n,m-dippip

Acronym

n,m-dippip

Name

n-gon - m-gon duoprismatic prism

Circumradius

sqrt[1/4+1/(4 sin²(π/n))+1/(4 sin²(π/m))]

Volume

nm/[16 tan(π/n) tan(π/m)]

Face vector

2nm, 5nm, 4nm+2n+2m, nm+3n+3m, n+m+2

Especially

n,n-dippip (m=n) 3,n-dippip (m=3) n,cube-dip (m=4) 5,n-dippip (m=5)

3 x m	4 x m	5 x m	6 x m	8 x m	10 x m	12 x m	(n,m)-dippip
tratrip	tracube	trapip	trahip	trop	tradip	tratwip	n x 3
	pent	pecube	hacube	ocube	dacube	twacube	n x 4
		pepip	pehip	pop	peddip	petwip	n x 5
			hahip	haop	hadip	hatwip	n x 6
				oop	oddip	otwip	n x 8
					daddip	datwip	n x 10
						twatwip	n x 12

Confer

general polytopal classes:: Wythoffian polytera segmentotera

Incidence matrix according to Dynkin symbol

x xno xmo   (n>2, m>2)

. . . . . | 2nm |  1   2   2 |  2  2  1   4  1 | 1  4 1  2  2 | 2 2 1
----------+-----+------------+-----------------+--------------+------
x . . . . |   2 | nm   *   * |  2  2  0   0  0 | 1  4 1  0  0 | 2 2 0
. x . . . |   2 |  * 2nm   * |  1  0  1   2  0 | 1  2 0  2  1 | 2 1 1
. . . x . |   2 |  *   * 2nm |  0  1  0   2  1 | 0  2 1  1  2 | 1 2 1
----------+-----+------------+-----------------+--------------+------
x x . . . |   4 |  2   2   0 | nm  *  *   *  * | 1  2 0  0  0 | 2 1 0
x . . x . |   4 |  2   0   2 |  * nm  *   *  * | 0  2 1  0  0 | 1 2 0
. xno . . |   n |  0   n   0 |  *  * 2m   *  * | 1  0 0  2  0 | 2 0 1
. x . x . |   4 |  0   2   2 |  *  *  * 2nm  * | 0  1 0  1  1 | 1 1 1
. . . xmo |   m |  0   0   m |  *  *  *   * 2n | 0  0 1  0  2 | 0 2 1
----------+-----+------------+-----------------+--------------+------
x xno . . ♦  2n |  n  2n   0 |  n  0  2   0  0 | m  * *  *  * | 2 0 0
x x . x . ♦   8 |  4   4   4 |  2  2  0   2  0 | * nm *  *  * | 1 1 0
x . . xmo ♦  2m |  m   0  2m |  0  m  0   0  2 | *  * n  *  * | 0 2 0
. xno x . ♦  2n |  0  2n   n |  0  0  2   n  0 | *  * * 2m  * | 1 0 1
. x . xmo ♦  2m |  0   m  2m |  0  0  0   m  2 | *  * *  * 2n | 0 1 1
----------+-----+------------+-----------------+--------------+------
x xno x . ♦  4n | 2n  4n  2n | 2n  n  4  2n  0 | 2  n 0  2  0 | m * *
x x . xmo ♦  4m | 2m  2m  4m |  m 2m  0  2m  4 | 0  m 2  0  2 | * n *
. xno xmo ♦  nm |  0  nm  nm |  0  0  m  nm  n | 0  0 0  m  n | * * 2

xxnoo xxmoo&#x   (n>2, m>2)   → height = 1
({n}{m}-dip || {n}{m}-dip)

o.no. o.mo.    | nm  * |  2  2  1  0  0 | 1  4 1  2  2 0  0 0 | 2 2 1  4 1 0 0 | 1 2 2 0
.on.o .om.o    |  * nm |  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 | nm  *  *  *  * | 1  2 0  1  0 0  0 0 | 2 1 1  2 0 0 0 | 1 2 1 0
.. .. x. ..    |  2  0 |  * nm  *  *  * | 0  2 1  0  1 0  0 0 | 1 2 0  2 1 0 0 | 1 1 2 0
oonoo oomoo&#x |  1  1 |  *  * nm  *  * | 0  0 0  2  2 0  0 0 | 0 0 1  4 1 0 0 | 0 2 2 0
.x .. .. ..    |  0  2 |  *  *  * nm  * | 0  0 0  1  0 1  2 0 | 0 0 1  2 0 2 1 | 0 2 1 1
.. .. .x ..    |  0  2 |  *  *  *  * nm | 0  0 0  0  1 0  2 1 | 0 0 0  2 1 1 2 | 0 1 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.no. .. ..    |  n  0 |  n  0  0  0  0 | m  * *  *  * *  * * | 2 0 1  0 0 0 0 | 1 2 0 0
x. .. x. ..    |  4  0 |  2  2  0  0  0 | * nm *  *  * *  * * | 1 1 0  1 0 0 0 | 1 1 1 0
.. .. x.mo.    |  m  0 |  0  m  0  0  0 | *  * n  *  * *  * * | 0 2 0  0 1 0 0 | 1 0 2 0
xx .. .. ..&#x |  2  2 |  1  0  2  1  0 | *  * * nm  * *  * * | 0 0 1  2 0 0 0 | 0 2 1 0
.. .. xx ..&#x |  2  2 |  0  1  2  0  1 | *  * *  * nm *  * * | 0 0 0  2 1 0 0 | 0 1 2 0
.xn.o .. ..    |  0  n |  0  0  0  n  0 | *  * *  *  * m  * * | 0 0 1  0 0 2 0 | 0 2 0 1
.x .. .x ..    |  0  4 |  0  0  0  2  2 | *  * *  *  * * nm * | 0 0 0  1 0 1 1 | 0 1 1 1
.. .. .xm.o    |  0  m |  0  0  0  0  m | *  * *  *  * *  * n | 0 0 0  0 1 0 2 | 0 0 2 1
---------------+-------+----------------+---------------------+----------------+--------
x.no. x. ..    ♦ 2n  0 | 2n  n  0  0  0 | 2  n 0  0  0 0  0 0 | m * *  * * * * | 1 1 0 0
x. .. x.mo.    ♦ 2m  0 |  m 2m  0  0  0 | 0  m 2  0  0 0  0 0 | * n *  * * * * | 1 0 1 0
xxnoo .. ..&#x ♦  n  n |  n  0  n  n  0 | 1  0 0  n  0 1  0 0 | * * m  * * * * | 0 2 0 0
xx .. xx ..&#x ♦  4  4 |  2  2  4  2  2 | 0  1 0  2  2 0  1 0 | * * * nm * * * | 0 1 1 0
.. .. xxmoo&#x ♦  m  m |  0  m  m  0  m | 0  0 1  0  m 0  0 1 | * * *  * n * * | 0 0 2 0
.xn.o .x ..    ♦  0 2n |  0  0  0 2n  n | 0  0 0  0  0 2  n 0 | * * *  * * m * | 0 1 0 1
.x .. .xm.o    ♦  0 2m |  0  0  0  m 2m | 0  0 0  0  0 0  m 2 | * * *  * * * n | 0 0 1 1
---------------+-------+----------------+---------------------+----------------+--------
x.no. x.mo.    ♦ nm  0 | nm nm  0  0  0 | m nm n  0  0 0  0 0 | m n 0  0 0 0 0 | 1 * * *
xxnoo xx ..&#x ♦ 2n 2n | 2n  n 2n 2n  n | 2  n 0 2n  n 2  n 0 | 1 0 2  n 0 1 0 | * m * *
xx .. xxmoo&#x ♦ 2m 2m |  m 2m 2m  m 2m | 0  m 2  m 2m 0  m 2 | 0 1 0  m 2 0 1 | * * n *
.xn.o .xm.o    ♦  0 nm |  0  0  0 nm nm | 0  0 0  0  0 m nm n | 0 0 0  0 0 m n | * * * 1

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