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 cityin approx. ASCII-art ``` x3x x3o x3o ``` Coordinates (1/sqrt(3), 0, 1/2, sqrt(5/12))          & all changes of sign in 3rd coord (-1/sqrt(12), 1/2, 1/2, sqrt(5/12))    & all changes of sign in 3rd & 4th coord (these two together describe the trip) (sqrt(3)/2, 1/2, 0, 0)                       & all changes of sign in 1st & 2nd coord (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° 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 Externallinks

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
```