Acronym n/d-ap
TOCID symbol (n/d)Q; if d>n/2 also: (n/(n-d))R = (n/d)Q
Name n/d-antiprism,
n-antiprism with winding number d
(for d>n/2 also: n/(n-d)-retroprism,

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Circumradius sqrt[(3-2 cos(π d/n))/(8-8 cos(π d/n))]
Height sqrt[(1+2 cos(π d/n))/(2+2 cos(π d/n))]
esp.: d<2n/3
Coordinates (cos(k π d/n)/[2 sin(π d/n)], sin(k π d/n)/[2 sin(π d/n)], (-1)k h/2)   all k integral
where h is the height given above
Vertex figure [33,n/d]
General of army if d=1:   is itself convex
if gcd(n,d)=1 and d odd:   use d=1 for its general
if gcd(n,d)=1 and d even: general is an n-prism instead
Colonel of regiment if d<n/2 it is itself locally convex
Especially n-ap (d=1)   n/2-ap (d=2)   azap (n=∞, d=1)
3/d 4/d 5/d 6/d 7/d 8/d 9/d 10/d {n/d}-ap oct squap pap hap heap oap eap dap trirp° * stap * shap (sithap) * steap * starp * gishap (gisthap) stoap * stiddap gisharp (gisthirp) * gisteap * storp gisterp *
*: Grünbaumian
°: degenerate
Confer
general polytopal classes:
segmentohedra
External

Incidence matrix according to Dynkin symbol

```s2sn/ds   (n>2,2n/3>d>1)

demi( . .   .  ) | 2n | 1 1  2 | 1  3
-----------------+----+--------+-----
s2s   .    |  2 | n *  * | 0  2
s .   s2*a |  2 | * n  * | 0  2
sefa( . sn/ds  ) |  2 | * * 2n | 1  1
-----------------+----+--------+-----
. sn/ds    ♦  n | 0 0  n | 2  *
sefa( s2sn/ds  ) |  3 | 1 1  1 | * 2n
```
```or
demi( . .   . )              | 2n |  2  2 | 1  3
-----------------------------+----+-------+-----
s2s   .  &  s .   s2*a |  2 | 2n  * | 0  2
sefa( . sn/ds )              |  2 |  * 2n | 1  1
-----------------------------+----+-------+-----
. sn/ds                ♦  n |  0  n | 2  *
sefa( s2sn/ds )              |  3 |  2  1 | * 2n

starting figure: x xn/dx
```

```s2s2n/do   (n>2,2n/3>d>1)

demi( . .    . ) | 2n |  2  2 | 1  3
-----------------+----+-------+-----
s2s    .   |  2 | 2n  * | 0  2
sefa( . s2n/do ) |  2 |  * 2n | 1  1
-----------------+----+-------+-----
. s2n/do   ♦  n |  0  n | 2  *
sefa( s2s2n/do ) |  3 |  2  1 | * 2n

starting figure: x x2n/do
```

```xon/dox&#x   (n>2,2n/3>d>1)   → height = sqrt[(1+2*cos(d*pi/n))/(2+2*cos(d*pi/n))]
({n/d} || dual {n/d})

o.n/do.    | n * | 2  2 0 | 1 2 1 0
.on/d.o    | * n | 0  2 2 | 0 1 2 1
-----------+-----+--------+--------
x.   ..    | 2 0 | n  * * | 1 1 0 0
oon/doo&#x | 1 1 | * 2n * | 0 1 1 0
..   .x    | 0 2 | *  * n | 0 0 1 1
-----------+-----+--------+--------
x.n/do.    | n 0 | n  0 0 | 1 * * *
xo   ..&#x | 2 1 | 1  2 0 | * n * *
..   ox&#x | 1 2 | 0  2 1 | * * n *
.on/d.x    | 0 n | 0  0 n | * * * 1

snubbed forms: son/dox&#x (n even)
```