o (n>2) . . . . . | 6n | 2 4 | 1 8 4 | 4 8 1 | 4 2 ----------+----+--------+----------+---------+---- x . . . . | 2 | 6n * | 1 4 0 | 4 4 0 | 4 1 . . x . . | 2 | * 12n | 0 2 2 | 1 4 1 | 2 2 ----------+----+--------+----------+---------+---- xno . . . | n | n 0 | 6 * * | 4 0 0 | 4 0 x . x . . | 4 | 2 2 | * 12n * | 1 2 0 | 2 1 . . x3o . | 3 | 0 3 | * * 8n | 0 2 1 | 1 2 ----------+----+--------+----------+---------+---- xno x . . ♦ 2n | 2n n | 2 n 0 | 12 * * | 2 0 x . x3o . ♦ 6 | 3 6 | 0 3 2 | * 8n * | 1 1 . . x3o4o ♦ 6 | 0 12 | 0 0 8 | * * n | 0 2 ----------+----+--------+----------+---------+---- xno x3o . ♦ 3n | 3n 3n | 3 3n n | 3 n 0 | 8 * x . x3o4o ♦ 12 | 6 24 | 0 12 16 | 0 8 2 | * n
xno o3x3o (n>2) . . . . . | 6n | 2 4 | 1 8 2 2 | 4 4 4 1 | 2 2 2 ----------+----+--------+-------------+------------+------ x . . . . | 2 | 6n * | 1 4 0 0 | 4 2 2 0 | 2 2 1 . . . x . | 2 | * 12n | 0 2 1 1 | 1 2 2 1 | 1 1 2 ----------+----+--------+-------------+------------+------ xno . . . | n | n 0 | 6 * * * | 4 0 0 0 | 2 2 0 x . . x . | 4 | 2 2 | * 12n * * | 1 1 1 0 | 1 1 1 . . o3x . | 3 | 0 3 | * * 4n * | 0 2 0 1 | 1 0 2 . . . x3o | 3 | 0 3 | * * * 4n | 0 0 2 1 | 0 1 2 ----------+----+--------+-------------+------------+------ xno . x . ♦ 2n | 2n n | 2 n 0 0 | 12 * * * | 1 1 0 x . o3x . ♦ 6 | 3 6 | 0 3 2 0 | * 4n * * | 1 0 1 x . . x3o ♦ 6 | 3 6 | 0 3 0 2 | * * 4n * | 0 1 1 . . o3x3o ♦ 6 | 0 12 | 0 0 4 4 | * * * n | 0 0 2 ----------+----+--------+-------------+------------+------ xno o3x . ♦ 3n | 3n 3n | 3 3n n 0 | 3 n 0 0 | 4 * * xno . x3o ♦ 3n | 3n 3n | 3 3n 0 n | 3 0 n 0 | * 4 * x . o3x3o ♦ 12 | 6 24 | 0 12 8 8 | 0 4 4 2 | * * n
xo3ox xxnoo&#x (n>2) → height = sqrt(2/3) = 0.816497
(3,n-dip || (dual 3),n-dip)
o.3o. o.no. | 3n * | 2 2 2 0 0 | 1 4 1 2 1 4 0 0 0 | 2 2 1 4 2 2 0 0 | 1 2 2 1 0
.o3.o .on.o | * 3n | 0 0 2 2 2 | 0 0 0 1 2 4 1 4 1 | 0 0 1 2 4 2 2 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x. .. .. .. | 2 0 | 3n * * * * | 1 2 0 1 0 0 0 0 0 | 2 1 1 2 0 0 0 0 | 1 2 1 0 0
.. .. x. .. | 2 0 | * 3n * * * | 0 2 1 0 0 2 0 0 0 | 1 2 0 2 1 2 0 0 | 1 2 2 1 0
oo3oo oonoo&#x | 1 1 | * * 6n * * | 0 0 0 1 1 2 0 0 0 | 0 0 1 2 2 1 0 0 | 0 1 1 1 0
.. .x .. .. | 0 2 | * * * 3n * | 0 0 0 0 1 0 1 2 0 | 0 0 1 0 2 0 2 1 | 0 2 0 1 1
.. .. .x .. | 0 2 | * * * * 3n | 0 0 0 0 0 2 0 2 1 | 0 0 0 1 2 2 1 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. .. .. | 3 0 | 3 0 0 0 0 | n * * * * * * * * | 2 0 1 0 0 0 0 0 | 1 2 0 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 | * 3n * * * * * * * | 1 1 0 1 0 0 0 0 | 1 1 1 0 0
.. .. x.no. | n 0 | 0 n 0 0 0 | * * 3 * * * * * * | 0 2 0 0 0 2 0 0 | 1 0 2 1 0
xo .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 3n * * * * * | 0 0 1 2 0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x | 1 2 | 0 0 2 1 0 | * * * * 3n * * * * | 0 0 1 0 2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * * 6n * * * | 0 0 0 1 1 1 0 0 | 0 1 1 1 0
.o3.x .. .. | 0 3 | 0 0 0 3 0 | * * * * * * n * * | 0 0 1 0 0 0 2 0 | 0 2 0 0 1
.. .x .x .. | 0 4 | 0 0 0 2 2 | * * * * * * * 3n * | 0 0 0 0 1 0 1 1 | 0 1 0 1 1
.. .. .xn.o | 0 n | 0 0 0 0 n | * * * * * * * * 3 | 0 0 0 0 0 2 0 2 | 0 0 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 0 | n * * * * * * * | 1 1 0 0 0
x. .. x.no. ♦ 2n 0 | n 2n 0 0 0 | 0 n 2 0 0 0 0 0 0 | * 3 * * * * * * | 1 0 1 0 0
xo3ox .. ..&#x ♦ 3 3 | 3 0 6 3 0 | 1 0 0 3 3 0 1 0 0 | * * n * * * * * | 0 2 0 0 0
xo .. xx ..&#x ♦ 4 2 | 2 2 4 0 1 | 0 1 0 2 0 2 0 0 0 | * * * 3n * * * * | 0 1 1 0 0
.. ox xx ..&#x ♦ 2 4 | 0 1 4 2 2 | 0 0 0 0 2 2 0 1 0 | * * * * 3n * * * | 0 1 0 1 0
.. .. xxnoo&#x ♦ n n | 0 n n 0 n | 0 0 1 0 0 n 0 0 1 | * * * * * 6 * * | 0 0 1 1 0
.o3.x .x .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 2 3 0 | * * * * * * n * | 0 1 0 0 1
.. .x .xn.o ♦ 0 2n | 0 0 0 n 2n | 0 0 0 0 0 0 0 n 2 | * * * * * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.no. ♦ 3n 0 | 3n 3n 0 0 0 | n 3n 3 0 0 0 0 0 0 | n 3 0 0 0 0 0 0 | 1 * * * *
xo3ox xx ..&#x ♦ 6 6 | 6 6 6 6 6 | 2 3 0 6 6 6 2 3 0 | 1 0 2 3 3 0 1 0 | * n * * *
xo .. xxnoo&#x ♦ 2n n | n 2n 2n 0 n | 0 n 2 n 0 2n 0 0 1 | 0 1 0 n 0 2 0 0 | * * 3 * *
.. ox xxnoo&#x ♦ n 2n | 0 n 2n n 2n | 0 0 1 0 n 2n 0 n 2 | 0 0 0 0 n 2 0 1 | * * * 3 *
.o3.x .xn.o ♦ 0 3n | 0 0 0 3n 3n | 0 0 0 0 0 0 n 3n 3 | 0 0 0 0 0 0 n 3 | * * * * 1
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