Acronym traf, K-4.6
Name triangular antifastegium,
triangle oct wedge,
{3} || gyro trip,
{3} || oct,
(vertex-) diminished rap
Segmentochoron display
Circumradius sqrt(3/5) = 0.774597
Lace city
in approx. ASCII-art
   x3o   
         
x3o   o3x
x o   o x   
            
   x x   o o
Dihedral angles
  • at {4} between squippy and trip:   arccos(-sqrt[1/6]) = 114.094843°
  • at {3} between oct and tet:   arccos(-1/4) = 104.477512°
  • at {3} between squippy and tet:   arccos(-1/4) = 104.477512°
  • at {3} between oct and oct:   arccos(1/4) = 75.522488°
  • at {3} between oct and squippy:   arccos(1/4) = 75.522488°
  • at {3} between oct and trip:   arccos(sqrt[1/6]) = 65.905157°
Confer
segmentochora family:
n-af  
uniform relative:
rap  
related segmentochora:
bidrap  
variations:
xo xo3ox&#q  
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

xoo3oxx&#x   → height(1,2) = height(1,3) = sqrt(2/3) = 0.816497
               height(2,3) = 1
( {3} || (dual {3} || dual {3}) )

o..3o..    | 3 * *  2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o.3.o.    | * 3 * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o3..o    | * * 3 | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
-----------+-------+-------------+-------------------+----------
x.. ...    | 2 0 0 | 3 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.3oo.&#x | 1 1 0 | * 6 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o3o.o&#x | 1 0 1 | * * 6 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x.    | 0 2 0 | * * * 3 * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo3.oo&#x | 0 1 1 | * * * * 3 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x    | 0 0 2 | * * * * * 3 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
-----------+-------+-------------+-------------------+----------
x..3o..    | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 3 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 3 * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 3 * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 3 * * * * | 0 1 0 1 0
ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 6 * * * | 0 0 1 1 0
.o.3.x.    | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 3 * | 0 0 0 1 1
..o3..x    | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+-------------+-------------------+----------
xo.3ox.&#x  3 3 0 | 3 6 0 3 0 0 | 1 3 3 0 0 0 1 0 0 | 1 * * * *
x.o3o.x&#x  3 0 3 | 3 0 6 0 0 3 | 1 0 0 3 3 0 0 0 1 | * 1 * * *
xoo ...&#x  2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 3 * *
... oxx&#x  1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * 3 *
.oo3.xx&#x  0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 0 1 3 1 | * * * * 1

xo3ox ox&#x   → height = sqrt(5/12) = 0.645497
({3} || gyro trip)

o.3o. o.    | 3 *  2  4 0 0 | 1 4 2 2 0 0 | 2 2 1 0
.o3.o .o    | * 6 | 0  2 2 1 | 0 1 2 2 1 2 | 1 1 2 1
------------+-----+----------+-------------+--------
x. .. ..    | 2 0 | 3  * * * | 1 2 0 0 0 0 | 2 1 0 0
oo3oo oo&#x | 1 1 | * 12 * * | 0 1 1 1 0 0 | 1 1 1 0
.. .x ..    | 0 2 | *  * 6 * | 0 0 1 0 1 1 | 1 0 1 1
.. .. .x    | 0 2 | *  * * 3 | 0 0 0 2 0 2 | 0 1 2 1
------------+-----+----------+-------------+--------
x.3o. ..    | 3 0 | 3  0 0 0 | 1 * * * * * | 2 0 0 0
xo .. ..&#x | 2 1 | 1  2 0 0 | * 6 * * * * | 1 1 0 0
.. ox ..&#x | 1 2 | 0  2 1 0 | * * 6 * * * | 1 0 1 0
.. .. ox&#x | 1 2 | 0  2 0 1 | * * * 6 * * | 0 1 1 0
.o3.x ..    | 0 3 | 0  0 3 0 | * * * * 2 * | 1 0 0 1
.. .x .x    | 0 4 | 0  0 2 2 | * * * * * 3 | 0 0 1 1
------------+-----+----------+-------------+--------
xo3ox ..&#x  3 3 | 3  6 3 0 | 1 3 3 0 1 0 | 2 * * *
xo .. ox&#x  2 2 | 1  4 0 1 | 0 2 0 2 0 0 | * 3 * *
.. ox ox&#x  1 4 | 0  4 2 2 | 0 0 2 2 0 1 | * * 3 *
.o3.x .x     0 6 | 0  0 6 3 | 0 0 0 0 2 3 | * * * 1

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

o..3o..    | 3 * *  2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o.3.o.    | * 3 * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o3..o    | * * 3 | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
-----------+-------+-------------+-------------------+----------
x.. ...    | 2 0 0 | 3 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.3oo.&#x | 1 1 0 | * 6 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o3o.o&#x | 1 0 1 | * * 6 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x.    | 0 2 0 | * * * 3 * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo3.oo&#x | 0 1 1 | * * * * 3 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x    | 0 0 2 | * * * * * 3 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
-----------+-------+-------------+-------------------+----------
x..3o..    | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 3 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 3 * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 3 * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 3 * * * * | 0 1 0 1 0
ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 6 * * * | 0 0 1 1 0
.o.3.x.    | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 3 * | 0 0 0 1 1
..o3..x    | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+-------------+-------------------+----------
xo.3ox.&#x  3 3 0 | 3 6 0 3 0 0 | 1 3 3 0 0 0 1 0 0 | 1 * * * *
x.o3o.x&#x  3 0 3 | 3 0 6 0 0 3 | 1 0 0 3 3 0 0 0 1 | * 1 * * *
xoo ...&#x  2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 3 * *
... oxx&#x  1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * 3 *
.oo3.xx&#x  0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 0 1 3 1 | * * * * 1

tet || squippy   → height = sqrt(5/8) = 0.790569

2 * * * | 1 2 2 0 0 0 0 0 0 | 2 2 1 2 1 0 0 0 0 0 0 | 1 2 1 1 0 0  top edge of tet
* 2 * *  0 2 0 1 2 1 0 0 0 | 1 0 2 2 0 1 1 2 0 0 0 | 1 1 0 2 1 0  bottom edge of tet
* * 4 * | 0 0 1 0 1 0 1 1 1 | 0 1 0 1 1 0 1 1 1 1 1 | 0 1 1 1 1 1  top base of squippy
* * * 1  0 0 0 0 0 2 0 0 4 | 0 0 0 0 0 1 0 4 0 2 2 | 0 0 0 2 2 1  bottom tip of squippy
--------+-------------------+-----------------------+------------
2 0 0 0 | 1 * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0
1 1 0 0 | * 4 * * * * * * * | 1 0 1 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
1 0 1 0 | * * 4 * * * * * * | 0 1 0 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
0 2 0 0 | * * * 1 * * * * * | 0 0 2 0 0 1 0 0 0 0 0 | 1 0 0 2 0 0
0 1 1 0 | * * * * 4 * * * * | 0 0 0 1 0 0 1 1 0 0 0 | 0 1 0 1 1 0
0 1 0 1 | * * * * * 2 * * * | 0 0 0 0 0 1 0 2 0 0 0 | 0 0 0 2 1 0
0 0 2 0 | * * * * * * 2 * * | 0 1 0 0 0 0 1 0 1 1 0 | 0 1 1 0 1 1
0 0 2 0 | * * * * * * * 2 * | 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 1 0 1
0 0 1 1 | * * * * * * * * 4 | 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1
--------+-------------------+-----------------------+------------
2 1 0 0 | 1 2 0 0 0 0 0 0 0 | 2 * * * * * * * * * * | 1 1 0 0 0 0
2 0 2 0 | 1 0 2 0 0 0 1 0 0 | * 2 * * * * * * * * * | 0 1 1 0 0 0
1 2 0 0 | 0 2 0 1 0 0 0 0 0 | * * 2 * * * * * * * * | 1 0 0 1 0 0
1 1 1 0 | 0 1 1 0 1 0 0 0 0 | * * * 4 * * * * * * * | 0 1 0 1 0 0
1 0 2 0 | 0 0 2 0 0 0 0 1 0 | * * * * 2 * * * * * * | 0 0 1 1 0 0
0 2 0 1 | 0 0 0 1 0 2 0 0 0 | * * * * * 1 * * * * * | 0 0 0 2 0 0  gyrated {3}
0 1 2 0 | 0 0 0 0 2 0 1 0 0 | * * * * * * 2 * * * * | 0 1 0 0 1 0
0 1 1 1 | 0 0 0 0 1 1 0 0 1 | * * * * * * * 4 * * * | 0 0 0 1 1 0
0 0 4 0 | 0 0 0 0 0 0 2 2 0 | * * * * * * * * 1 * * | 0 0 1 0 0 1
0 0 2 1 | 0 0 0 0 0 0 1 0 2 | * * * * * * * * * 2 * | 0 0 0 0 1 1
0 0 2 1 | 0 0 0 0 0 0 0 1 2 | * * * * * * * * * * 2 | 0 0 0 1 0 1
--------+-------------------+-----------------------+------------
2 2 0 0 | 1 4 0 1 0 0 0 0 0 | 2 0 2 0 0 0 0 0 0 0 0 | 1 * * * * *  tet
2 1 2 0 | 1 2 2 0 2 0 1 0 0 | 1 1 0 2 0 0 1 0 0 0 0 | * 2 * * * *  squippy
2 0 4 0 | 1 0 4 0 0 0 2 2 0 | 0 2 0 0 2 0 0 0 1 0 0 | * * 1 * * *  trip
1 2 2 1 | 0 2 2 1 2 2 0 1 2 | 0 0 1 2 1 1 0 2 0 0 1 | * * * 2 * *  oct
0 1 2 1 | 0 0 0 0 2 1 1 0 2 | 0 0 0 0 0 0 1 2 0 1 0 | * * * * 2 *  tet
0 0 4 1 | 0 0 0 0 0 0 2 2 4 | 0 0 0 0 0 0 0 0 1 2 2 | * * * * * 1  squippy

© 2004-2018
top of page