Acronym tracufbil
Name triangular-cupofastegia biluna,
{3} || tricu || {3},
0.419569-luna of gyspid
Circumradius 1
Lace city
in approx. ASCII-art
   x3o  
        
x3o  x3x
        
   x3o  
Dihedral angles
  • at {3} between tet and tet:   arccos(-7/8) = 151.044976°
  • at {6} between tricu and tricu:   arccos(-7/8) = 151.044976°
  • 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 trip and trip:   arccos(-1/4) = 104.477512°
  • at {3} between tet 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
more general:
n-cufbil  
uniform relative:
spid  
related segmentochora:
tet || co   tet || tricu   tricuf  
general polytopal classes:
luna   bistratic lace towers  

This luna is somehow more general as its fraction comes out to be non-rational: the wedge angle is arccos(-7/8), accordingly that fraction is arccos(-7/8) / 360° = 0.419569.

Alternatively it can be seen as external blend of 2 tricufs.

Note that this polychoron does not qualify as segmentochoron just because it is not monostratic. As can be seen in the lace city display or from the dihedral angles, the trip and the tricu are not parallel here. Even so, this bicuf happens to be orbiform and hence a circumradius does exist.


Incidence matrix according to Dynkin symbol

xxxx3ooox&#xr   → height(1,2) = height(2,3) = 1
                  height(1,4) = height(3,4) = sqrt(2/3) = 0.816497

o...3o...    | 3 * * * | 2 1 2 0 0 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0 0
.o..3.o..    | * 3 * * | 0 1 0 2 1 2 0 0 0 0 | 0 2 0 0 2 1 2 2 1 2 0 0 0 0 | 1 0 2 1 1 2 1 0
..o.3..o.    | * * 3 * | 0 0 0 0 1 0 2 2 0 0 | 0 0 0 0 0 0 2 0 0 2 1 2 1 0 | 0 0 0 0 1 2 1 1
...o3...o    | * * * 6 | 0 0 1 0 0 1 0 1 1 1 | 0 0 1 1 1 0 0 1 1 1 0 1 1 1 | 0 1 1 1 0 1 1 1
-------------+---------+---------------------+-----------------------------+----------------
x... ....    | 2 0 0 0 | 3 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0
oo..3oo..&#x | 1 1 0 0 | * 3 * * * * * * * * | 0 2 0 0 1 0 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0 0
o..o3o..o&#x | 1 0 0 1 | * * 6 * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
.x.. ....    | 0 2 0 0 | * * * 3 * * * * * * | 0 1 0 0 0 1 1 1 0 0 0 0 0 0 | 1 0 1 0 1 1 0 0
.oo.3.oo.&#x | 0 1 1 0 | * * * * 3 * * * * * | 0 0 0 0 0 0 2 0 0 2 0 0 0 0 | 0 0 0 0 1 2 1 0
.o.o3.o.o&#x | 0 1 0 1 | * * * * * 6 * * * * | 0 0 0 0 1 0 0 1 1 1 0 0 0 0 | 0 0 1 1 0 1 1 0
..x. ....    | 0 0 2 0 | * * * * * * 3 * * * | 0 0 0 0 0 0 1 0 0 0 1 1 0 0 | 0 0 0 0 1 1 0 1
..oo3..oo&#x | 0 0 1 1 | * * * * * * * 6 * * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 | 0 0 0 0 0 1 1 1
...x ....    | 0 0 0 2 | * * * * * * * * 3 * | 0 0 1 0 0 0 0 1 0 0 0 1 0 1 | 0 1 1 0 0 1 0 1
.... ...x    | 0 0 0 2 | * * * * * * * * * 3 | 0 0 0 1 0 0 0 0 1 0 0 0 1 1 | 0 1 0 1 0 0 1 1
-------------+---------+---------------------+-----------------------------+----------------
x...3o...    | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0
xx.. ....&#x | 2 2 0 0 | 1 2 0 1 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * | 1 0 1 0 0 0 0 0
x..x ....&#x | 2 0 0 2 | 1 0 2 0 0 0 0 0 1 0 | * * 3 * * * * * * * * * * * | 0 1 1 0 0 0 0 0
.... o..x&#x | 1 0 0 2 | 0 0 2 0 0 0 0 0 0 1 | * * * 3 * * * * * * * * * * | 0 1 0 1 0 0 0 0
oo.o3oo.o&#x | 1 1 0 1 | 0 1 1 0 0 1 0 0 0 0 | * * * * 6 * * * * * * * * * | 0 0 1 1 0 0 0 0
.x..3.o..    | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 | * * * * * 1 * * * * * * * * | 1 0 0 0 1 0 0 0
.xx. ....&#x | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 0 | * * * * * * 3 * * * * * * * | 0 0 0 0 1 1 0 0
.x.x ....&#x | 0 2 0 2 | 0 0 0 1 0 2 0 0 1 0 | * * * * * * * 3 * * * * * * | 0 0 1 0 0 1 0 0
.... .o.x&#x | 0 1 0 2 | 0 0 0 0 0 2 0 0 0 1 | * * * * * * * * 3 * * * * * | 0 0 0 1 0 0 1 0
.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 0 | * * * * * * * * * 6 * * * * | 0 0 0 0 0 1 1 0
..x.3..o.    | 0 0 3 0 | 0 0 0 0 0 0 3 0 0 0 | * * * * * * * * * * 1 * * * | 0 0 0 0 1 0 0 1
..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 0 | * * * * * * * * * * * 3 * * | 0 0 0 0 0 1 0 1
.... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 1 1
...x3...x    | 0 0 0 6 | 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * 1 | 0 1 0 0 0 0 0 1
-------------+---------+---------------------+-----------------------------+----------------
xx..3oo..&#x  3 3 0 0 | 3 3 0 3 0 0 0 0 0 0 | 1 3 0 0 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * * *
x..x3o..x&#x  3 0 0 6 | 3 0 6 0 0 0 0 0 3 3 | 1 0 3 3 0 0 0 0 0 0 0 0 0 1 | * 1 * * * * * *
xx.x ....&#x  2 2 0 2 | 1 2 2 1 0 2 0 0 1 0 | 0 1 1 0 2 0 0 1 0 0 0 0 0 0 | * * 3 * * * * *
.... oo.x&#x  1 1 0 2 | 0 1 2 0 0 2 0 0 0 1 | 0 0 0 1 2 0 0 0 1 0 0 0 0 0 | * * * 3 * * * *
.xx.3.oo.&#x  0 3 3 0 | 0 0 0 3 3 0 3 0 0 0 | 0 0 0 0 0 1 3 0 0 0 1 0 0 0 | * * * * 1 * * *
.xxx ....&#x  0 2 2 2 | 0 0 0 1 2 2 1 2 1 0 | 0 0 0 0 0 0 1 1 0 2 0 1 0 0 | * * * * * 3 * *
.... .oox&#x  0 1 1 2 | 0 0 0 0 1 2 0 2 0 1 | 0 0 0 0 0 0 0 0 1 2 0 0 1 0 | * * * * * * 3 *
..xx3..ox&#x  0 0 3 6 | 0 0 0 0 0 0 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * 1
or
o...3o...    & | 6 * * | 2 1  2 0 0 0 0 | 1 2 2 1  2 0 0 0 0 | 1 1 2 1
.o..3.o..      | * 3 * | 0 2  0 2 2 0 0 | 0 4 0 0  4 1 2 1 0 | 2 0 4 2
...o3...o      | * * 6 | 0 0  2 0 1 1 1 | 0 0 2 2  2 0 1 1 1 | 0 2 2 2
---------------+-------+----------------+--------------------+--------
x... ....    & | 2 0 0 | 6 *  * * * * * | 1 1 1 0  0 0 0 0 0 | 1 1 1 0
oo..3oo..&#x & | 1 1 0 | * 6  * * * * * | 0 2 0 0  2 0 0 0 0 | 1 0 2 1
o..o3o..o&#x & | 1 0 1 | * * 12 * * * * | 0 0 1 1  1 0 0 0 0 | 0 1 1 1
.x.. ....      | 0 2 0 | * *  * 3 * * * | 0 2 0 0  0 1 1 0 0 | 2 0 2 0
.o.o3.o.o&#x   | 0 1 1 | * *  * * 6 * * | 0 0 0 0  2 0 1 1 0 | 0 0 2 2
...x ....      | 0 0 2 | * *  * * * 3 * | 0 0 2 0  0 0 1 0 1 | 0 2 2 0
.... ...x      | 0 0 2 | * *  * * * * 3 | 0 0 0 2  0 0 0 1 1 | 0 2 0 2
---------------+-------+----------------+--------------------+--------
x...3o...    & | 3 0 0 | 3 0  0 0 0 0 0 | 2 * * *  * * * * * | 1 1 0 0
xx.. ....&#x & | 2 2 0 | 1 2  0 1 0 0 0 | * 6 * *  * * * * * | 1 0 1 0
x..x ....&#x & | 2 0 2 | 1 0  2 0 0 1 0 | * * 6 *  * * * * * | 0 1 1 0
.... o..x&#x & | 1 0 2 | 0 0  2 0 0 0 1 | * * * 6  * * * * * | 0 1 0 1
oo.o3oo.o&#x & | 1 1 1 | 0 1  1 0 1 0 0 | * * * * 12 * * * * | 0 0 1 1
.x..3.o..      | 0 3 0 | 0 0  0 3 0 0 0 | * * * *  * 1 * * * | 2 0 0 0
.x.x ....&#x   | 0 2 2 | 0 0  0 1 2 1 0 | * * * *  * * 3 * * | 0 0 2 0
.... .o.x&#x   | 0 1 2 | 0 0  0 0 2 0 1 | * * * *  * * * 3 * | 0 0 0 2
...x3...x      | 0 0 6 | 0 0  0 0 0 3 3 | * * * *  * * * * 1 | 0 2 0 0
---------------+-------+----------------+--------------------+--------
xx..3oo..&#x &  3 3 0 | 3 3  0 3 0 0 0 | 1 3 0 0  0 1 0 0 0 | 2 * * *
x..x3o..x&#x &  3 0 6 | 3 0  6 0 0 3 3 | 1 0 3 3  0 0 0 0 1 | * 2 * *
xx.x ....&#x &  2 2 2 | 1 2  2 1 2 1 0 | 0 1 1 0  2 0 1 0 0 | * * 6 *
.... oo.x&#x &  1 1 2 | 0 1  2 0 2 0 1 | 0 0 0 1  2 0 0 1 0 | * * * 6

{3} || pseudo tricu || {3}   → both heights = sqrt(5/8) = 0.790569

o(..).3o(..).    | 3 * * * | 2 1 2 0 0 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0 0
.(o.).3.(o.).    | * 3 * * | 0 1 0 2 2 1 0 0 0 0 | 0 2 0 0 2 1 2 1 2 2 0 0 0 0 | 1 0 2 1 1 2 1 0
.(.o).3.(.o).    | * * 6 * | 0 0 1 0 1 0 1 1 1 0 | 0 0 1 1 1 0 1 1 0 1 1 1 1 0 | 0 1 1 1 0 1 1 1
.(..)o3.(..)o    | * * * 3 | 0 0 0 0 0 1 0 0 2 2 | 0 0 0 0 0 0 0 0 2 2 0 2 1 1 | 0 0 0 0 1 2 1 1
-----------------+---------+---------------------+-----------------------------+----------------
x(..). .(..).    | 2 0 0 0 | 3 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0
o(o.).3o(o.).&#x | 1 1 0 0 | * 3 * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0 0
o(.o).3o(.o).&#x | 1 0 1 0 | * * 6 * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
.(x.). .(..).    | 0 2 0 0 | * * * 3 * * * * * * | 0 1 0 0 0 1 1 0 1 0 0 0 0 0 | 1 0 1 0 1 1 0 0
.(oo).3.(oo).&#x | 0 1 1 0 | * * * * 6 * * * * * | 0 0 0 0 1 0 1 1 0 1 0 0 0 0 | 0 0 1 1 0 1 1 0
.(o.)o3.(o.)o&#x | 0 1 0 1 | * * * * * 3 * * * * | 0 0 0 0 0 0 0 0 2 2 0 0 0 0 | 0 0 0 0 1 2 1 0
.(.x). .(..).    | 0 0 2 0 | * * * * * * 3 * * * | 0 0 1 0 0 0 1 0 0 0 1 1 0 0 | 0 1 1 0 0 1 0 1
.(..). .(.x).    | 0 0 2 0 | * * * * * * * 3 * * | 0 0 0 1 0 0 0 1 0 0 1 0 1 0 | 0 1 0 1 0 0 1 1
.(.o)o3.(.o)o&#x | 0 0 1 1 | * * * * * * * * 6 * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 | 0 0 0 0 0 1 1 1
.(..)x .(..).    | 0 0 0 2 | * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 1 0 0 1 0 1 | 0 0 0 0 1 1 0 1
-----------------+---------+---------------------+-----------------------------+----------------
x(..).3o(..).    | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0
x(x.). .(..).&#x | 2 2 0 0 | 1 2 0 1 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * | 1 0 1 0 0 0 0 0
x(.x). .(..).&#x | 2 0 2 0 | 1 0 2 0 0 0 1 0 0 0 | * * 3 * * * * * * * * * * * | 0 1 1 0 0 0 0 0
.(..). o(.x).&#x | 1 0 2 0 | 0 0 2 0 0 0 0 1 0 0 | * * * 3 * * * * * * * * * * | 0 1 0 1 0 0 0 0
o(oo).3o(oo).&#x | 1 1 1 0 | 0 1 1 0 1 0 0 0 0 0 | * * * * 6 * * * * * * * * * | 0 0 1 1 0 0 0 0
.(x.).3.(o.).    | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 | * * * * * 1 * * * * * * * * | 1 0 0 0 1 0 0 0
.(xx). .(..).&#x | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 0 | * * * * * * 3 * * * * * * * | 0 0 1 0 0 1 0 0
.(..). .(ox).&#x | 0 1 2 0 | 0 0 0 0 2 0 0 1 0 0 | * * * * * * * 3 * * * * * * | 0 0 0 1 0 0 1 0
.(x.)x .(..).&#x | 0 2 0 2 | 0 0 0 1 0 2 0 0 0 1 | * * * * * * * * 3 * * * * * | 0 0 0 0 1 1 0 0
.(oo)o3.(oo)o&#x | 0 1 1 1 | 0 0 0 0 1 1 0 0 1 0 | * * * * * * * * * 6 * * * * | 0 0 0 0 0 1 1 0
.(.x).3.(.x).    | 0 0 6 0 | 0 0 0 0 0 0 3 3 0 0 | * * * * * * * * * * 1 * * * | 0 1 0 0 0 0 0 1
.(.x)x .(..).&#x | 0 0 2 2 | 0 0 0 0 0 0 1 0 2 1 | * * * * * * * * * * * 3 * * | 0 0 0 0 0 1 0 1
.(..). .(.x)o&#x | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 1 1
.(..)x3.(..)o    | 0 0 0 3 | 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 0 0 1
-----------------+---------+---------------------+-----------------------------+----------------
x(x.).3o(o.).&#x  3 3 0 0 | 3 3 0 3 0 0 0 0 0 0 | 1 3 0 0 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * * *
x(.x).3o(.x).&#x  3 0 6 0 | 3 0 6 0 0 0 3 3 0 0 | 1 0 3 3 0 0 0 0 0 0 1 0 0 0 | * 1 * * * * * *
x(xx). .(..).&#x  2 2 2 0 | 1 2 2 1 2 0 1 0 0 0 | 0 1 1 0 2 0 1 0 0 0 0 0 0 0 | * * 3 * * * * *
.(..). o(ox).&#x  1 1 2 0 | 0 1 2 0 2 0 0 1 0 0 | 0 0 0 1 2 0 0 1 0 0 0 0 0 0 | * * * 3 * * * *
.(x.)x3.(o.)o&#x  0 3 0 3 | 0 0 0 3 0 3 0 0 0 3 | 0 0 0 0 0 1 0 0 3 0 0 0 0 1 | * * * * 1 * * *
.(xx)x .(..).&#x  0 2 2 2 | 0 0 0 1 2 2 1 0 2 1 | 0 0 0 0 0 0 1 0 1 2 0 1 0 0 | * * * * * 3 * *
.(..). .(ox)o&#x  0 1 2 1 | 0 0 0 0 2 1 0 1 2 0 | 0 0 0 0 0 0 0 1 0 2 0 0 1 0 | * * * * * * 3 *
.(.x)x3.(.x)o&#x  0 0 6 3 | 0 0 0 0 0 0 3 3 6 3 | 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * 1

oCo xxx3oox&#xt   → height(1,2) = sqrt(3/8) = 0.612372
                    height(2,3) = 1/sqrt(24) = 0.204124
                    C = sqrt(5/2) = 1.581139

o.. o..3o..    | 3 * * | 2 2 2 0  0 0 0 | 1 4 2 1  4 0 0 0 0 | 2 4 2 0
.o. .o.3.o.    | * 6 * | 0 1 0 2  2 0 0 | 0 2 0 0  2 1 2 1 0 | 1 2 1 1
..o ..o3..o    | * * 6 | 0 0 1 0  2 1 1 | 0 0 1 1  2 0 2 2 1 | 0 2 2 2
---------------+-------+----------------+--------------------+--------
... x.. ...    | 2 0 0 | 3 * * *  * * * | 1 2 1 0  0 0 0 0 0 | 2 2 0 0
oo. oo.3oo.&#x | 1 1 0 | * 6 * *  * * * | 0 2 0 0  2 0 0 0 0 | 1 2 1 0
o.o o.o3o.o&#x | 1 0 1 | * * 6 *  * * * | 0 0 1 1  2 0 0 0 0 | 0 2 2 0
... .x. ...    | 0 2 0 | * * * 6  * * * | 0 1 0 0  0 1 1 0 0 | 1 1 0 1
.oo .oo3.oo&#x | 0 1 1 | * * * * 12 * * | 0 0 0 0  1 0 1 1 0 | 0 1 1 1
... ..x ...    | 0 0 2 | * * * *  * 3 * | 0 0 1 0  0 0 2 0 1 | 0 2 0 2
... ... ..x    | 0 0 2 | * * * *  * * 3 | 0 0 0 1  0 0 0 2 1 | 0 0 2 2
---------------+-------+----------------+--------------------+--------
... x..3o..    | 3 0 0 | 3 0 0 0  0 0 0 | 1 * * *  * * * * * | 2 0 0 0
... xx. ...&#x | 2 2 0 | 1 2 0 1  0 0 0 | * 6 * *  * * * * * | 1 1 0 0
... x.x ...&#x | 2 0 2 | 1 0 2 0  0 1 0 | * * 3 *  * * * * * | 0 2 0 0
... ... o.x&#x | 1 0 2 | 0 0 2 0  0 0 1 | * * * 3  * * * * * | 0 0 2 0
ooo ooo3ooo&#x | 1 1 1 | 0 1 1 0  1 0 0 | * * * * 12 * * * * | 0 1 1 0
... .x.3.o.    | 0 3 0 | 0 0 0 3  0 0 0 | * * * *  * 2 * * * | 1 0 0 1
... .xx ...&#x | 0 2 2 | 0 0 0 1  2 1 0 | * * * *  * * 6 * * | 0 1 0 1
... ... .ox&#x | 0 1 2 | 0 0 0 0  2 0 1 | * * * *  * * * 6 * | 0 0 1 1
... ..x3..x    | 0 0 6 | 0 0 0 0  0 3 3 | * * * *  * * * * 1 | 0 0 0 2
---------------+-------+----------------+--------------------+--------
... xx.3oo.&#x  3 3 0 | 3 3 0 3  0 0 0 | 1 3 0 0  0 1 0 0 0 | 2 * * *
... xxx ...&#x  2 2 2 | 1 2 2 1  2 1 0 | 0 1 1 0  2 0 1 0 0 | * 6 * *
... ... oox&#x  1 1 2 | 0 1 2 0  2 0 1 | 0 0 0 1  2 0 0 1 0 | * * 6 *
... .xx3.ox&#x  0 3 6 | 0 0 0 3  6 3 3 | 0 0 0 0  0 1 3 3 1 | * * * 2

© 2004-2018
top of page