|
Acronym
|
tridafup (alt.: pabdidot)
|
|
Name
|
triangular duoantifastegiaprism,
triangular duoantiwedge,
triddip atop bidual triddip,
central segment of vertex first dot,
parabidiminished dot
|
|
Circumradius
|
sqrt(3)/2 = 0.866025
|
Lace city
in approx. ASCII-art
|
o x3o x o3x -- traf
x x3o o o3x -- inv. traf
\ \
\ +------- o3x o3x (triddip)
+------------ x3o x3o (bidual triddip)
|
|
Coordinates
|
-
(1/2, 1/2, -1/sqrt(12), -1/sqrt(12), 1/sqrt(12)) & all changes of sign in first 2 coords & simultanuous changes of sign in others
-
(0, 0, 1/sqrt(3), 1/sqrt(3), 1/sqrt(12)) & all changes of sign in first 2 coords & simultanuous changes of sign in others
-
(1/2, 0, -1/sqrt(12), -1/sqrt(3), 1/sqrt(12)) & all changes of sign in first 2 coords & simultanuous changes of sign in others
-
(0, 1/2, 1/sqrt(3), 1/sqrt(12), 1/sqrt(12)) & all changes of sign in first 2 coords & simultanuous changes of sign in others
|
|
Face vector
|
18, 72, 102, 60, 14
|
|
Confer
|
- uniform relative:
-
dot
- more general:
-
n,m-dafup
- general polytopal classes:
-
scaliform
segmentotera
lace simplices
|
External
links
|
|
This polyteron can also be obtained as a bidiminishing of dot in its vertex first orientation,
cutting off a triddippy on either end.
In fact, the trafs, shown in the lace city above, are nothing but accordingly diminished raps.
Incidence matrix according to Dynkin symbol
xo3ox xo3ox&#x → height = 1/sqrt(3) = 0.577350
(triddip || bidual triddip)
o.3o. o.3o. | 9 * | 2 2 4 0 0 | 1 4 1 4 2 4 2 0 0 0 | 2 2 2 4 2 2 1 2 0 0 | 1 2 1 2 1 0
.o3.o .o3.o | * 9 | 0 0 4 2 2 | 0 0 0 2 4 2 4 1 4 1 | 0 0 2 1 2 2 4 2 2 2 | 0 1 2 1 2 1
---------------+-----+------------+-------------------------+---------------------+------------
x. .. .. .. | 2 0 | 9 * * * * | 1 2 0 2 0 0 0 0 0 0 | 2 1 2 2 1 0 0 0 0 0 | 1 2 1 1 0 0
.. .. x. .. | 2 0 | * 9 * * * | 0 2 1 0 0 2 0 0 0 0 | 1 2 0 2 0 1 0 2 0 0 | 1 1 0 2 1 0
oo3oo oo3oo&#x | 1 1 | * * 36 * * | 0 0 0 1 1 1 1 0 0 0 | 0 0 1 1 1 1 1 1 0 0 | 0 1 1 1 1 0
.. .x .. .. | 0 2 | * * * 9 * | 0 0 0 0 2 0 0 1 2 0 | 0 0 2 0 0 1 2 0 2 1 | 0 1 2 0 1 1
.. .. .. .x | 0 2 | * * * * 9 | 0 0 0 0 0 0 2 0 2 1 | 0 0 0 0 1 0 2 2 1 2 | 0 0 1 1 2 1
---------------+-----+------------+-------------------------+---------------------+------------
x.3o. .. .. | 3 0 | 3 0 0 0 0 | 3 * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 | 1 2 1 0 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 | * 9 * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 0 1 0 0
.. .. x.3o. | 3 0 | 0 3 0 0 0 | * * 3 * * * * * * * | 0 2 0 0 0 0 0 2 0 0 | 1 0 0 2 1 0
xo .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 18 * * * * * * | 0 0 1 1 1 0 0 0 0 0 | 0 1 1 1 0 0
.. ox .. ..&#x | 1 2 | 0 0 2 1 0 | * * * * 18 * * * * * | 0 0 1 0 0 1 1 0 0 0 | 0 1 1 0 1 0
.. .. xo ..&#x | 2 1 | 0 1 2 0 0 | * * * * * 18 * * * * | 0 0 0 1 0 1 0 1 0 0 | 0 1 0 1 1 0
.. .. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * * * * 18 * * * | 0 0 0 0 1 0 1 1 0 0 | 0 0 1 1 1 0
.o3.x .. .. | 0 3 | 0 0 0 3 0 | * * * * * * * 3 * * | 0 0 2 0 0 0 0 0 2 0 | 0 1 2 0 0 1
.. .x .. .x | 0 4 | 0 0 0 2 2 | * * * * * * * * 9 * | 0 0 0 0 0 0 1 0 1 1 | 0 0 1 0 1 1
.. .. .o3.x | 0 3 | 0 0 0 0 3 | * * * * * * * * * 3 | 0 0 0 0 0 0 0 2 0 2 | 0 0 0 1 2 1
---------------+-----+------------+-------------------------+---------------------+------------
x.3o. x. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * | 1 1 0 0 0 0
x. .. x.3o. ♦ 6 0 | 3 6 0 0 0 | 0 3 2 0 0 0 0 0 0 0 | * 3 * * * * * * * * | 1 0 0 1 0 0
xo3ox .. ..&#x ♦ 3 3 | 3 0 6 3 0 | 1 0 0 3 3 0 0 1 0 0 | * * 6 * * * * * * * | 0 1 1 0 0 0
xo .. xo ..&#x ♦ 4 1 | 2 2 4 0 0 | 0 1 0 2 0 2 0 0 0 0 | * * * 9 * * * * * * | 0 1 0 1 0 0
xo .. .. ox&#x ♦ 2 2 | 1 0 4 0 1 | 0 0 0 2 0 0 2 0 0 0 | * * * * 9 * * * * * | 0 0 1 1 0 0
.. ox xo ..&#x ♦ 2 2 | 0 1 4 1 0 | 0 0 0 0 2 2 0 0 0 0 | * * * * * 9 * * * * | 0 1 0 0 1 0
.. ox .. ox&#x ♦ 1 4 | 0 0 4 2 2 | 0 0 0 0 2 0 2 0 1 0 | * * * * * * 9 * * * | 0 0 1 0 1 0
.. .. xo3ox&#x ♦ 3 3 | 0 3 6 0 3 | 0 0 1 0 0 3 3 0 0 1 | * * * * * * * 6 * * | 0 0 0 1 1 0
.o3.x .. .x ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 0 2 3 0 | * * * * * * * * 3 * | 0 0 1 0 0 1
.. .x .o3.x ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * 3 | 0 0 0 0 1 1
---------------+-----+------------+-------------------------+---------------------+------------
x.3o. x.3o. ♦ 9 0 | 9 9 0 0 0 | 3 9 3 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 | 1 * * * * *
xo3ox xo ..&#x ♦ 6 3 | 6 3 12 3 0 | 2 3 0 6 6 6 0 1 0 0 | 1 0 2 3 0 3 0 0 0 0 | * 3 * * * *
xo3ox .. ox&#x ♦ 3 6 | 3 0 12 6 3 | 1 0 0 6 6 0 6 2 3 0 | 0 0 2 0 3 0 3 0 1 0 | * * 3 * * *
xo .. xo3ox&#x ♦ 6 3 | 3 6 12 0 3 | 0 3 2 6 0 6 6 0 0 1 | 0 1 0 3 3 0 0 2 0 0 | * * * 3 * *
.. ox xo3ox&#x ♦ 3 6 | 0 3 12 3 6 | 0 0 1 0 6 6 6 0 3 2 | 0 0 0 0 0 3 3 2 0 1 | * * * * 3 *
.o3.x .o3.x ♦ 0 9 | 0 0 0 9 9 | 0 0 0 0 0 0 0 3 9 3 | 0 0 0 0 0 0 0 0 3 3 | * * * * * 1
or (top = bottom)
o.3o. o.3o. & | 18 | 2 2 4 | 1 4 1 6 6 | 2 2 2 5 4 2 | 1 3 3
-----------------+----+----------+--------------+---------------+------
x. .. .. .. & | 2 | 18 * * | 1 2 0 2 0 | 2 1 2 2 1 0 | 1 3 1
.. .. x. .. & | 2 | * 18 * | 0 2 1 0 2 | 1 2 0 2 1 2 | 1 1 3
oo3oo oo3oo&#x | 2 | * * 36 | 0 0 0 2 2 | 0 0 1 2 2 1 | 0 2 2
-----------------+----+----------+--------------+---------------+------
x.3o. .. .. & | 3 | 3 0 0 | 6 * * * * | 2 0 2 0 0 0 | 1 3 0
x. .. x. .. & | 4 | 2 2 0 | * 18 * * * | 1 1 0 1 0 0 | 1 1 1
.. .. x.3o. & | 3 | 0 3 0 | * * 6 * * | 0 2 0 0 0 2 | 1 0 3
xo .. .. ..&#x & | 3 | 1 0 2 | * * * 36 * | 0 0 1 1 1 0 | 0 2 1
.. .. xo ..&#x & | 3 | 0 1 2 | * * * * 36 | 0 0 0 1 1 1 | 0 1 2
-----------------+----+----------+--------------+---------------+------
x.3o. x. .. & ♦ 6 | 6 3 0 | 2 3 0 0 0 | 6 * * * * * | 1 1 0
x. .. x.3o. & ♦ 6 | 3 6 0 | 0 3 2 0 0 | * 6 * * * * | 1 0 1
xo3ox .. ..&#x ♦ 6 | 6 0 6 | 2 0 0 6 0 | * * 6 * * * | 0 2 0
xo .. xo ..&#x & ♦ 5 | 2 2 4 | 0 1 0 2 2 | * * * 18 * * | 0 1 1
xo .. .. ox&#x & ♦ 4 | 1 1 4 | 0 0 0 2 2 | * * * * 18 * | 0 1 1
.. .. xo3ox&#x ♦ 6 | 0 6 6 | 0 0 2 0 6 | * * * * * 6 | 0 0 2
-----------------+----+----------+--------------+---------------+------
x.3o. x.3o. & ♦ 9 | 9 9 0 | 3 9 3 0 0 | 3 3 0 0 0 0 | 2 * *
xo3ox xo ..&#x & ♦ 9 | 9 3 12 | 3 3 0 12 6 | 1 0 2 3 3 0 | * 6 *
xo .. xo3ox&#x & ♦ 9 | 3 9 12 | 0 3 3 6 12 | 0 1 0 3 3 2 | * * 6
or (top = bottom, left = right)
o.3o. o.3o. & | 18 | 4 4 | 2 4 12 | 4 4 5 4 | 1 6
-----------------+----+-------+----------+-------------+-----
x. .. .. .. & | 2 | 36 * | 1 2 2 | 3 2 2 1 | 1 4
oo3oo oo3oo&#x | 2 | * 36 | 0 0 4 | 0 2 2 2 | 0 4
-----------------+----+-------+----------+-------------+-----
x.3o. .. .. & | 3 | 3 0 | 12 * * | 2 2 0 0 | 1 3
x. .. x. .. & | 4 | 4 0 | * 18 * | 2 0 1 0 | 1 2
xo .. .. ..&#x & | 3 | 1 2 | * * 72 | 0 1 1 1 | 0 3
-----------------+----+-------+----------+-------------+-----
x.3o. x. .. & ♦ 6 | 9 0 | 2 3 0 | 12 * * * | 1 1
xo3ox .. ..&#x & ♦ 6 | 6 6 | 2 0 6 | * 12 * * | 0 2
xo .. xo ..&#x & ♦ 5 | 4 4 | 0 1 4 | * * 18 * | 0 2
xo .. .. ox&#x & ♦ 4 | 2 4 | 0 0 4 | * * * 18 | 0 2
-----------------+----+-------+----------+-------------+-----
x.3o. x.3o. & ♦ 9 | 18 0 | 6 9 0 | 6 0 0 0 | 2 *
xo3ox xo ..&#x & ♦ 9 | 12 12 | 3 3 18 | 1 2 3 3 | * 12