Acronym tricuf, K-4.25
Name trigonal cupofastegium,
hexagon - triangle-prismatic wedge,
triangle orthobicupolaic ring,
{6} || trip,
{3} || tricu,
0.209785-luna of small prismatodecachoron
Segmentochoron display
Circumradius 1
Lace city
in approx. ASCII-art 
   x3x   
         
x3o   x3o
Coordinates
  1. (1/sqrt(3), 0, 1/2, sqrt(5/12))          & all changes of sign in 3rd coord
  2. (-1/sqrt(12), 1/2, 1/2, sqrt(5/12))    & all changes of sign in 3rd & 4th coord
    (these two together describe the trip)
  3. (sqrt(3)/2, 1/2, 0, 0)                       & all changes of sign in 1st & 2nd coord
  4. (0, 1, 0, 0)                                     & all changes of sign in 2nd coord
    (these two together describe the {6})
(centered both in the hexagon and in the circumcenter)
Dihedral angles
  • at {4} between trip and trip:   arccos(-2/3) = 131.810315°
  • at {3} between tet and trip:   arccos[-sqrt(3/8)] = 127.761244°
  • at {3} between tet and tricu:   arccos(1/4) = 75.522488°
  • at {6} between tricu and tricu:   arccos(1/4) = 75.522488°
  • at {4} between tricu and trip:   arccos(sqrt[1/6]) = 65.905157°
  • at {3} between tricu and trip:   arccos(sqrt[3/8]) = 52.238756°
Face vector 12, 27, 24, 9
Confer
uniform relative:
spid  
segmentochora family:
{2n} || n-p  
related segmentochora:
tet || co   tet || tricu  
blends:
octatut,tricuf-blend  
general polytopal classes:
luna   segmentochora   lace simplices  
External
links 		polytopewiki

This luna is somehow more general as its fraction comes out to be non-rational: the wedge angle is arccos(1/4), accordingly that fraction is arccos(1/4) / 360° = 0.209785.


Incidence matrix according to Dynkin symbol

xx3ox xo&#x   → height = sqrt(5/12) = 0.645497
(trip || {6})

o.3o. o.    | 6 * | 2 1  2 0 0 | 1 2 2 1 2 0 | 1 1 2 1
.o3.o .o    | * 6 | 0 0  2 1 1 | 0 0 2 2 1 1 | 0 2 1 1
------------+-----+------------+-------------+--------
x. .. ..    | 2 0 | 6 *  * * * | 1 1 1 0 0 0 | 1 1 1 0
.. .. x.    | 2 0 | * 3  * * * | 0 2 0 0 2 0 | 1 0 2 1
oo3oo oo&#x | 1 1 | * * 12 * * | 0 0 1 1 1 0 | 0 1 1 1
.x .. ..    | 0 2 | * *  * 3 * | 0 0 2 0 0 1 | 0 2 1 0
.. .x ..    | 0 2 | * *  * * 3 | 0 0 0 2 0 1 | 0 2 0 1
------------+-----+------------+-------------+--------
x.3o. ..    | 3 0 | 3 0  0 0 0 | 2 * * * * * | 1 1 0 0
x. .. x.    | 4 0 | 2 2  0 0 0 | * 3 * * * * | 1 0 1 0
xx .. ..&#x | 2 2 | 1 0  2 1 0 | * * 6 * * * | 0 1 1 0
.. ox ..&#x | 1 2 | 0 0  2 0 1 | * * * 6 * * | 0 1 0 1
.. .. xo&#x | 2 1 | 0 1  2 0 0 | * * * * 6 * | 0 0 1 1
.x3.x ..    | 0 6 | 0 0  0 3 3 | * * * * * 1 | 0 2 0 0
------------+-----+------------+-------------+--------
x.3o. x.    ♦ 6 0 | 6 3  0 0 0 | 2 3 0 0 0 0 | 1 * * *
xx3ox ..&#x ♦ 3 6 | 3 0  6 3 3 | 1 0 3 3 0 1 | * 2 * *
xx .. xo&#x ♦ 4 2 | 2 2  4 1 0 | 0 1 2 0 2 0 | * * 3 *
.. ox xo&#x ♦ 2 2 | 0 1  4 0 1 | 0 0 0 2 2 0 | * * * 3


xxx3oxo&#x   → height(1,2) = height(2,3) = sqrt(2/3) = 0.816497
               height(1,3) = 1

o..3o..    | 3 * * | 2 2 1 0 0 0 0 | 1 2 1 2 2 0 0 0 0 | 1 1 2 1 0
.o.3.o.    | * 6 * | 0 1 0 1 1 1 0 | 0 1 1 0 1 1 1 1 0 | 1 0 1 1 1
..o3..o    | * * 3 | 0 0 1 0 0 2 2 | 0 0 0 2 2 0 2 1 1 | 0 1 2 1 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 1 0 0 0 0 | 1 0 1 1 0
o.o3o.o&#x | 1 0 1 | * * 3 * * * * | 0 0 0 2 2 0 0 0 0 | 0 1 2 1 0
.x. ...    | 0 2 0 | * * * 3 * * * | 0 1 0 0 0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0 2 0 | * * * * 3 * * | 0 0 1 0 0 1 0 1 0 | 1 0 0 1 1
.oo3.oo    | 0 1 1 | * * * * * 6 * | 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
..x ...    | 0 0 2 | * * * * * * 3 | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1
-----------+-------+---------------+-------------------+----------
x..3o..    | 3 0 0 | 3 0 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * 3 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * 3 * * * * * * | 1 0 0 1 0
x.x ...&#x | 2 0 2 | 1 0 2 0 0 0 1 | * * * 3 * * * * * | 0 1 1 0 0
ooo3ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * 6 * * * * | 0 0 1 1 0
.x.3.x.    | 0 6 0 | 0 0 0 3 3 0 0 | * * * * * 1 * * * | 1 0 0 0 1
.xx ...&#x | 0 2 2 | 0 0 0 1 0 2 1 | * * * * * * 3 * * | 0 0 1 0 1
... .xo&#x | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * * 3 * | 0 0 0 1 1
..x3..o    | 0 0 4 | 0 0 0 0 0 0 4 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+---------------+-------------------+----------
xx.3ox.&#x ♦ 3 6 0 | 3 6 0 3 3 0 0 | 1 3 3 0 0 1 0 0 0 | 1 * * * *
x.x3o.o&#x ♦ 3 0 3 | 3 0 3 0 0 0 3 | 1 0 0 3 0 0 0 0 1 | * 1 * * *
xxx ...&#x ♦ 2 2 2 | 1 2 2 1 0 2 1 | 0 1 0 1 2 0 1 0 0 | * * 3 * *
... oxo&#x ♦ 1 2 1 | 0 2 1 0 1 2 0 | 0 0 1 0 2 0 0 1 0 | * * * 3 *
.xx3.oo&#x ♦ 0 6 3 | 0 0 0 3 3 6 3 | 0 0 0 0 0 1 3 3 1 | * * * * 1

or
o..3o..     & | 6 * | 2  2 1 0 0 | 1 2 1 2 2 0 | 1 1 2 1
.o.3.o.       | * 6 | 0  2 0 1 1 | 0 2 2 0 1 1 | 2 0 1 1
--------------+-----+------------+-------------+--------
x.. ...     & | 2 0 | 6  * * * * | 1 1 0 1 0 0 | 1 1 1 0
oo.3oo.&#x  & | 1 1 | * 12 * * * | 0 1 1 0 1 0 | 1 0 1 1
o.o3o.o&#x    | 2 0 | *  * 3 * * | 0 0 0 2 2 0 | 0 1 2 1
.x. ...       | 0 2 | *  * * 3 * | 0 2 0 0 0 1 | 2 0 1 0
... .x.       | 0 2 | *  * * * 3 | 0 0 2 0 0 1 | 2 0 0 1
--------------+-----+------------+-------------+--------
x..3o..     & | 3 0 | 3  0 0 0 0 | 2 * * * * * | 1 1 0 0
xx. ...&#x  & | 2 2 | 1  2 0 1 0 | * 6 * * * * | 1 0 1 0
... ox.&#x  & | 1 2 | 0  2 0 0 1 | * * 6 * * * | 1 0 0 1
x.x ...&#x    | 4 0 | 2  0 2 0 0 | * * * 3 * * | 0 1 1 0
ooo3ooo&#x    | 2 1 | 0  2 1 0 0 | * * * * 6 * | 0 0 1 1
.x.3.x.       | 0 6 | 0  0 0 3 3 | * * * * * 1 | 2 0 0 0
--------------+-----+------------+-------------+--------
xx.3ox.&#x  & ♦ 3 6 | 3  6 0 3 3 | 1 3 3 0 0 1 | 2 * * *
x.x3o.o&#x    ♦ 6 0 | 6  0 3 0 0 | 2 0 0 3 0 0 | * 1 * *
xxx ...&#x    ♦ 4 2 | 2  4 2 1 0 | 0 2 0 1 2 0 | * * 3 *
... oxo&#x    ♦ 2 2 | 0  4 1 0 1 | 0 0 2 0 2 0 | * * * 3


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

o..3o..    | 3 * * | 2 2 1 0 0 0 0 | 1 2 1 2 2 0 0 0 0 | 1 1 2 1 0
.o.3.o.    | * 6 * | 0 1 0 1 1 1 0 | 0 1 1 0 1 1 1 1 0 | 1 0 1 1 1
..o3..o    | * * 3 | 0 0 1 0 0 2 2 | 0 0 0 2 2 0 2 1 1 | 0 1 2 1 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 1 0 0 0 0 | 1 0 1 1 0
o.o3o.o&#x | 1 0 1 | * * 3 * * * * | 0 0 0 2 2 0 0 0 0 | 0 1 2 1 0
.x. ...    | 0 2 0 | * * * 3 * * * | 0 1 0 0 0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0 2 0 | * * * * 3 * * | 0 0 1 0 0 1 0 1 0 | 1 0 0 1 1
.oo3.oo    | 0 1 1 | * * * * * 6 * | 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1
..x ...    | 0 0 2 | * * * * * * 3 | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1
-----------+-------+---------------+-------------------+----------
x..3o..    | 3 0 0 | 3 0 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xx. ...&#x | 2 2 0 | 1 2 0 1 0 0 0 | * 3 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * 3 * * * * * * | 1 0 0 1 0
x.x ...&#x | 2 0 2 | 1 0 2 0 0 0 1 | * * * 3 * * * * * | 0 1 1 0 0
ooo3ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * 6 * * * * | 0 0 1 1 0
.x.3.x.    | 0 6 0 | 0 0 0 3 3 0 0 | * * * * * 1 * * * | 1 0 0 0 1
.xx ...&#x | 0 2 2 | 0 0 0 1 0 2 1 | * * * * * * 3 * * | 0 0 1 0 1
... .xo&#x | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * * 3 * | 0 0 0 1 1
..x3..o    | 0 0 4 | 0 0 0 0 0 0 4 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+---------------+-------------------+----------
xx.3ox.&#x ♦ 3 6 0 | 3 6 0 3 3 0 0 | 1 3 3 0 0 1 0 0 0 | 1 * * * *
x.x3o.o&#x ♦ 3 0 3 | 3 0 3 0 0 0 3 | 1 0 0 3 0 0 0 0 1 | * 1 * * *
xxx ...&#x ♦ 2 2 2 | 1 2 2 1 0 2 1 | 0 1 0 1 2 0 1 0 0 | * * 3 * *
... oxo&#x ♦ 1 2 1 | 0 2 1 0 1 2 0 | 0 0 1 0 2 0 0 1 0 | * * * 3 *
.xx3.oo&#x ♦ 0 6 3 | 0 0 0 3 3 6 3 | 0 0 0 0 0 1 3 3 1 | * * * * 1

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