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 |
|
Face vector | 15, 39, 40, 16 |
Confer |
|
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 though, 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
© 2004-2024 | top of page |