n,tet-dip

Acronym	n,tet-dip
Name	n-gon - tetrahedron duoprism, n-gonal duofastegium, n-gonal prism disphenoid
Circumradius	sqrt[3/8+1/(4 sin²(π/n))]
Lace city in approx. ASCII-art	x x-n-x o x-n-x o x-n-x
Lace hyper city in approx. ASCII-art	x-n-x x-n-x x-n-x x-n-x (disphenoid in configuration space)
Face vector	4n, 10n, 10n+4, 5n+6, n+4
Especially	tratet (n=3) squatet (n=4) petet (n=5) hatet (n=6) otet (n=8) stotet (n=8/3)
Confer	general polytopal classes: Wythoffian polytera segmentotera

Incidence matrix according to Dynkin symbol

xno x3o3o   (n>2)

. . . . . | 4n |  2  3 | 1  6  3 | 3  6 1 | 3 2
----------+----+-------+---------+--------+----
x . . . . |  2 | 4n  * | 1  3  0 | 3  3 0 | 3 1
. . x . . |  2 |  * 6n | 0  2  2 | 1  4 1 | 2 2
----------+----+-------+---------+--------+----
xno . . . |  n |  n  0 | 4  *  * | 3  0 0 | 3 0
x . x . . |  4 |  2  2 | * 6n  * | 1  2 0 | 2 1
. . x3o . |  3 |  0  3 | *  * 4n | 0  2 1 | 1 2
----------+----+-------+---------+--------+----
xno x . . ♦ 2n | 2n  n | 2  n  0 | 6  * * | 2 0
x . x3o . ♦  6 |  3  6 | 0  3  2 | * 4n * | 1 1
. . x3o3o ♦  4 |  0  6 | 0  0  4 | *  * n | 0 2
----------+----+-------+---------+--------+----
xno x3o . ♦ 3n | 3n 3n | 3 3n  n | 3  n 0 | 4 *
x . x3o3o ♦  8 |  4 12 | 0  6  8 | 0  4 2 | * n

ox3oo xxnoo&#x   (n>2)   → height = sqrt(2/3) = 0.816497
({n} || 3,n-dip)

o.3o. o.no.    | n  * | 2  3  0  0 | 1  3  6 0  0 0 | 1  6 3 0 0 | 2 3 0
.o3.o .on.o    | * 3n | 0  1  2  2 | 0  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
---------------+------+------------+----------------+------------+------
.. .. x. ..    | 2  0 | n  *  *  * | 1  0  3 0  0 0 | 0  3 3 0 0 | 1 3 0
oo3oo oonoo&#x | 1  1 | * 3n  *  * | 0  2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
.x .. .. ..    | 0  2 | *  * 3n  * | 0  1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
.. .. .x ..    | 0  2 | *  *  * 3n | 0  0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
---------------+------+------------+----------------+------------+------
.. .. x.no.    | n  0 | n  0  0  0 | 1  *  * *  * * | 0  0 3 0 0 | 0 3 0
ox .. .. ..&#x | 1  2 | 0  2  1  0 | * 3n  * *  * * | 1  2 0 0 0 | 2 1 0
.. .. xx ..&#x | 2  2 | 1  2  0  1 | *  * 3n *  * * | 0  2 1 0 0 | 1 2 0
.x3.o .. ..    | 0  3 | 0  0  3  0 | *  *  * n  * * | 1  0 0 2 0 | 2 0 1
.x .. .x ..    | 0  4 | 0  0  2  2 | *  *  * * 3n * | 0  1 0 1 1 | 1 1 1
.. .. .xn.o    | 0  n | 0  0  0  n | *  *  * *  * 3 | 0  0 1 0 2 | 0 2 1
---------------+------+------------+----------------+------------+------
ox3oo .. ..&#x ♦ 1  3 | 0  3  3  0 | 0  3  0 1  0 0 | n  * * * * | 2 0 0
ox .. xx ..&#x ♦ 2  4 | 1  4  2  2 | 0  2  2 0  1 0 | * 3n * * * | 1 1 0
.. .. xxnoo&#x ♦ n  n | n  n  0  n | 1  0  n 0  0 1 | *  * 3 * * | 0 2 0
.x3.o .x ..    ♦ 0  6 | 0  0  6  3 | 0  0  0 2  3 0 | *  * * n * | 1 0 1
.x .. .xn.o    ♦ 0 2n | 0  0  n 2n | 0  0  0 0  n 2 | *  * * * 3 | 0 1 1
---------------+------+------------+----------------+------------+------
ox3oo xx ..    ♦ 2  6 | 1  6  6  3 | 0  6  3 2  3 0 | 2  3 0 1 0 | n * *
ox .. xxnoo&#x ♦ n 2n | n 2n  n 2n | 1  n 2n 0  n 2 | 0  n 2 0 1 | * 3 *
.x3.o .xn.o    ♦ 0 3n | 0  0 3n 3n | 0  0  0 n 3n 3 | 0  0 0 n 3 | * * 1

ox xo xxnoo&#x   (n>2)   → height = 1/sqrt(2) = 0.707107
(n-p || lacing-ortho n-p)

o. o. o.no.    | 2n  * | 1  2  2 0  0 | 2 1  1  2  4 0 0 | 1 1  2  4 2 0 | 2 1 2
.o .o .on.o    |  * 2n | 0  0  2 1  2 | 0 0  2  1  4 2 1 | 0 1  4  2 2 1 | 2 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. .. ..    |  2  0 | n  *  * *  * | 2 0  0  2  0 0 0 | 1 1  0  2 0 0 | 2 0 2
.. .. x. ..    |  2  0 | * 2n  * *  * | 1 1  0  0  2 0 0 | 1 0  1  2 2 0 | 1 1 2
oo oo oonoo&#x |  1  1 | *  * 4n *  * | 0 0  1  1  2 0 0 | 0 1  2  2 1 0 | 2 1 1
.x .. .. ..    |  0  2 | *  *  * n  * | 0 0  2  0  0 2 0 | 0 1  4  0 0 1 | 2 2 0
.. .. .x ..    |  0  2 | *  *  * * 2n | 0 0  0  0  2 1 1 | 0 0  2  1 2 1 | 1 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. x. ..    |  4  0 | 2  2  0 0  0 | n *  *  *  * * * | 1 0  0  2 0 0 | 1 0 2
.. .. x.no.    |  n  0 | 0  n  0 0  0 | * 2  *  *  * * * | 1 0  0  0 2 0 | 0 1 2
ox .. .. ..&#x |  1  2 | 0  0  2 1  0 | * * 2n  *  * * * | 0 1  2  0 0 0 | 2 1 0
.. xo .. ..&#x |  2  1 | 1  0  2 0  0 | * *  * 2n  * * * | 0 1  0  2 0 0 | 2 0 1
.. .. xx ..&#x |  2  2 | 0  1  2 0  1 | * *  *  * 4n * * | 0 0  1  1 1 0 | 1 1 1
.x .. .x ..    |  0  4 | 0  0  0 2  2 | * *  *  *  * n * | 0 0  2  0 0 1 | 1 2 0
.. .. .xn.o    |  0  n | 0  0  0 0  n | * *  *  *  * * 2 | 0 0  0  0 2 1 | 0 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. x.no.    ♦ 2n  0 | n 2n  0 0  0 | n 2  0  0  0 0 0 | 1 *  *  * * * | 0 0 2
ox xo .. ..&#x ♦  2  2 | 1  0  4 1  0 | 0 0  2  2  0 0 0 | * n  *  * * * | 2 0 0
ox .. xx ..&#x ♦  2  4 | 0  1  4 2  2 | 0 0  2  0  2 1 0 | * * 2n  * * * | 1 1 0
.. xo xx ..&#x ♦  4  2 | 2  2  4 0  1 | 1 0  0  2  2 0 0 | * *  * 2n * * | 1 0 1
.. .. xxnoo&#x ♦  n  n | 0  n  n 0  n | 0 1  0  0  n 0 1 | * *  *  * 4 * | 0 1 1
.x .. .xn.o    ♦  0 2n | 0  0  0 n 2n | 0 0  0  0  0 n 2 | * *  *  * * 1 | 0 2 0
---------------+-------+--------------+------------------+---------------+------
ox xo xx ..&#x ♦  4  4 | 2  2  8 2  2 | 1 0  4  4  4 1 0 | 0 2  2  2 0 0 | n * *
ox .. xxnoo&#x ♦  n 2n | 0  n 2n n 2n | 0 1  n  0 2n n 2 | 0 0  n  0 2 1 | * 2 *
.. xo xxnoo&#x ♦ 2n  n | n 2n 2n 0  n | n 2  0  n 2n 0 1 | 1 0  0  n 2 0 | * * 2

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