Acronym bidrap, K-4.8 Name bidiminished rectified pentachoron,antiduowedge,square - tetrahedral wedge,digonal gyrobicupolaic ring,{4} || tet,line || ortho trip Segmentochoron display ` ©` (these providing possible orientations: as "squippy || {3}", as "tet || {4}", resp. as "trip || ortho line") Circumradius sqrt(3/5) = 0.774597 Lace cityin approx. ASCII-art ```x o o x x x ``` Dihedral angles at {4} between squippy and trip:   arccos(-1/sqrt(6)) = 114.094843° at {3} between squippy and tet:   arccos(-1/4) = 104.477512° at {3} between squippy and squippy:   arccos(1/4) = 75.522488° at {3} between squippy and trip:   arccos(sqrt[1/6]) = 65.905157° at {4} between trip and trip:   arccos(2/3) = 48.189685° Confer segmentochora family: {2n} || n-ap   uniform relative: rap   related segmentochora: trippy   variations: xxo oxx&#q   general polytopal classes: segmentochora   lace simplices Externallinks

The rap can be considered as tet || oct. Now diminish the bottom oct at both opposing tips down to the equatorial square. At the top tet the same diminishings just scratch at the pair of opposing edges. Either diminishing chops off a trippy.

Incidence matrix according to Dynkin symbol

```xxo oxx&#x   → height(1,2) = height(2,3) = sqrt(3)/2 = 0.866025
height(1,3) = 1/sqrt(2) = 0.707107

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

```{4} || tet   → height = sqrt(5/8) = 0.790569

4 * | 2 2 0 0 | 1 2 2 1 0 | 2 2 0
* 4 | 0 2 1 2 | 0 2 1 2 3 | 1 3 1
------+---------+-----------+------
2 0 | 4 * * * | 1 1 1 0 0 | 2 1 0
1 1 | * 8 * * | 0 1 1 1 0 | 1 2 0
0 2 | * * 2 * | 0 2 0 0 2 | 1 2 1
0 2 | * * * 4 | 0 0 0 1 2 | 0 2 1
------+---------+-----------+------
4 0 | 4 0 0 0 | 1 * * * * | 2 0 0
2 2 | 1 2 1 0 | * 4 * * * | 1 1 0
2 1 | 1 2 0 0 | * * 4 * * | 1 1 0
1 2 | 0 2 0 1 | * * * 4 * | 0 2 0
0 3 | 0 0 1 2 | * * * * 4 | 0 1 1
------+---------+-----------+------
♦ 4 2 | 4 4 1 0 | 1 2 2 0 0 | 2 * *
♦ 2 3 | 1 4 1 2 | 0 1 1 2 1 | * 4 *
♦ 0 4 | 0 0 2 4 | 0 0 0 0 4 | * * 1
```

```{3} || squippy   → height = sqrt(5/8) = 0.790569

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

```line || ortho trip   → height = sqrt(5/12) = 0.645497

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