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 city
in 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  

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

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