Acronym n/d-pyp Name n/d-pyramidal prism, line || n/d-prism Segmentochoron display Circumradius sqrt[1/4+1/(4-1/sin2[π d/n])] Confer general polytopal classes: segmentochora Especially tepe (n=3, d=1)   squippyp (n=4, d=1)   peppyp (n=5, d=1)   stappyp (n=5, d=2)   hippyp (n=6, d=1)

The height formula given below shows that only 2 < n/d < 6 is possible. The maximal height would be obtained at n/d = 2 with upright latteral triangles but then degenerate base, the other extremal value n/d = 6 would generate a height of zero.

Incidence matrix according to Dynkin symbol

```xx ox-n/d-oo&#x   (2<n/d<6)   → height = sqrt(1-[1/4 *sin^2(π d/n)])
(line || {n/d}-p)

o. o.-n/d-o.    | 2  * | 1  n 0  0 | n  n 0 0 | n 1 0
.o .o-n/d-.o    | * 2n | 0  1 1  2 | 1  2 2 1 | 2 1 1
----------------+------+-----------+----------+------
x. ..     ..    | 2  0 | 1  * *  * | n  0 0 0 | n 0 0
oo oo-n/d-oo&#x | 1  1 | * 2n *  * | 1  2 0 0 | 2 1 0
.x ..     ..    | 0  2 | *  * n  * | 1  0 2 0 | 2 0 1
.. .x     ..    | 0  2 | *  * * 2n | 0  1 1 1 | 1 1 1
----------------+------+-----------+----------+------
xx ..     ..&#x | 2  2 | 1  2 1  0 | n  * * * | 2 0 0
.. ox     ..&#x | 1  2 | 0  2 0  1 | * 2n * * | 1 1 0
.x .x     ..    | 0  4 | 0  0 2  2 | *  * n * | 1 0 1
.. .x-n/d-.o    | 0  n | 0  0 0  n | *  * * 2 | 0 1 1
----------------+------+-----------+----------+------
xx ox     ..&#x ♦ 2  4 | 1  4 2  2 | 2  2 1 0 | n * *
.. ox-n/d-oo&#x ♦ 1  n | 0  n 0  n | 0  n 0 1 | * 2 *
.x .x-n/d-.o    ♦ 0 2n | 0  0 n 2n | 0  0 n 2 | * * 1
```

```{n/d}-py || {n/d}-py   (2<n/d<6)   → height = 1

1 * * * | n 1 0 0 0 0 | n n 0 0 0 0 | 1 n 0 0  top-tip
* n * * | 1 0 2 1 0 0 | 2 1 1 0 0 0 | 1 2 1 0  top-base
* * 1 * | 0 1 0 0 n 0 | 0 n 0 0 n 0 | 0 n 0 1  bottom-tip
* * * n | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1  bottom-base
----------+-------------+-------------+--------
1 1 0 0 | n * * * * * | 2 1 0 0 0 0 | 1 2 0 0
1 0 1 0 | * 1 * * * * | 0 n 0 0 0 0 | 0 n 0 0
0 2 0 0 | * * n * * * | 1 0 1 1 0 0 | 1 1 1 0
0 1 0 1 | * * * n * * | 0 1 0 2 0 0 | 0 2 1 0
0 0 1 1 | * * * * n * | 0 1 0 0 2 0 | 0 2 0 1
0 0 0 2 | * * * * * n | 0 0 0 1 1 1 | 0 1 1 1
----------+-------------+-------------+--------
1 2 0 0 | 2 0 1 0 0 0 | n * * * * * | 1 1 0 0
1 1 1 1 | 1 1 0 1 1 0 | * n * * * * | 0 2 0 0
0 n 0 0 | 0 0 n 0 0 0 | * * 1 * * * | 1 0 1 0
0 2 0 2 | 0 0 1 2 0 1 | * * * n * * | 0 1 1 0
0 0 1 2 | 0 0 0 0 2 1 | * * * * n * | 0 1 0 1
0 0 0 n | 0 0 0 0 0 n | * * * * * 1 | 0 0 1 1
----------+-------------+-------------+--------
♦ 1 n 0 0 | n 0 n 0 0 0 | n 0 1 0 0 0 | 1 * * *
♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * n * *
♦ 0 n 0 n | 0 0 n n 0 n | 0 0 1 n 0 1 | * * 1 *
♦ 0 0 1 n | 0 0 0 0 n n | 0 0 0 0 n 1 | * * * 1
```

```oxxo-n/d-oooo&#xr   (2<n/d<6)   → height(1,2) = height(3,4) = sqrt(1-[1/4 *sin^2(π/n)])
height(1,4) = height(2,3) = 1
( (pt || {n/d})  ||  (pt || {n/d}) )

o...-n/d-o...     | 1 * * * | n 1 0 0 0 0 | n n 0 0 0 0 | 1 n 0 0
.o..-n/d-.o..     | * n * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
..o.-n/d-..o.     | * * n * | 0 0 0 1 2 1 | 0 1 0 2 1 2 | 0 2 1 1
...o-n/d-...o     | * * * 1 | 0 1 0 0 0 n | 0 n 0 0 0 n | 0 n 0 1
------------------+---------+-------------+-------------+--------
oo..-n/d-oo..&#x  | 1 1 0 0 | n * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o..o-n/d-o..o&#x  | 1 0 0 1 | * 1 * * * * | 0 n 0 0 0 0 | 0 n 0 0
.x..     ....     | 0 2 0 0 | * * n * * * | 1 0 1 1 0 0 | 1 1 1 0
.oo.-n/d-.oo.&#x  | 0 1 1 0 | * * * n * * | 0 1 0 2 0 0 | 0 2 1 0
..x.     ....     | 0 0 2 0 | * * * * n * | 0 0 0 1 1 1 | 0 1 1 1
..oo-n/d-..oo&#x  | 0 0 1 1 | * * * * * n | 0 1 0 0 0 2 | 0 2 0 1
------------------+---------+-------------+-------------+--------
ox..     ....&#x  | 1 2 0 0 | 2 0 1 0 0 0 | n * * * * * | 1 1 0 0
oooo-n/d-oooo&#xr | 1 1 1 1 | 1 1 0 1 0 1 | * n * * * * | 0 2 0 0
.x..-n/d-.o..     | 0 n 0 0 | 0 0 n 0 0 0 | * * 1 * * * | 1 0 1 0
.xx.     ....&#x  | 0 2 2 0 | 0 0 1 2 1 0 | * * * n * * | 0 1 1 0
..x.-n/d-..o.     | 0 0 n 0 | 0 0 0 0 n 0 | * * * * 1 * | 0 0 1 1
..xo     ....&#x  | 0 0 2 1 | 0 0 0 0 1 2 | * * * * * n | 0 1 0 1
------------------+---------+-------------+-------------+--------
ox..-n/d-oo..&#x  ♦ 1 n 0 0 | n 0 n 0 0 0 | n 0 1 0 0 0 | 1 * * *
oxxo     ....&#xr ♦ 1 2 2 1 | 2 1 1 2 1 2 | 1 2 0 1 0 1 | * n * *
.xx.-n/d-.oo.&#x  ♦ 0 n n 0 | 0 0 n n n 0 | 0 0 1 n 1 0 | * * 1 *
..xo-n/d-..oo&#x  ♦ 0 0 n 1 | 0 0 0 0 n n | 0 0 0 0 1 n | * * * 1
```

```o(xo)x-n/d-o(oo)o&#xt   (2<n/d<6)
(pt || ({n/d} || pt) || para {n/d})

o(..).-n/d-o(..).     | 1 * * * | n 1 0 0 0 0 | n n 0 0 0 0 | 1 n 0 0
.(o.).-n/d-.(o.).     | * n * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.(.o).-n/d-.(.o).     | * * 1 * | 0 1 0 0 n 0 | 0 n 0 0 n 0 | 0 n 0 1
.(..)o-n/d-.(..)o     | * * * n | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1
----------------------+---------+-------------+-------------+--------
o(o.).-n/d-o(o.).&#x  | 1 1 0 0 | n * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o(.o).-n/d-o(.o).&#x  | 1 0 1 0 | * 1 * * * * | 0 n 0 0 0 0 | 0 n 0 0
.(x.).     .(..).     | 0 2 0 0 | * * n * * * | 1 0 1 1 0 0 | 1 1 1 0
.(o.)o-n/d-.(o.)o&#x  | 0 1 0 1 | * * * n * * | 0 1 0 2 0 0 | 0 2 1 0
.(.o)o-n/d-.(.o)o&#x  | 0 0 1 1 | * * * * n * | 0 1 0 0 2 0 | 0 2 0 1
.(..)x     .(..).     | 0 0 0 2 | * * * * * n | 0 0 0 1 1 1 | 0 1 1 1
----------------------+---------+-------------+-------------+--------
o(x.).     .(..).&#x  | 1 2 0 0 | 2 0 1 0 0 0 | n * * * * * | 1 1 0 0
o(oo)o-n/d-o(oo)o&#xt | 1 1 1 1 | 1 1 0 1 1 0 | * n * * * * | 0 2 0 0
.(x.).-n/d-.(o.).     | 0 n 0 0 | 0 0 n 0 0 0 | * * 1 * * * | 1 0 1 0
.(x.)x     .(..).&#x  | 0 2 0 2 | 0 0 1 2 0 1 | * * * n * * | 0 1 1 0
.(.o)x     .(..).&#x  | 0 0 1 2 | 0 0 0 0 2 1 | * * * * n * | 0 1 0 1
.(..)x-n/d-.(..)o     | 0 0 0 n | 0 0 0 0 0 n | * * * * * 1 | 0 0 1 1
----------------------+---------+-------------+-------------+--------
o(x.).-n/d-o(o.).&#x  ♦ 1 n 0 0 | n 0 n 0 0 0 | n 0 1 0 0 0 | 1 * * *
o(xo)x     .(..).&#xt ♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * n * *
.(x.)x-n/d-.(o.)o&#x  ♦ 0 n 0 n | 0 0 n n 0 n | 0 0 1 n 0 1 | * * 1 *
.(.o)x-n/d-.(.o)o&#x  ♦ 0 0 1 n | 0 0 0 0 n n | 0 0 0 0 n 1 | * * * 1
```