| Acronym | 3,n-dippip |
| Name | triangle - n-gon duoprismatic prism |
| Circumradius | sqrt[7/12+1/(4 sin2(π/n))] |
| Face vector | 6n, 15n, 14n+6, 6n+9, n+5 |
| Especially | tratrip (n=3) tracube (n=4) trapip (n=5) trahip (n=6) |
| Confer |
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Incidence matrix according to Dynkin symbol
x x3o xno (n>2) . . . . . | 6n | 1 2 2 | 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1 ----------+----+----------+---------------+-------------+------ x . . . . | 2 | 3n * * | 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0 . x . . . | 2 | * 6n * | 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1 . . . x . | 2 | * * 6n | 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1 ----------+----+----------+---------------+-------------+------ x x . . . | 4 | 2 2 0 | 3n * * * * | 1 2 0 0 0 | 2 1 0 x . . x . | 4 | 2 0 2 | * 3n * * * | 0 2 1 0 0 | 1 2 0 . x3o . . | 3 | 0 3 0 | * * 2n * * | 1 0 0 2 0 | 2 0 1 . x . x . | 4 | 0 2 2 | * * * 6n * | 0 1 0 1 1 | 1 1 1 . . . xno | n | 0 0 n | * * * * 6 | 0 0 1 0 2 | 0 2 1 ----------+----+----------+---------------+-------------+------ x x3o . . ♦ 6 | 3 6 0 | 3 0 2 0 0 | n * * * * | 2 0 0 x x . x . ♦ 8 | 4 4 4 | 2 2 0 2 0 | * 3n * * * | 1 1 0 x . . xno ♦ 2n | n 0 2n | 0 n 0 0 2 | * * 3 * * | 0 2 0 . x3o x . ♦ 6 | 0 6 3 | 0 0 2 3 0 | * * * 2n * | 1 0 1 . x . xno ♦ 2n | 0 n 2n | 0 0 0 n 2 | * * * * 6 | 0 1 1 ----------+----+----------+---------------+-------------+------ x x3o x . ♦ 12 | 6 12 6 | 6 3 4 6 0 | 2 3 0 2 0 | n * * x x . xno ♦ 4n | 2n 2n 4n | n 2n 0 2n 4 | 0 n 2 0 2 | * 3 * . x3o xno ♦ 3n | 0 3n 3n | 0 0 n 3n 3 | 0 0 0 n 3 | * * 2
xx3oo xxnoo&#x (n>2) → height = 1
({3}{n}-dip || {3}{n}-dip)
o.3o. o.no. | 3n * | 2 2 1 0 0 | 1 4 1 2 2 0 0 0 | 2 2 1 4 1 0 0 | 1 2 2 0
.o3.o .on.o | * 3n | 0 0 1 2 2 | 0 0 0 2 2 1 4 1 | 0 0 1 4 1 2 2 | 0 2 2 1
---------------+-------+----------------+---------------------+----------------+--------
x. .. .. .. | 2 0 | 3n * * * * | 1 2 0 1 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0
.. .. x. .. | 2 0 | * 3n * * * | 0 2 1 0 1 0 0 0 | 1 2 0 2 1 0 0 | 1 1 2 0
oo3oo oonoo&#x | 1 1 | * * 3n * * | 0 0 0 2 2 0 0 0 | 0 0 1 4 1 0 0 | 0 2 2 0
.x .. .. .. | 0 2 | * * * 3n * | 0 0 0 1 0 1 2 0 | 0 0 1 2 0 2 1 | 0 2 1 1
.. .. .x .. | 0 2 | * * * * 3n | 0 0 0 0 1 0 2 1 | 0 0 0 2 1 1 2 | 0 1 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. .. .. | 3 0 | 3 0 0 0 0 | n * * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 | * 3n * * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0
.. .. x.no. | n 0 | 0 n 0 0 0 | * * 3 * * * * * | 0 2 0 0 1 0 0 | 1 0 2 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 3n * * * * | 0 0 1 2 0 0 0 | 0 2 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * 3n * * * | 0 0 0 2 1 0 0 | 0 1 2 0
.x3.o .. .. | 0 3 | 0 0 0 3 0 | * * * * * n * * | 0 0 1 0 0 2 0 | 0 2 0 1
.x .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * * 3n * | 0 0 0 1 0 1 1 | 0 1 1 1
.. .. .xn.o | 0 n | 0 0 0 0 n | * * * * * * * 3 | 0 0 0 0 1 0 2 | 0 0 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. x. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 | n * * * * * * | 1 1 0 0
x. .. x.no. ♦ 2n 0 | n 2n 0 0 0 | 0 n 2 0 0 0 0 0 | * 3 * * * * * | 1 0 1 0
xx3oo .. ..&#x ♦ 3 3 | 3 0 3 3 0 | 1 0 0 3 0 1 0 0 | * * n * * * * | 0 2 0 0
xx .. xx ..&#x ♦ 4 4 | 2 2 4 2 2 | 0 1 0 2 2 0 1 0 | * * * 3n * * * | 0 1 1 0
.. .. xxnoo&#x ♦ n n | 0 n n 0 n | 0 0 1 0 n 0 0 1 | * * * * 3 * * | 0 0 2 0
.x3.o .x .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 2 3 0 | * * * * * n * | 0 1 0 1
.x .. .xn.o ♦ 0 2n | 0 0 0 n 2n | 0 0 0 0 0 0 n 2 | * * * * * * 3 | 0 0 1 1
---------------+-------+----------------+---------------------+----------------+--------
x.3o. x.no. ♦ 3n 0 | 3n 3n 0 0 0 | n 3n 3 0 0 0 0 0 | n 3 0 0 0 0 0 | 1 * * *
xx3oo xx ..&#x ♦ 6 6 | 6 3 6 6 3 | 2 3 0 6 3 2 3 0 | 1 0 2 3 0 1 0 | * n * *
xx .. xxnoo&#x ♦ 2n 2n | n 2n 2n n 2n | 0 n 2 n 2n 0 n 2 | 0 1 0 n 2 0 1 | * * 3 *
.x3.o .xn.o ♦ 0 3n | 0 0 0 3n 3n | 0 0 0 0 0 n 3n 3 | 0 0 0 0 0 n 3 | * * * 1
ox xx xxnoo&#x (n>2) → height = sqrt(3)/2 = 0.866025
({n}-p || {4}{n}-dip)
o. o. o.no. | 2n * | 1 2 2 0 0 0 | 2 1 1 2 4 0 0 0 0 | 1 1 2 4 2 0 0 0 | 2 1 2 0
.o .o .on.o | * 4n | 0 0 1 1 1 2 | 0 0 1 1 2 1 2 2 1 | 0 1 2 2 1 2 1 1 | 2 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. .. .. | 2 0 | n * * * * * | 2 0 0 2 0 0 0 0 0 | 1 1 0 4 0 0 0 0 | 2 0 2 0
.. .. x. .. | 2 0 | * 2n * * * * | 1 1 0 0 2 0 0 0 0 | 1 0 1 2 2 0 0 0 | 1 1 2 0
oo oo oonoo&#x | 1 1 | * * 4n * * * | 0 0 1 1 2 0 0 0 0 | 0 1 2 2 1 0 0 0 | 2 1 1 0
.x .. .. .. | 0 2 | * * * 2n * * | 0 0 1 0 0 1 2 0 0 | 0 1 2 0 0 2 1 0 | 2 1 0 1
.. .x .. .. | 0 2 | * * * * 2n * | 0 0 0 1 0 1 0 2 0 | 0 1 0 2 0 2 0 1 | 2 0 1 1
.. .. .x .. | 0 2 | * * * * * 4n | 0 0 0 0 1 0 1 1 1 | 0 0 1 1 1 1 1 1 | 1 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. x. .. | 4 0 | 2 2 0 0 0 0 | n * * * * * * * * | 1 0 0 2 0 0 0 0 | 1 0 2 0
.. .. x.no. | n 0 | 0 n 0 0 0 0 | * 2 * * * * * * * | 1 0 0 0 2 0 0 0 | 0 1 2 0
ox .. .. ..&#x | 1 2 | 0 0 2 1 0 0 | * * 2n * * * * * * | 0 1 2 0 0 0 0 0 | 2 1 0 0
.. xx .. ..&#x | 2 2 | 1 0 2 0 1 0 | * * * 2n * * * * * | 0 1 0 2 0 0 0 0 | 2 0 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 0 1 | * * * * 4n * * * * | 0 0 1 1 1 0 0 0 | 1 1 1 0
.x .x .. .. | 0 4 | 0 0 0 2 2 0 | * * * * * n * * * | 0 1 0 0 0 2 0 0 | 2 0 0 1
.x .. .x .. | 0 4 | 0 0 0 2 0 2 | * * * * * * 2n * * | 0 0 1 0 0 1 1 0 | 1 1 0 1
.. .x .x .. | 0 4 | 0 0 0 0 2 2 | * * * * * * * 2n * | 0 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .xn.o | 0 n | 0 0 0 0 0 n | * * * * * * * * 4 | 0 0 0 0 1 0 1 1 | 0 1 1 1
---------------+-------+------------------+------------------------+-------------------+--------
.. x. x.no. ♦ 2n 0 | n 2n 0 0 0 0 | n 2 0 0 0 0 0 0 0 | 1 * * * * * * * | 0 0 2 0
ox xx .. ..&#x ♦ 2 4 | 1 0 4 2 2 0 | 0 0 2 2 0 1 0 0 0 | * n * * * * * * | 2 0 0 0
ox .. xx ..&#x ♦ 2 4 | 0 1 4 2 0 2 | 0 0 2 0 2 0 1 0 0 | * * 2n * * * * * | 1 1 0 0
.. xx xx ..&#x ♦ 4 4 | 2 2 4 0 2 2 | 1 0 0 2 2 0 0 1 0 | * * * 2n * * * * | 1 0 1 0
.. .. xxnoo&#x ♦ n n | 0 n n 0 0 n | 0 1 0 0 n 0 0 0 1 | * * * * 4 * * * | 0 1 1 0
.x .x .x .. ♦ 0 8 | 0 0 0 4 4 4 | 0 0 0 0 0 2 2 2 0 | * * * * * n * * | 1 0 0 1
.x .. .xn.o ♦ 0 2n | 0 0 0 n 0 2n | 0 0 0 0 0 0 n 0 2 | * * * * * * 2 * | 0 1 0 1
.. .x .xn.o ♦ 0 2n | 0 0 0 0 n 2n | 0 0 0 0 0 0 0 n 2 | * * * * * * * 2 | 0 0 1 1
---------------+-------+------------------+------------------------+-------------------+--------
ox xx xx ..&#x ♦ 4 8 | 2 2 8 4 4 4 | 1 0 4 4 4 2 2 2 0 | 0 2 2 2 0 1 0 0 | n * * *
ox .. xxnoo&#x ♦ n 2n | 0 n 2n n 0 2n | 0 1 n 0 2n 0 n 0 2 | 0 0 n 0 2 0 1 0 | * 2 * *
.. xx xxnoo&#x ♦ 2n 2n | n 2n 2n 0 n 2n | n 2 0 n 2n 0 0 n 2 | 1 0 0 n 2 0 0 1 | * * 2 *
.x .x .xn.o ♦ 0 4n | 0 0 0 2n 2n 4n | 0 0 0 0 0 n 2n 2n 4 | 0 0 0 0 0 n 2 2 | * * * 1
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