Acronym n/d,2n/d-dipcup Name n/d,2n/d-dip cupoliprism Circumradius sqrt([7+4 cos(π d/n)-2 cos2(π d/n)]/[8-8 cos2(π d/n)]) Especially squatet (n=2,d=1)*   thiddipcup (n=3,d=1) Confer general polytopal classes: scaliform

These are all scaliform polytera. They even are convex if d=1.

* The case n/d = 2 (squatet) would be included here by concept. It just has a different incidence matrix, as the n/d-gons then become degenerate.

Incidence matrix according to Dynkin symbol

```xx-n/d-xo xx-n/d-ox&#x   (4/3 < n/d < 4)   → height = sqrt[1 - 1/(2 sin2(π d/n))]
((2n/d,n/d)-dip || (n/d,2n/d)-dip)

o.-n/d-o. o.-n/d-o.    | 2nn   * |  1  1   2   2   0  0  0 | 1  2  2  1   2   2   2   1  0  0  0 0 | 2 1 1  2  2  1  2  1  1 0 0 0 | 1 2 1 1 1 0
.o-n/d-.o .o-n/d-.o    |   * 2nn |  0  0   0   2   2  1  1 | 0  0  0  0   2   1   2   2  1  2  2 1 | 0 0 0  1  2  2  1  1  2 1 1 2 | 0 1 1 2 1 1
-----------------------+---------+-------------------------+---------------------------------------+-------------------------------+------------
x.     .. ..     ..    |   2   0 | nn  *   *   *   *  *  * | 1  2  0  0   2   0   0   0  0  0  0 0 | 2 1 0  2  2  1  0  0  0 0 0 0 | 1 2 1 1 0 0
..     x. ..     ..    |   2   0 |  * nn   *   *   *  *  * | 1  0  2  0   0   2   0   0  0  0  0 0 | 2 0 1  2  0  0  2  1  0 0 0 0 | 1 2 1 0 1 0
..     .. x.     ..    |   2   0 |  *  * 2nn   *   *  *  * | 0  1  1  1   0   0   1   0  0  0  0 0 | 1 1 1  0  1  0  1  0  1 0 0 0 | 1 1 0 1 1 0
oo-n/d-oo oo-n/d-oo&#x |   1   1 |  *  *   * 4nn   *  *  * | 0  0  0  0   1   1   1   1  0  0  0 0 | 0 0 0  1  1  1  1  1  1 0 0 0 | 0 1 1 1 1 0
.x     .. ..     ..    |   0   2 |  *  *   *   * 2nn  *  * | 0  0  0  0   1   0   0   0  1  1  1 0 | 0 0 0  1  1  1  0  0  0 1 1 1 | 0 1 1 1 0 1
..     .. .x     ..    |   0   2 |  *  *   *   *   * nn  * | 0  0  0  0   0   0   2   0  0  2  0 1 | 0 0 0  0  2  0  1  0  2 1 0 2 | 0 1 0 2 1 1
..     .. ..     .x    |   0   2 |  *  *   *   *   *  * nn | 0  0  0  0   0   0   0   2  0  0  2 1 | 0 0 0  0  0  2  0  1  2 0 1 2 | 0 0 1 2 1 1
-----------------------+---------+-------------------------+---------------------------------------+-------------------------------+------------
x.-n/d-x. ..     ..    |  2n   0 |  n  n   0   0   0  0  0 | n  *  *  *   *   *   *   *  *  *  * * | 2 0 0  2  0  0  0  0  0 0 0 0 | 1 2 1 0 0 0
x.     .. x.     ..    |   4   0 |  2  0   2   0   0  0  0 | * nn  *  *   *   *   *   *  *  *  * * | 1 1 0  0  1  0  0  0  0 0 0 0 | 1 1 0 1 0 0
..     x. x.     ..    |   4   0 |  0  2   2   0   0  0  0 | *  * nn  *   *   *   *   *  *  *  * * | 1 0 1  0  0  0  1  0  0 0 0 0 | 1 1 0 0 1 0
..     .. x.-n/d-o.    |   n   0 |  0  0   n   0   0  0  0 | *  *  * 2n   *   *   *   *  *  *  * * | 0 1 1  0  0  0  0  0  1 0 0 0 | 1 0 0 1 1 0
xx     .. ..     ..&#x |   2   2 |  1  0   0   2   1  0  0 | *  *  *  * 2nn   *   *   *  *  *  * * | 0 0 0  1  1  1  0  0  0 0 0 0 | 0 1 1 1 0 0
..     xo ..     ..&#x |   2   1 |  0  1   0   2   0  0  0 | *  *  *  *   * 2nn   *   *  *  *  * * | 0 0 0  1  0  0  1  1  0 0 0 0 | 0 1 1 0 1 0
..     .. xx     ..&#x |   2   2 |  0  0   1   2   0  1  0 | *  *  *  *   *   * 2nn   *  *  *  * * | 0 0 0  0  1  0  1  0  1 0 0 0 | 0 1 0 1 1 0
..     .. ..     ox&#x |   1   2 |  0  0   0   2   0  0  1 | *  *  *  *   *   *   * 2nn  *  *  * * | 0 0 0  0  0  1  0  1  1 0 0 0 | 0 0 1 1 1 0
.x-n/d-.o ..     ..    |   0   n |  0  0   0   0   n  0  0 | *  *  *  *   *   *   *   * 2n  *  * * | 0 0 0  1  0  0  0  0  0 1 1 0 | 0 1 1 0 0 1
.x     .. .x     ..    |   0   4 |  0  0   0   0   2  2  0 | *  *  *  *   *   *   *   *  * nn  * * | 0 0 0  0  1  0  0  0  0 1 0 1 | 0 1 0 1 0 1
.x     .. ..     .x    |   0   4 |  0  0   0   0   2  0  2 | *  *  *  *   *   *   *   *  *  * nn * | 0 0 0  0  0  1  0  0  0 0 1 1 | 0 0 1 1 0 1
..     .. .x-n/d-.x    |   0  2n |  0  0   0   0   0  n  n | *  *  *  *   *   *   *   *  *  *  * n | 0 0 0  0  0  0  0  0  2 0 0 2 | 0 0 0 2 1 1
-----------------------+---------+-------------------------+---------------------------------------+-------------------------------+------------
x.-n/d-x. x.     ..    ♦  4n   0 | 2n 2n  2n   0   0  0  0 | 2  n  n  0   0   0   0   0  0  0  0 0 | n * *  *  *  *  *  *  * * * * | 1 1 0 0 0 0
x.     .. x.-n/d-o.    ♦  2n   0 |  n  0  2n   0   0  0  0 | 0  n  0  2   0   0   0   0  0  0  0 0 | * n *  *  *  *  *  *  * * * * | 1 0 0 1 0 0
..     x. x.-n/d-o.    ♦  2n   0 |  0  n  2n   0   0  0  0 | 0  0  n  2   0   0   0   0  0  0  0 0 | * * n  *  *  *  *  *  * * * * | 1 0 0 0 1 0
xx-n/d-xo ..     ..&#x ♦  2n   n |  n  n   0  2n   n  0  0 | 1  0  0  0   n   n   0   0  1  0  0 0 | * * * 2n  *  *  *  *  * * * * | 0 1 1 0 0 0
xx     .. xx     ..&#x ♦   4   4 |  2  0   2   4   2  2  0 | 0  1  0  0   2   0   2   0  0  1  0 0 | * * *  * nn  *  *  *  * * * * | 0 1 0 1 0 0
xx     .. ..     ox&#x ♦   2   4 |  1  0   0   4   2  0  2 | 0  0  0  0   2   0   0   2  0  0  1 0 | * * *  *  * nn  *  *  * * * * | 0 0 1 1 0 0
..     xo xx     ..&#x ♦   4   2 |  0  2   2   4   0  1  0 | 0  0  1  0   0   2   2   0  0  0  0 0 | * * *  *  *  * nn  *  * * * * | 0 1 0 0 1 0
..     xo ..     ox&#x ♦   2   2 |  0  1   0   4   0  0  1 | 0  0  0  0   0   2   0   2  0  0  0 0 | * * *  *  *  *  * nn  * * * * | 0 0 1 0 1 0
..     .. xx-n/d-ox&#x ♦   n  2n |  0  0   n  2n   0  n  n | 0  0  0  1   0   0   n   n  0  0  0 1 | * * *  *  *  *  *  * 2n * * * | 0 0 0 1 1 0
.x-n/d-.o .x     ..    ♦   0  2n |  0  0   0   0  2n  n  0 | 0  0  0  0   0   0   0   0  2  n  0 0 | * * *  *  *  *  *  *  * n * * | 0 1 0 0 0 1
.x-n/d-.o ..     .x    ♦   0  2n |  0  0   0   0  2n  0  n | 0  0  0  0   0   0   0   0  2  0  n 0 | * * *  *  *  *  *  *  * * n * | 0 0 1 0 0 1
.x     .. .x-n/d-.x    ♦   0  4n |  0  0   0   0  2n 2n 2n | 0  0  0  0   0   0   0   0  0  n  n 2 | * * *  *  *  *  *  *  * * * n | 0 0 0 1 0 1
-----------------------+---------+-------------------------+---------------------------------------+-------------------------------+------------
x.-n/d-x. x.-n/d-o.    ♦ 2nn   0 | nn nn 2nn   0   0  0  0 | n nn nn 2n   0   0   0   0  0  0  0 0 | n n n  0  0  0  0  0  0 0 0 0 | 1 * * * * *
xx-n/d-xo xx     ..&#x ♦  4n  2n | 2n 2n  2n  4n  2n  n  0 | 2  n  n  0  2n  2n  2n   0  2  n  0 0 | 1 0 0  2  n  0  n  0  0 1 0 0 | * n * * * *
xx-n/d-xo ..     ox&#x ♦  2n  2n |  n  n   0  4n  2n  0  n | 1  0  0  0  2n  2n   0  2n  2  0  n 0 | 0 0 0  2  0  n  0  n  0 0 1 0 | * * n * * *
xx     .. xx-n/d-ox&#x ♦  2n  4n |  n  0  2n  4n  2n 2n 2n | 0  n  0  2  2n   0  2n  2n  0  n  n 2 | 0 1 0  0  n  n  0  0  2 0 0 1 | * * * n * *
..     xo xx-n/d-ox&#x ♦  2n  2n |  0  n  2n  4n   0  n  n | 0  0  n  2   0  2n  2n  2n  0  0  0 1 | 0 0 1  0  0  0  n  n  2 0 0 0 | * * * * n *
.x-n/d-.o .x-n/d-.x    ♦   0 2nn |  0  0   0   0 2nn nn nn | 0  0  0  0   0   0   0   0 2n nn nn n | 0 0 0  0  0  0  0  0  0 n n n | * * * * * 1
```
```or
o.-n/d-o. o.-n/d-o.    & | 4nn |   1   1   2   2 |  1   2   2  1   4   3 |  2  1  1  3  2   3  1 | 1  3  2
-------------------------+-----+-----------------+-----------------------+-----------------------+--------
x.     .. ..     ..    & |   2 | 2nn   *   *   * |  1   2   0  0   2   0 |  2  1  0  2  2   1  0 | 1  3  1
..     x. ..     ..    & |   2 |   * 2nn   *   * |  1   0   2  0   0   1 |  2  0  1  2  0   2  1 | 1  2  2
..     .. x.     ..    & |   2 |   *   * 4nn   * |  0   1   1  1   1   0 |  1  1  1  1  1   1  0 | 1  2  1
oo-n/d-oo oo-n/d-oo&#x   |   2 |   *   *   * 4nn |  0   0   0  0   2   2 |  0  0  0  2  1   2  1 | 0  2  2
-------------------------+-----+-----------------+-----------------------+-----------------------+--------
x.-n/d-x. ..     ..    & |  2n |   n   n   0   0 | 2n   *   *  *   *   * |  2  0  0  2  0   0  0 | 1  2  1
x.     .. x.     ..    & |   4 |   2   0   2   0 |  * 2nn   *  *   *   * |  1  1  0  0  1   0  0 | 1  2  0
..     x. x.     ..    & |   4 |   0   2   2   0 |  *   * 2nn  *   *   * |  1  0  1  0  0   1  0 | 1  1  1
..     .. x.-n/d-o.    & |   n |   0   0   n   0 |  *   *   * 4n   *   * |  0  1  1  1  0   0  0 | 1  1  1
xx     .. ..     ..&#x & |   4 |   1   0   1   2 |  *   *   *  * 4nn   * |  0  0  0  1  1   1  0 | 0  2  1
..     xo ..     ..&#x & |   3 |   0   1   0   2 |  *   *   *  *   * 4nn |  0  0  0  1  0   1  1 | 0  1  2
-------------------------+-----+-----------------+-----------------------+-----------------------+--------
x.-n/d-x. x.     ..    & ♦  4n |  2n  2n  2n   0 |  2   n   n  0   0   0 | 2n  *  *  *  *   *  * | 1  1  0
x.     .. x.-n/d-o.    & ♦  2n |   n   0  2n   0 |  0   n   0  2   0   0 |  * 2n  *  *  *   *  * | 1  1  0
..     x. x.-n/d-o.    & ♦  2n |   0   n  2n   0 |  0   0   n  2   0   0 |  *  * 2n  *  *   *  * | 1  0  1
xx-n/d-xo ..     ..&#x & ♦  3n |   n   n   n  2n |  1   0   0  1   n   n |  *  *  * 4n  *   *  * | 0  1  1
xx     .. xx     ..&#x   ♦   8 |   4   0   4   4 |  0   2   0  0   4   0 |  *  *  *  * nn   *  * | 0  2  0
xx     .. ..     ox&#x & ♦   6 |   1   2   2   4 |  0   0   1  0   2   2 |  *  *  *  *  * 2nn  * | 0  1  1
..     xo ..     ox&#x   ♦   4 |   0   2   0   4 |  0   0   0  0   0   4 |  *  *  *  *  *   * nn | 0  0  2
-------------------------+-----+-----------------+-----------------------+-----------------------+--------
x.-n/d-x. x.-n/d-o.    & ♦ 2nn |  nn  nn 2nn   0 |  n  nn  nn 2n   0   0 |  n  n  n  0  0   0  0 | 2  *  *
xx-n/d-xo xx     ..&#x & ♦  6n |  3n  2n  4n  4n |  2  2n   n  2  4n  2n |  1  1  0  2  n   n  0 | * 2n  *
xx-n/d-xo ..     ox&#x & ♦  4n |   n  2n  2n  4n |  1   0   n  2  2n  4n |  0  0  1  2  0   n  n | *  * 2n
```

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