Acronym hippyp Name hexagon-pyramidal prism,line || hip Circumradius ∞   i.e. flat in euclidean space Dihedral angles at {4} between trip and trip:   180° at {6} between hip and hippy:   90° at {3} between hippy and trip:   90° at {4} between hip and trip:   0° Confer general pyramid-prisms: n-pyp   uniform relative: tiph   general polytopal classes: decomposition   lace simplices

It either can be thought of as a degenerate 4D segmentotope with zero height, or as a 3D euclidean decomposition of the larger base into smaller bits.

Incidence matrix according to Dynkin symbol

```xx ox6oo&#x   → height = 0
(line || hip)

o. o.6o.    | 2  * | 1  6 0  0 | 6  6 0 0 | 6 1 0
.o .o6.o    | * 12 | 0  1 1  2 | 1  2 2 1 | 2 1 1
------------+------+-----------+----------+------
x. .. ..    | 2  0 | 1  * *  * | 6  0 0 0 | 6 0 0
oo oo6oo&#x | 1  1 | * 12 *  * | 1  2 0 0 | 2 1 0
.x .. ..    | 0  2 | *  * 6  * | 1  0 2 0 | 2 0 1
.. .x ..    | 0  2 | *  * * 12 | 0  1 1 1 | 1 1 1
------------+------+-----------+----------+------
xx .. ..&#x | 2  2 | 1  2 1  0 | 6  * * * | 2 0 0
.. ox ..&#x | 1  2 | 0  2 0  1 | * 12 * * | 1 1 0
.x .x ..    | 0  4 | 0  0 2  2 | *  * 6 * | 1 0 1
.. .x6.o    | 0  6 | 0  0 0  6 | *  * * 2 | 0 1 1
------------+------+-----------+----------+------
xx ox ..&#x ♦ 2  4 | 1  4 2  2 | 2  2 1 0 | 6 * *
.. ox6oo&#x ♦ 1  6 | 0  6 0  6 | 0  6 0 1 | * 2 *
.x .x6.o    ♦ 0 12 | 0  0 6 12 | 0  0 6 2 | * * 1
```

```xx ox3ox&#x   → height = 0
(line || hip)

o. o.3o.    | 2  * | 1  6 0 0 0 | 6 3 3 0 0 0 | 3 3 1 0
.o .o3.o    | * 12 | 0  1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1
------------+------+------------+-------------+--------
x. .. ..    | 2  0 | 1  * * * * | 6 0 0 0 0 0 | 3 3 0 0
oo oo3oo&#x | 1  1 | * 12 * * * | 1 1 1 0 0 0 | 1 1 1 0
.x .. ..    | 0  2 | *  * 6 * * | 1 0 0 1 1 0 | 1 1 0 1
.. .x ..    | 0  2 | *  * * 6 * | 0 1 0 1 0 1 | 1 0 1 1
.. .. .x    | 0  2 | *  * * * 6 | 0 0 1 0 1 1 | 0 1 1 1
------------+------+------------+-------------+--------
xx .. ..&#x | 2  2 | 1  2 1 0 0 | 6 * * * * * | 1 1 0 0
.. ox ..&#x | 1  2 | 0  2 0 1 0 | * 6 * * * * | 1 0 1 0
.. .. ox&#x | 1  2 | 0  2 0 0 1 | * * 6 * * * | 0 1 1 0
.x .x ..    | 0  4 | 0  0 2 2 0 | * * * 3 * * | 1 0 0 1
.x .. .x    | 0  4 | 0  0 2 0 2 | * * * * 3 * | 0 1 0 1
.. .x3.x    | 0  6 | 0  0 0 3 3 | * * * * * 2 | 0 0 1 1
------------+------+------------+-------------+--------
xx ox ..&#x ♦ 2  4 | 1  4 2 2 0 | 2 2 0 1 0 0 | 3 * * *
xx .. ox&#x ♦ 2  4 | 1  4 2 0 2 | 2 0 2 0 1 0 | * 3 * *
.. ox3ox&#x ♦ 1  6 | 0  6 0 3 3 | 0 3 3 0 0 1 | * * 2 *
.x .x3.x    ♦ 0 12 | 0  0 6 6 6 | 0 0 0 3 3 2 | * * * 1
```

```hippy || hippy   → height = 1

1 * * * | 6 1 0 0 0 0 | 6 6 0 0 0 0 | 1 6 0 0  top-tip
* 6 * * | 1 0 2 1 0 0 | 2 1 1 0 0 0 | 1 2 1 0  top-base
* * 1 * | 0 1 0 0 6 0 | 0 6 0 0 6 0 | 0 6 0 1  bottom-tip
* * * 6 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1  bottom-base
----------+-------------+-------------+--------
1 1 0 0 | 6 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
1 0 1 0 | * 1 * * * * | 0 6 0 0 0 0 | 0 6 0 0
0 2 0 0 | * * 6 * * * | 1 0 1 1 0 0 | 1 1 1 0
0 1 0 1 | * * * 6 * * | 0 1 0 2 0 0 | 0 2 1 0
0 0 1 1 | * * * * 6 * | 0 1 0 0 2 0 | 0 2 0 1
0 0 0 2 | * * * * * 6 | 0 0 0 1 1 1 | 0 1 1 1
----------+-------------+-------------+--------
1 2 0 0 | 2 0 1 0 0 0 | 6 * * * * * | 1 1 0 0
1 1 1 1 | 1 1 0 1 1 0 | * 6 * * * * | 0 2 0 0
0 6 0 0 | 0 0 6 0 0 0 | * * 1 * * * | 1 0 1 0
0 2 0 2 | 0 0 1 2 0 1 | * * * 6 * * | 0 1 1 0
0 0 1 2 | 0 0 0 0 2 1 | * * * * 6 * | 0 1 0 1
0 0 0 6 | 0 0 0 0 0 6 | * * * * * 1 | 0 0 1 1
----------+-------------+-------------+--------
♦ 1 6 0 0 | 6 0 6 0 0 0 | 6 0 1 0 0 0 | 1 * * *
♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 6 * *
♦ 0 6 0 6 | 0 0 6 6 0 5 | 0 0 1 6 0 1 | * * 1 *
♦ 0 0 1 6 | 0 0 0 0 6 6 | 0 0 0 0 6 1 | * * * 1
```