3,n-dippip

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	general duoprism-prisms: n,m-dippip general polytopal classes: Wythoffian polytera segmentotera

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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