2n/d-p

Acronym

2n/d-p

TOCID symbol

t(n/d)P

Name

2n/d-prism,
2n-prism with winding number d

Circumradius

sqrt[1/4+1/(4 sin²(π d/2n))]

Vertex figure

[4²,2n/d]

General of army

if d=1: is itself convex
if gcd(2n,d)=1: use a (stretched) 2n-p for its general
if gcd(2n,d)=2: use a (stretched) n-p for its general

Colonel of regiment

(is itself locally convex)

Face vector

4n, 6n, 2n+2

Especially

2n-p (d=1) 2n/2-p (d=2)

4/d	6/d	8/d	10/d	12/d	{2n/d}-p
cube	hip	op	dip	twip	2n/1
	2trip *	2cube *	2pip *	2hip *	2n/2
		stop	stiddip	3cube *	2n/3

*: Grünbaumian

Confer

general prisms:: n/d-p
general polytopal classes:: Wythoffian polyhedra

For d even it looks like a compound of two n/(d:2)-prisms (see n/d-p), and indeed vertices, edges, and {4}-faces coincide by pairs.

Incidence matrix according to Dynkin symbol

x x2n/do   (n/2>d>1)

. .    . | 4n |  1  2 |  2 1
---------+----+-------+-----
x .    . |  2 | 2n  * |  2 0
. x    . |  2 |  * 4n |  1 1
---------+----+-------+-----
x x    . |  4 |  2  2 | 2n *
. x2n/do | 2n |  0 2n |  * 2

snubbed forms: x2s2n/do, s2s2n/do

x xn/dx   (n/2>d>1)

. .   . | 4n |  1  1  1 | 1 1 1
--------+----+----------+------
x .   . |  2 | 2n  *  * | 1 1 0
. x   . |  2 |  * 2n  * | 1 0 1
. .   x |  2 |  *  * 2n | 0 1 1
--------+----+----------+------
x x   . |  4 |  2  2  0 | n * *
x .   x |  4 |  2  0  2 | * n *
. xn/dx | 2n |  0  n  n | * * 2

snubbed forms: x2sn/dx (n even), s2sn/dx (n even), x2sn/ds, x2sn/ds (n even), s2sn/ds

x2s2n/dx   (n/2>d>1)

demi( . .    . ) | 4n |  1  1  1 | 1 1 1
-----------------+----+----------+------
demi( x .    . ) |  2 | 2n  *  * | 0 1 1
demi( . .    x ) |  2 |  * 2n  * | 1 1 0
sefa( . s2n/dx ) |  2 |  *  * 2n | 1 0 1
-----------------+----+----------+------
      . s2n/dx   ♦ 2n |  0  n  n | 2 * *
demi( x .    x ) |  4 |  2  2  0 | * n *
sefa( x2s2n/dx ) |  4 |  2  0  2 | * * n

starting figure: x x2n/dx

x2s2n/ds   (n/2>d>1)

demi( . .    . ) | 4n |  1  2 | 1  2
-----------------+----+-------+-----
demi( x .    . ) |  2 | 2n  * | 0  2
sefa( . s2n/ds ) |  2 |  * 4n | 1  1
-----------------+----+-------+-----
      . s2n/ds   ♦ 2n |  0 2n | 2  *
sefa( x2s2n/ds ) |  4 |  2  2 | * 2n

starting figure: x x2n/dx

s2s2n/dx   (n/2>d>1)

demi( . .    . ) | 4n |  1  1  1 | 1  2
-----------------+----+----------+-----
      s2s        |  2 | 2n  *  * | 0  2
demi( . .    x ) |  2 |  * 2n  * | 1  1
sefa( . s2n/dx ) |  2 |  *  * 2n | 1  1
-----------------+----+----------+-----
        s2n/dx   ♦ 2n |  0  n  n | 2  *
sefa( s2s2n/dx ) |  4 |  2  1  1 | * 2n

starting figure: x x2n/dx

xx2n/doo&#x   (n/2>d>1)   → height = 1
({2n/d} || {2n/d})

o.2n/do.    | 2n  * |  2  1  0 | 1  2 0
.o2n/d.o    |  * 2n |  0  1  2 | 0  2 1
------------+-------+----------+-------
x.    ..    |  2  0 | 2n  *  * | 1  1 0
oo2n/doo&#x |  1  1 |  * 2n  * | 0  2 0
.x    ..    |  0  2 |  *  * 2n | 0  1 1
------------+-------+----------+-------
x.2n/do.    | 2n  0 | 2n  0  0 | 1  * *
xx    ..&#x |  2  2 |  1  2  1 | * 2n *
.x2n/d.o    |  0 2n |  0  0 2n | *  * 1

xxn/dxx&#x   (n/2>d>1)   → height = 1
({2n/d} || {2n/d})

o.n/do.    | 2n  * | 1 1  1 0 0 | 1 1 1 0
.on/d.o    |  * 2n | 0 0  1 1 1 | 0 1 1 1
-----------+-------+------------+--------
x.   ..    |  2  0 | n *  * * * | 1 1 0 0
..   x.    |  2  0 | * n  * * * | 1 0 1 0
oon/doo&#x |  1  1 | * * 2n * * | 0 1 1 0
.x   ..    |  0  2 | * *  * n * | 0 1 0 1
..   .x    |  0  2 | * *  * * n | 0 0 1 1
-----------+-------+------------+--------
x.n/dx.    | 2n  0 | n n  0 0 0 | 1 * * *
xx   ..&#x |  2  2 | 1 0  2 1 0 | * n * *
..   xx&#x |  2  2 | 0 1  2 0 1 | * * n *
.xn/d.x    |  0 2n | 0 0  0 n n | * * * 1

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