Acronym squippyp, K-4.12 Name square-pyramidal prism,J1 prism,line || cube,digonal magnabicupolaic ring |,>,O device line prism pyramid prism = ||>| Segmentochoron display Circumradius sqrt(3)/2 = 0.866025 Lace cityin approx. ASCII-art ``` x o x x x x ``` Coordinates (1/sqrt(2), 0, 0, 1/2)   & all permutations in all but last coord., all changes of sign in all but first coord. Volume sqrt(2)/6 = 0.235702 Dihedral angles at {4} between trip and trip:   arccos(-1/3) = 109.471221° at {4} between squippy and cube:   90° at {3} between squippy and trip:   90° at {4} between cube and trip:   arccos(1/sqrt(3)) = 54.735610° Confer related segmentochora: n-pyp   {n} || 2n-p   ope   related CRFs: esquippidpy   general polytopal classes: segmentochora   lace simplices Externallinks

Incidence matrix according to Dynkin symbol

```xx ox4oo&#x   → height = 1/sqrt(2) = 0.707107
(line || cube)

o. o.4o.    | 2 * | 1 4 0 0 | 4 4 0 0 | 4 1 0
.o .o4.o    | * 8 | 0 1 1 2 | 1 2 2 1 | 2 1 1
------------+-----+---------+---------+------
x. .. ..    | 2 0 | 1 * * * | 4 0 0 0 | 4 0 0
oo oo4oo&#x | 1 1 | * 8 * * | 1 2 0 0 | 2 1 0
.x .. ..    | 0 2 | * * 4 * | 1 0 2 0 | 2 0 1
.. .x ..    | 0 2 | * * * 8 | 0 1 1 1 | 1 1 1
------------+-----+---------+---------+------
xx .. ..&#x | 2 2 | 1 2 1 0 | 4 * * * | 2 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 | * 8 * * | 1 1 0
.x .x ..    | 0 4 | 0 0 2 2 | * * 4 * | 1 0 1
.. .x4.o    | 0 4 | 0 0 0 4 | * * * 2 | 0 1 1
------------+-----+---------+---------+------
xx ox ..&#x ♦ 2 4 | 1 4 2 2 | 2 2 1 0 | 4 * *
.. ox4oo&#x ♦ 1 4 | 0 4 0 4 | 0 4 0 1 | * 2 *
.x .x4.o    ♦ 0 8 | 0 0 4 8 | 0 0 4 2 | * * 1
```

```xx ox ox&#x   → height = 1/sqrt(2) = 0.707107
(line || cube)

o. o. o.    | 2 * | 1 4 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0
.o .o .o    | * 8 | 0 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1
------------+-----+-----------+-------------+--------
x. .. ..    | 2 0 | 1 * * * * | 4 0 0 0 0 0 | 2 2 0 0
oo oo oo&#x | 1 1 | * 8 * * * | 1 1 1 0 0 0 | 1 1 1 0
.x .. ..    | 0 2 | * * 4 * * | 1 0 0 1 1 0 | 1 1 0 1
.. .x ..    | 0 2 | * * * 4 * | 0 1 0 1 0 1 | 1 0 1 1
.. .. .x    | 0 2 | * * * * 4 | 0 0 1 0 1 1 | 0 1 1 1
------------+-----+-----------+-------------+--------
xx .. ..&#x | 2 2 | 1 2 1 0 0 | 4 * * * * * | 1 1 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 0 | * 4 * * * * | 1 0 1 0
.. .. ox&#x | 1 2 | 0 2 0 0 1 | * * 4 * * * | 0 1 1 0
.x .x ..    | 0 4 | 0 0 2 2 0 | * * * 2 * * | 1 0 0 1
.x .. .x    | 0 4 | 0 0 2 0 2 | * * * * 2 * | 0 1 0 1
.. .x .x    | 0 4 | 0 0 0 2 2 | * * * * * 2 | 0 0 1 1
------------+-----+-----------+-------------+--------
xx ox ..&#x ♦ 2 4 | 1 4 2 2 0 | 2 2 0 1 0 0 | 2 * * *
xx .. ox&#x ♦ 2 4 | 1 4 2 0 2 | 2 0 2 0 1 0 | * 2 * *
.. ox ox&#x ♦ 1 4 | 0 4 0 2 2 | 0 2 2 0 0 1 | * * 2 *
.x .x .x    ♦ 0 8 | 0 0 4 4 4 | 0 0 0 2 2 2 | * * * 1
```

```oxx xxx&#x   → height(1,2) = height(1,3) = sqrt(3)/2 = 0.866025
height(2,3) = 1

o.. o..    | 2 * * | 1 2 2 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 | 1 1 1 2 0
.o. .o.    | * 4 * | 0 1 0 1 1 1 0 0 | 1 1 0 0 1 1 1 1 0 | 1 0 1 1 1
..o ..o    | * * 4 | 0 0 1 0 0 1 1 1 | 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1
-----------+-------+-----------------+-------------------+----------
... x..    | 2 0 0 | 1 * * * * * * * | 0 2 0 2 0 0 0 0 0 | 1 1 0 2 0
oo. oo.&#x | 1 1 0 | * 4 * * * * * * | 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0
o.o o.o&#x | 1 0 1 | * * 4 * * * * * | 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.x. ...    | 0 2 0 | * * * 2 * * * * | 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0 2 0 | * * * * 2 * * * | 0 1 0 0 0 1 0 1 0 | 1 0 0 1 1
.oo .oo&#x | 0 1 1 | * * * * * 4 * * | 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
..x ...    | 0 0 2 | * * * * * * 2 * | 0 0 1 0 0 0 1 0 1 | 0 1 1 0 1
... ..x    | 0 0 2 | * * * * * * * 2 | 0 0 0 1 0 0 0 1 1 | 0 1 0 1 1
-----------+-------+-----------------+-------------------+----------
ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 0 0 | 2 * * * * * * * * | 1 0 1 0 0
... xx.&#x | 2 2 0 | 1 2 0 0 1 0 0 0 | * 2 * * * * * * * | 1 0 0 1 0
o.x ...&#x | 1 0 2 | 0 0 2 0 0 0 1 0 | * * 2 * * * * * * | 0 1 1 0 0
... x.x&#x | 2 0 2 | 1 0 2 0 0 0 0 1 | * * * 2 * * * * * | 0 1 0 1 0
ooo ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 0 | * * * * 4 * * * * | 0 0 1 1 0
.x. .x.    | 0 4 0 | 0 0 0 2 2 0 0 0 | * * * * * 1 * * * | 1 0 0 0 1
.xx ...&#x | 0 2 2 | 0 0 0 1 0 2 1 0 | * * * * * * 2 * * | 0 0 1 0 1
... .xx&#x | 0 2 2 | 0 0 0 0 1 2 0 1 | * * * * * * * 2 * | 0 0 0 1 1
..x ..x    | 0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+-----------------+-------------------+----------
ox. xx.&#x ♦ 2 4 0 | 1 4 0 2 2 0 0 0 | 2 2 0 0 0 1 0 0 0 | 1 * * * *
o.x x.x&#x ♦ 2 0 4 | 1 0 4 0 0 0 2 2 | 0 0 2 2 0 0 0 0 1 | * 1 * * *
oxx ...&#x ♦ 1 2 2 | 0 2 2 1 0 2 1 0 | 1 0 1 0 2 0 1 0 0 | * * 2 * *
... xxx&#x ♦ 2 2 2 | 1 2 2 0 1 2 0 1 | 0 1 0 1 2 0 0 1 0 | * * * 2 *
.xx .xx&#x ♦ 0 4 4 | 0 0 0 2 2 4 2 2 | 0 0 0 0 0 1 2 2 1 | * * * * 1
```

```{4} || trip   → height = sqrt(2/3) = 0.816497

4 * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
* 2 * | 0 0 2 0 1 2 0 0 | 0 2 1 0 0 2 2 1 0 | 1 0 2 1 1
* * 4 | 0 0 0 1 0 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
--------+-----------------+-------------------+----------
2 0 0 | 2 * * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
2 0 0 | * 2 * * * * * * | 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
1 1 0 | * * 4 * * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
1 0 1 | * * * 4 * * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
0 2 0 | * * * * 1 * * * | 0 2 0 0 0 0 2 0 0 | 1 0 2 0 1
0 1 1 | * * * * * 4 * * | 0 0 0 0 0 1 1 1 0 | 0 0 1 1 1
0 0 2 | * * * * * * 2 * | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1
0 0 2 | * * * * * * * 2 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
--------+-----------------+-------------------+----------
4 0 0 | 2 2 0 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
2 2 0 | 1 0 2 0 1 0 0 0 | * 2 * * * * * * * | 1 0 1 0 0
2 1 0 | 0 1 2 0 0 0 0 0 | * * 2 * * * * * * | 1 0 0 1 0
2 0 2 | 1 0 0 2 0 0 1 0 | * * * 2 * * * * * | 0 1 1 0 0
2 0 2 | 0 1 0 2 0 0 0 1 | * * * * 2 * * * * | 0 1 0 1 0
1 1 1 | 0 0 1 1 0 1 0 0 | * * * * * 4 * * * | 0 0 1 1 0
0 2 2 | 0 0 0 0 1 2 1 0 | * * * * * * 2 * * | 0 0 1 0 1
0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * * * 2 * | 0 0 0 1 1
0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * 1 | 0 1 0 0 1
--------+-----------------+-------------------+----------
♦ 4 2 0 | 2 2 4 0 1 0 0 0 | 1 2 2 0 0 0 0 0 0 | 1 * * * *
♦ 4 0 4 | 2 2 0 4 0 0 2 2 | 1 0 0 2 2 0 0 0 1 | * 1 * * *
♦ 2 2 2 | 1 0 2 2 1 2 1 0 | 0 1 0 1 0 2 1 0 0 | * * 2 * *
♦ 2 1 2 | 0 1 2 2 0 2 0 1 | 0 0 1 0 1 2 0 1 0 | * * * 2 *
♦ 0 2 4 | 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 2 2 1 | * * * * 1
```

```squippy || squippy   → height = 1

1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0  top-tip
* 4 * * | 1 0 2 1 0 0 | 2 1 1 0 0 0 | 1 2 1 0  top-base
* * 1 * | 0 1 0 0 4 0 | 0 4 0 0 4 0 | 0 4 0 1  bottom-tip
* * * 4 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1  bottom-base
----------+-------------+-------------+--------
1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
1 0 1 0 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0
0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0
0 1 0 1 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0
0 0 1 1 | * * * * 4 * | 0 1 0 0 2 0 | 0 2 0 1
0 0 0 2 | * * * * * 4 | 0 0 0 1 1 1 | 0 1 1 1
----------+-------------+-------------+--------
1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0
1 1 1 1 | 1 1 0 1 1 0 | * 4 * * * * | 0 2 0 0
0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0
0 2 0 2 | 0 0 1 2 0 1 | * * * 4 * * | 0 1 1 0
0 0 1 2 | 0 0 0 0 2 1 | * * * * 4 * | 0 1 0 1
0 0 0 4 | 0 0 0 0 0 4 | * * * * * 1 | 0 0 1 1
----------+-------------+-------------+--------
♦ 1 4 0 0 | 4 0 4 0 0 0 | 4 0 1 0 0 0 | 1 * * *
♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 4 * *
♦ 0 4 0 4 | 0 0 4 4 0 4 | 0 0 1 4 0 1 | * * 1 *
♦ 0 0 1 4 | 0 0 0 0 4 4 | 0 0 0 0 4 1 | * * * 1
```

```oxxo4oooo&#xr   → height(1,2) = height(3,4) = sqrt(1-[1/4 *sin^2(π/n)])
height(1,4) = height(2,3) = 1
( (pt || {4})  ||  (pt || {4}) )

o...4o...     | 1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0
.o..4.o..     | * 4 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
..o.4..o.     | * * 4 * | 0 0 0 1 2 1 | 0 1 0 2 1 2 | 0 2 1 1
...o4...o     | * * * 1 | 0 1 0 0 0 4 | 0 4 0 0 0 4 | 0 4 0 1
--------------+---------+-------------+-------------+--------
oo..4oo..&#x  | 1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o..o4o..o&#x  | 1 0 0 1 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0
.x.. ....     | 0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0
.oo.4.oo.&#x  | 0 1 1 0 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0
..x. ....     | 0 0 2 0 | * * * * 4 * | 0 0 0 1 1 1 | 0 1 1 1
..oo4..oo&#x  | 0 0 1 1 | * * * * * 4 | 0 1 0 0 0 2 | 0 2 0 1
--------------+---------+-------------+-------------+--------
ox.. ....&#x  | 1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0
oooo4oooo&#xr | 1 1 1 1 | 1 1 0 1 0 1 | * 4 * * * * | 0 2 0 0
.x..4.o..     | 0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0
.xx. ....&#x  | 0 2 2 0 | 0 0 1 2 1 0 | * * * 4 * * | 0 1 1 0
..x.4..o.     | 0 0 4 0 | 0 0 0 0 4 0 | * * * * 1 * | 0 0 1 1
..xo ....&#x  | 0 0 2 1 | 0 0 0 0 1 2 | * * * * * 4 | 0 1 0 1
--------------+---------+-------------+-------------+--------
ox..4oo..&#x  ♦ 1 4 0 0 | 4 0 4 0 0 0 | 4 0 1 0 0 0 | 1 * * *
oxxo ....&#xr ♦ 1 2 2 1 | 2 1 1 2 1 2 | 1 2 0 1 0 1 | * 4 * *
.xx.4.oo.&#x  ♦ 0 4 4 0 | 0 0 4 4 4 0 | 0 0 1 4 1 0 | * * 1 *
..xo4..oo&#x  ♦ 0 0 4 1 | 0 0 0 0 4 4 | 0 0 0 0 1 4 | * * * 1
```

```o(xo)x4o(oo)o&#xt
(pt || ({4} || pt) || para {4})

o(..).4o(..).     | 1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0
.(o.).4.(o.).     | * 4 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.(.o).4.(.o).     | * * 1 * | 0 1 0 0 4 0 | 0 4 0 0 4 0 | 0 4 0 1
.(..)o4.(..)o     | * * * 4 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1
------------------+---------+-------------+-------------+--------
o(o.).4o(o.).&#x  | 1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o(.o).4o(.o).&#x  | 1 0 1 0 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0
.(x.). .(..).     | 0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0
.(o.)o4.(o.)o&#x  | 0 1 0 1 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0
.(.o)o4.(.o)o&#x  | 0 0 1 1 | * * * * 4 * | 0 1 0 0 2 0 | 0 2 0 1
.(..)x .(..).     | 0 0 0 2 | * * * * * 4 | 0 0 0 1 1 1 | 0 1 1 1
------------------+---------+-------------+-------------+--------
o(x.). .(..).&#x  | 1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0
o(oo)o4o(oo)o&#xt | 1 1 1 1 | 1 1 0 1 1 0 | * 4 * * * * | 0 2 0 0
.(x.).4.(o.).     | 0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0
.(x.)x .(..).&#x  | 0 2 0 2 | 0 0 1 2 0 1 | * * * 4 * * | 0 1 1 0
.(.o)x .(..).&#x  | 0 0 1 2 | 0 0 0 0 2 1 | * * * * 4 * | 0 1 0 1
.(..)x4.(..)o     | 0 0 0 4 | 0 0 0 0 0 4 | * * * * * 1 | 0 0 1 1
------------------+---------+-------------+-------------+--------
o(x.).4o(o.).&#x  ♦ 1 4 0 0 | 4 0 4 0 0 0 | 4 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 | * 4 * *
.(x.)x4.(o.)o&#x  ♦ 0 4 0 4 | 0 0 4 4 0 4 | 0 0 1 4 0 1 | * * 1 *
.(.o)x4.(.o)o&#x  ♦ 0 0 1 4 | 0 0 0 0 4 4 | 0 0 0 0 4 1 | * * * 1
```