(tut,tut,tut)-trigonic
- more general:
- n,tut-dip
- general polytopal classes:
- Wythoffian polytera segmentotera lace simplices
links
| Acronym | tratut (alt.: tuttut tuttric) |
| Name |
triangle truncated-tetrahedron duoprism, (tut,tut,tut)-trigonic |
| Circumradius | sqrt(41/24) = 1.307032 |
| Volume | 23 sqrt(6)/48 = 1.173714 |
| Face vector | 36, 90, 90, 45, 11 |
| Confer |
|
|
External links |
|
Incidence matrix according to Dynkin symbol
x3o x3x3o . . . . . | 36 | 2 1 2 | 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2 ----------+----+----------+----------------+--------------+------ x . . . . | 2 | 36 * * | 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1 . . x . . | 2 | * 18 * | 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2 . . . x . | 2 | * * 36 | 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2 ----------+----+----------+----------------+--------------+------ x3o . . . | 3 | 3 0 0 | 12 * * * * | 1 2 0 0 0 | 2 1 0 x . x . . | 4 | 2 2 0 | * 18 * * * | 1 0 2 0 0 | 2 0 1 x . . x . | 4 | 2 0 2 | * * 36 * * | 0 1 1 1 0 | 1 1 1 . . x3x . | 6 | 0 3 3 | * * * 12 * | 0 0 2 0 1 | 1 0 2 . . . x3o | 3 | 0 0 3 | * * * * 12 | 0 0 0 2 1 | 0 1 2 ----------+----+----------+----------------+--------------+------ x3o x . . ♦ 6 | 6 3 0 | 2 3 0 0 0 | 6 * * * * | 2 0 0 x3o . x . ♦ 6 | 6 0 3 | 2 0 3 0 0 | * 12 * * * | 1 1 0 x . x3x . ♦ 12 | 6 6 6 | 0 3 3 2 0 | * * 12 * * | 1 0 1 x . . x3o ♦ 6 | 3 0 6 | 0 0 3 0 2 | * * * 12 * | 0 1 1 . . x3x3o ♦ 12 | 0 6 12 | 0 0 0 4 4 | * * * * 3 | 0 0 2 ----------+----+----------+----------------+--------------+------ x3o x3x . ♦ 18 | 18 9 9 | 6 9 9 3 0 | 3 3 3 0 0 | 4 * * x3o . x3o ♦ 9 | 9 0 9 | 3 0 9 0 3 | 0 3 0 3 0 | * 4 * x . x3x3o ♦ 24 | 12 12 24 | 0 6 12 8 8 | 0 0 4 4 2 | * * 3
x3o2x3o4s
demi( . . . . . ) | 36 | 2 2 1 | 1 4 1 2 2 | 2 2 1 1 4 | 1 2 2
------------------+----+----------+----------------+--------------+------
demi( x . . . . ) | 2 | 36 * * | 1 2 0 1 0 | 2 1 1 0 2 | 1 1 2
demi( . . x . . ) | 2 | * 36 * | 0 2 1 0 1 | 1 2 0 1 2 | 1 2 1
. . . o4s | 2 | * * 18 | 0 0 0 2 2 | 0 0 1 1 4 | 0 2 2
------------------+----+----------+----------------+--------------+------
demi( x3o . . . ) | 3 | 3 0 0 | 12 * * * * | 2 0 1 0 0 | 1 0 2
demi( x . x . . ) | 4 | 2 2 0 | * 36 * * * | 1 1 0 0 1 | 1 1 1
demi( . . x3o . ) | 3 | 0 3 0 | * * 12 * * | 0 2 0 1 0 | 1 2 0
x . 2 o4s | 4 | 2 0 2 | * * * 18 * | 0 0 1 0 2 | 0 1 2
sefa( . . x3o4s ) | 6 | 0 3 3 | * * * * 12 | 0 0 0 1 2 | 0 2 1
------------------+----+----------+----------------+--------------+------
demi( x3o x . . ) ♦ 6 | 6 3 0 | 2 3 0 0 0 | 12 * * * * | 1 0 1
demi( x . x3o . ) ♦ 6 | 3 6 0 | 0 3 2 0 0 | * 12 * * * | 1 1 0
x3o 2 o4s ♦ 6 | 6 0 3 | 2 0 0 3 0 | * * 6 * * | 0 0 2
. . x3o4s ♦ 12 | 0 12 6 | 0 0 4 0 4 | * * * 3 * | 0 2 0
sefa( x 2 x3o4s ) ♦ 12 | 6 6 6 | 0 3 0 3 2 | * * * * 12 | 0 1 1
------------------+----+----------+----------------+--------------+------
demi( x3o x3o . ) ♦ 9 | 9 9 0 | 3 9 3 0 0 | 3 3 0 0 0 | 4 * *
x 2 x3o4s ♦ 24 | 12 24 12 | 0 12 8 6 8 | 0 4 0 2 4 | * 3 *
sefa( x3o2x3o4s ) ♦ 18 | 18 9 9 | 6 9 0 9 3 | 3 0 3 0 3 | * * 4
starting figure: x3o x3o4x
ox oo3xx3xx&#x → height = sqrt(3)/2 = 0.866025
(tut || tuttip)
o. o.3o.3o. | 12 * | 2 1 2 0 0 0 | 1 2 1 4 2 0 0 0 0 | 1 2 1 2 4 0 0 0 | 1 2 2 0
.o .o3.o3.o | * 24 | 0 0 1 1 2 1 | 0 0 1 2 1 2 1 1 2 | 0 2 1 1 2 1 2 1 | 1 2 1 1
---------------+-------+------------------+-----------------------+------------------+--------
.. .. x. .. | 2 0 | 12 * * * * * | 1 1 0 2 0 0 0 0 0 | 1 1 0 2 2 0 0 0 | 1 1 2 0
.. .. .. x. | 2 0 | * 6 * * * * | 0 2 0 0 2 0 0 0 0 | 1 0 1 0 4 0 0 0 | 0 2 2 0
oo oo3oo3oo&#x | 1 1 | * * 24 * * * | 0 0 1 2 1 0 0 0 0 | 0 2 1 1 2 0 0 0 | 1 2 1 0
.x .. .. .. | 0 2 | * * * 12 * * | 0 0 1 0 0 2 1 0 0 | 0 2 1 0 0 1 2 0 | 1 2 0 1
.. .. .x .. | 0 2 | * * * * 24 * | 0 0 0 1 0 1 0 1 1 | 0 1 0 1 1 1 1 1 | 1 1 1 1
.. .. .. .x | 0 2 | * * * * * 12 | 0 0 0 0 1 0 1 0 2 | 0 0 1 0 2 0 2 1 | 0 2 1 1
---------------+-------+------------------+-----------------------+------------------+--------
.. o.3x. .. | 3 0 | 3 0 0 0 0 0 | 4 * * * * * * * * | 1 0 0 2 0 0 0 0 | 1 0 2 0
.. .. x.3x. | 6 0 | 3 3 0 0 0 0 | * 4 * * * * * * * | 1 0 0 0 2 0 0 0 | 0 1 2 0
ox .. .. ..&#x | 1 2 | 0 0 2 1 0 0 | * * 12 * * * * * * | 0 2 1 0 0 0 0 0 | 1 2 0 0
.. .. xx ..&#x | 2 2 | 1 0 2 0 1 0 | * * * 24 * * * * * | 0 1 0 1 1 0 0 0 | 1 1 1 0
.. .. .. xx&#x | 2 2 | 0 1 2 0 0 1 | * * * * 12 * * * * | 0 0 1 0 2 0 0 0 | 0 2 1 0
.x .. .x .. | 0 4 | 0 0 0 2 2 0 | * * * * * 12 * * * | 0 1 0 0 0 1 1 0 | 1 1 0 1
.x .. .. .x | 0 4 | 0 0 0 2 0 2 | * * * * * * 6 * * | 0 0 1 0 0 0 2 0 | 0 2 0 1
.. .o3.x .. | 0 3 | 0 0 0 0 3 0 | * * * * * * * 8 * | 0 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x3.x | 0 6 | 0 0 0 0 3 3 | * * * * * * * * 8 | 0 0 0 0 1 0 1 1 | 0 1 1 1
---------------+-------+------------------+-----------------------+------------------+--------
.. o.3x.3x. ♦ 12 0 | 12 6 0 0 0 0 | 4 4 0 0 0 0 0 0 0 | 1 * * * * * * * | 0 0 2 0
ox .. xx ..&#x ♦ 2 4 | 1 0 4 2 2 0 | 0 0 2 2 0 1 0 0 0 | * 12 * * * * * * | 1 1 0 0
ox .. .. xx&#x ♦ 2 4 | 0 1 4 2 0 2 | 0 0 2 0 2 0 1 0 0 | * * 6 * * * * * | 0 2 0 0
.. oo3xx ..&#x ♦ 3 3 | 3 0 3 0 3 0 | 1 0 0 3 0 0 0 1 0 | * * * 8 * * * * | 1 0 1 0
.. .. xx3xx&#x ♦ 6 6 | 3 3 6 0 3 3 | 0 1 0 3 3 0 0 0 1 | * * * * 8 * * * | 0 1 1 0
.x .o3.x .. ♦ 0 6 | 0 0 0 3 6 0 | 0 0 0 0 0 3 0 2 0 | * * * * * 4 * * | 1 0 0 1
.x .. .x3.x ♦ 0 12 | 0 0 0 6 6 6 | 0 0 0 0 0 3 3 0 2 | * * * * * * 4 * | 0 1 0 1
.. .o3.x3.x ♦ 0 12 | 0 0 0 0 12 6 | 0 0 0 0 0 0 0 4 4 | * * * * * * * 2 | 0 0 1 1
---------------+-------+------------------+-----------------------+------------------+--------
ox oo3xx ..&#x ♦ 3 6 | 3 0 6 3 6 0 | 1 0 3 6 0 3 0 2 0 | 0 3 0 2 0 1 0 0 | 4 * * *
ox .. xx3xx&#x ♦ 6 12 | 3 3 12 6 6 6 | 0 1 6 6 6 3 3 0 2 | 0 3 3 0 2 0 1 0 | * 4 * *
.. oo3xx3xx&#x ♦ 12 12 | 12 6 12 0 12 6 | 4 4 0 12 6 0 0 4 4 | 1 0 0 4 4 0 0 1 | * * 2 *
.x .o3.x3.x ♦ 0 24 | 0 0 0 12 24 12 | 0 0 0 0 0 12 6 8 8 | 0 0 0 0 0 4 4 2 | * * * 1
ooo3xxx3xxx&#x → all heights = 1 o..3o..3o.. | 12 * * | 2 1 1 1 0 0 0 0 0 | 1 2 2 1 1 2 1 0 0 0 0 0 0 | 1 1 2 2 1 1 2 0 0 0 0 | 1 1 2 1 0 .o.3.o.3.o. | * 12 * | 0 0 1 0 2 1 1 0 0 | 0 0 2 1 1 0 0 1 2 2 1 0 0 | 0 1 2 2 1 0 0 1 1 2 0 | 1 1 2 0 1 ..o3..o3..o | * * 12 | 0 0 0 1 0 0 1 2 1 | 0 0 0 0 1 2 1 0 0 2 1 1 2 | 0 0 0 2 1 1 2 0 1 2 1 | 0 1 2 1 1 ---------------+----------+-------------------------+-------------------------------+------------------------+---------- ... x.. ... | 2 0 0 | 12 * * * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 0 0 | 1 1 1 1 0 0 0 0 0 0 0 | 1 1 1 1 0 ... ... x.. | 2 0 0 | * 6 * * * * * * * | 0 2 0 1 0 0 1 0 0 0 0 0 0 | 1 0 2 0 1 0 2 0 0 0 0 | 1 0 2 1 0 oo.3oo.3oo.&#x | 1 1 0 | * * 12 * * * * * * | 0 0 2 1 1 0 0 0 0 0 0 0 0 | 0 1 2 2 1 0 0 0 0 0 0 | 1 1 2 0 0 o.o3o.o3o.o&#x | 1 0 1 | * * * 12 * * * * * | 0 0 0 0 1 2 1 0 0 0 0 0 0 | 0 0 0 2 1 1 2 0 0 0 0 | 0 1 2 1 0 ... .x. ... | 0 2 0 | * * * * 12 * * * * | 0 0 1 0 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 ... ... .x. | 0 2 0 | * * * * * 6 * * * | 0 0 0 1 0 0 0 0 2 0 1 0 0 | 0 0 2 0 1 0 0 1 0 2 0 | 1 0 2 0 1 .oo3.oo3.oo&#x | 0 1 1 | * * * * * * 12 * * | 0 0 0 0 1 0 0 0 0 2 1 0 0 | 0 0 0 2 1 0 0 0 1 2 0 | 0 1 2 0 1 ... ..x ... | 0 0 2 | * * * * * * * 12 * | 0 0 0 0 0 1 0 0 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 ... ... ..x | 0 0 2 | * * * * * * * * 6 | 0 0 0 0 0 0 1 0 0 0 1 0 2 | 0 0 0 0 1 0 2 0 0 2 1 | 0 0 2 1 1 ---------------+----------+-------------------------+-------------------------------+------------------------+---------- o..3x.. ... | 3 0 0 | 3 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * | 1 1 0 0 0 1 0 0 0 0 0 | 1 1 0 1 0 ... x..3x.. | 6 0 0 | 3 3 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * | 1 0 1 0 0 0 1 0 0 0 0 | 1 0 1 1 0 ... xx. ...&#x | 2 2 0 | 1 0 2 0 1 0 0 0 0 | * * 12 * * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 ... ... xx.&#x | 2 2 0 | 0 1 2 0 0 1 0 0 0 | * * * 6 * * * * * * * * * | 0 0 2 0 1 0 0 0 0 0 0 | 1 0 2 0 0 ooo3ooo3ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 0 0 | * * * * 12 * * * * * * * * | 0 0 0 2 1 0 0 0 0 0 0 | 0 1 2 0 0 ... x.x ...&#x | 2 0 2 | 1 0 0 2 0 0 0 1 0 | * * * * * 12 * * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 ... ... x.x&#x | 2 0 2 | 0 1 0 2 0 0 0 0 1 | * * * * * * 6 * * * * * * | 0 0 0 0 1 0 2 0 0 0 0 | 0 0 2 1 0 .o.3.x. ... | 0 3 0 | 0 0 0 0 3 0 0 0 0 | * * * * * * * 4 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 ... .x.3.x. | 0 6 0 | 0 0 0 0 3 3 0 0 0 | * * * * * * * * 4 * * * * | 0 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 ... .xx ...&#x | 0 2 2 | 0 0 0 0 1 0 2 1 0 | * * * * * * * * * 12 * * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 ... ... .xx&#x | 0 2 2 | 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * 6 * * | 0 0 0 0 1 0 0 0 0 2 0 | 0 0 2 0 1 ..o3..x ... | 0 0 3 | 0 0 0 0 0 0 0 3 0 | * * * * * * * * * * * 4 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 ... ..x3..x | 0 0 6 | 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ---------------+----------+-------------------------+-------------------------------+------------------------+---------- o..3x..3x.. ♦ 12 0 0 | 12 6 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 1 0 0 1 0 oo.3xx. ...&#x ♦ 3 3 0 | 3 0 3 0 3 0 0 0 0 | 1 0 3 0 0 0 0 1 0 0 0 0 0 | * 4 * * * * * * * * * | 1 1 0 0 0 ... xx.3xx.&#x ♦ 6 6 0 | 3 3 6 0 3 3 0 0 0 | 0 1 3 3 0 0 0 0 1 0 0 0 0 | * * 4 * * * * * * * * | 1 0 1 0 0 ... xxx ...&#x ♦ 2 2 2 | 1 0 2 2 1 0 2 1 0 | 0 0 1 0 2 1 0 0 0 1 0 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0 ... ... xxx&#x ♦ 2 2 2 | 0 1 2 2 0 1 2 0 1 | 0 0 0 1 2 0 1 0 0 0 1 0 0 | * * * * 6 * * * * * * | 0 0 2 0 0 o.o3x.x ...&#x ♦ 3 0 3 | 3 0 0 3 0 0 0 3 0 | 1 0 0 0 0 3 0 0 0 0 0 1 0 | * * * * * 4 * * * * * | 0 1 0 1 0 ... x.x3x.x&#x ♦ 6 0 6 | 3 3 0 6 0 0 0 3 3 | 0 1 0 0 0 3 3 0 0 0 0 0 1 | * * * * * * 4 * * * * | 0 0 1 1 0 .o.3.x.3.x. ♦ 0 12 0 | 0 0 0 0 12 6 0 0 0 | 0 0 0 0 0 0 0 4 4 0 0 0 0 | * * * * * * * 1 * * * | 1 0 0 0 1 .oo3.xx ...&#x ♦ 0 3 3 | 0 0 0 0 3 0 3 3 0 | 0 0 0 0 0 0 0 1 0 3 0 1 0 | * * * * * * * * 4 * * | 0 1 0 0 1 ... .xx3.xx&#x ♦ 0 6 6 | 0 0 0 0 3 3 6 3 3 | 0 0 0 0 0 0 0 0 1 3 3 0 1 | * * * * * * * * * 4 * | 0 0 1 0 1 ..o3..x3..x ♦ 0 0 12 | 0 0 0 0 0 0 0 12 6 | 0 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * 1 | 0 0 0 1 1 ---------------+----------+-------------------------+-------------------------------+------------------------+---------- oo.3xx.3xx.&#x ♦ 12 12 0 | 12 6 12 0 12 6 0 0 0 | 4 4 12 6 0 0 0 4 4 0 0 0 0 | 1 4 4 0 0 0 0 1 0 0 0 | 1 * * * * ooo3xxx ...&#x ♦ 3 3 3 | 3 0 3 3 3 0 3 3 0 | 1 0 3 0 3 3 0 1 0 3 0 1 0 | 0 1 0 3 0 1 0 0 1 0 0 | * 4 * * * ... xxx3xxx&#x ♦ 6 6 6 | 3 3 6 6 3 3 6 3 3 | 0 1 3 3 6 3 3 0 1 3 3 0 1 | 0 0 1 3 3 0 1 0 0 1 0 | * * 4 * * o.o3x.x3x.x&#x ♦ 12 0 12 | 12 6 0 12 0 0 0 12 6 | 4 4 0 0 0 12 6 0 0 0 0 4 4 | 1 0 0 0 0 4 4 0 0 0 1 | * * * 1 * .oo3.xx3.xx&#x ♦ 0 12 12 | 0 0 0 0 12 6 12 12 6 | 0 0 0 0 0 0 0 4 4 12 6 4 4 | 0 0 0 0 0 0 0 1 4 4 1 | * * * * 1
© 2004-2024 | top of page |