|
Acronym
|
tot
|
|
Name
|
truncated triacontiditeron,
truncated pentacross
|
|
Field of sections
|
 ©
|
|
Circumradius
|
sqrt(5/2) = 1.581139
|
Inradius
wrt. hex
|
sqrt(2) = 1.414214
|
Inradius
wrt. tip
|
3/sqrt(10) = 0.948683
|
|
Vertex figure
|
 ©  ©
|
Lace city
in approx. ASCII-art
|
 ©
|
o3o4o x3o4o o3o4o -- x3o3o4o (hex)
o3o4o u3o4o o3o4o -- u3o3o4o (u-hex)
x3o4o u3o4o x3x4o u3o4o x3o4o -- x3x3o4o (thex)
o3o4o u3o4o o3o4o -- u3o3o4o (u-hex)
o3o4o x3o4o o3o4o -- x3o3o4o (hex)
|
|
|
Coordinates
|
(sqrt(2), 1/sqrt(2), 0, 0, 0) & all permutations, all changes of sign
|
|
Volume
|
119 sqrt(2)/15 = 11.219428
|
|
Surface
|
(5+76 sqrt(5))/3 = 58.313722
|
Dihedral angles
(at margins)
|
- at tut between tip and tip: arccos(-3/5) = 126.869898°
- at tet between hex and tip: arccos[-1/sqrt(5)] = 116.565051°
|
|
Face vector
|
80, 280, 400, 240, 42
|
|
Confer
|
- related CRFs:
-
hextum
- general polytopal classes:
-
Wythoffian polytera
lace simplices
partial Stott expansions
- analogs:
-
truncated orthoplex tOn
truncated Gossetic t(2n,1)
|
External
links
|
|
Incidence matrix according to Dynkin symbol
x3x3o3o4o
. . . . . | 80 | 1 6 | 6 12 | 12 8 | 8 1
----------+----+--------+--------+--------+------
x . . . . | 2 | 40 * ♦ 6 0 | 12 0 | 8 0
. x . . . | 2 | * 240 | 1 4 | 4 4 | 4 1
----------+----+--------+--------+--------+------
x3x . . . | 6 | 3 3 | 80 * | 4 0 | 4 0
. x3o . . | 3 | 0 3 | * 320 | 1 2 | 2 1
----------+----+--------+--------+--------+------
x3x3o . . ♦ 12 | 6 12 | 4 4 | 80 * | 2 0
. x3o3o . ♦ 4 | 0 6 | 0 4 | * 160 | 1 1
----------+----+--------+--------+--------+------
x3x3o3o . ♦ 20 | 10 30 | 10 20 | 5 5 | 32 *
. x3o3o4o ♦ 8 | 0 24 | 0 32 | 0 16 | * 10
x3x3o3o4/3o
. . . . . | 80 | 1 6 | 6 12 | 12 8 | 8 1
------------+----+--------+--------+--------+------
x . . . . | 2 | 40 * ♦ 6 0 | 12 0 | 8 0
. x . . . | 2 | * 240 | 1 4 | 4 4 | 4 1
------------+----+--------+--------+--------+------
x3x . . . | 6 | 3 3 | 80 * | 4 0 | 4 0
. x3o . . | 3 | 0 3 | * 320 | 1 2 | 2 1
------------+----+--------+--------+--------+------
x3x3o . . ♦ 12 | 6 12 | 4 4 | 80 * | 2 0
. x3o3o . ♦ 4 | 0 6 | 0 4 | * 160 | 1 1
------------+----+--------+--------+--------+------
x3x3o3o . ♦ 20 | 10 30 | 10 20 | 5 5 | 32 *
. x3o3o4/3o ♦ 8 | 0 24 | 0 32 | 0 16 | * 10
o3o3o *b3x3x
. . . . . | 80 | 6 1 | 12 6 | 4 4 12 | 1 4 4
-------------+----+--------+--------+----------+---------
. . . x . | 2 | 240 * | 4 1 | 2 2 4 | 1 2 2
. . . . x | 2 | * 40 ♦ 0 6 | 0 0 12 | 0 4 4
-------------+----+--------+--------+----------+---------
. o . *b3x . | 3 | 3 0 | 320 * | 1 1 1 | 1 1 1
. . . x3x | 6 | 3 3 | * 80 | 0 0 4 | 0 2 2
-------------+----+--------+--------+----------+---------
o3o . *b3x . ♦ 4 | 6 0 | 4 0 | 80 * * | 1 1 0
. o3o *b3x . ♦ 4 | 6 0 | 4 0 | * 80 * | 1 0 1
. o . *b3x3x ♦ 12 | 12 6 | 4 4 | * * 80 | 0 1 1
-------------+----+--------+--------+----------+---------
o3o3o *b3x . ♦ 8 | 24 0 | 32 0 | 8 8 0 | 10 * *
o3o . *b3x3x ♦ 20 | 30 10 | 20 10 | 5 0 5 | * 16 *
. o3o *b3x3x ♦ 20 | 30 10 | 20 10 | 0 5 5 | * * 16
xuxux3ooxoo3ooooo4ooooo&#xt → all heights = 1/sqrt(2) = 0.707107
(hex || pseudo u-hex || pseudo thex || pseudo u-hex || hex)
o....3o....3o....4o.... | 8 * * * * | 6 1 0 0 0 0 0 0 | 12 6 0 0 0 0 0 0 | 8 12 0 0 0 0 0 | 1 8 0 0 0
.o...3.o...3.o...4.o... | * 8 * * * | 0 1 6 0 0 0 0 0 | 0 6 12 0 0 0 0 0 | 0 12 8 0 0 0 0 | 0 8 1 0 0
..o..3..o..3..o..4..o.. | * * 48 * * | 0 0 1 1 4 1 0 0 | 0 1 4 4 4 1 4 0 | 0 4 4 4 4 4 0 | 0 4 1 4 0
...o.3...o.3...o.4...o. | * * * 8 * | 0 0 0 0 0 6 1 0 | 0 0 0 0 0 6 12 0 | 0 0 0 0 12 8 0 | 0 0 1 8 0
....o3....o3....o4....o | * * * * 8 | 0 0 0 0 0 0 1 6 | 0 0 0 0 0 6 0 12 | 0 0 0 0 12 0 8 | 0 0 0 8 1
----------------------------+------------+-----------------------+-------------------------+----------------------+------------
x.... ..... ..... ..... | 2 0 0 0 0 | 24 * * * * * * * | 4 1 0 0 0 0 0 0 | 4 4 0 0 0 0 0 | 1 4 0 0 0
oo...3oo...3oo...4oo...&#x | 1 1 0 0 0 | * 8 * * * * * * ♦ 0 6 0 0 0 0 0 0 | 0 12 0 0 0 0 0 | 0 8 0 0 0
.oo..3.oo..3.oo..4.oo..&#x | 0 1 1 0 0 | * * 48 * * * * * | 0 1 4 0 0 0 0 0 | 0 4 4 0 0 0 0 | 0 4 1 0 0
..x.. ..... ..... ..... | 0 0 2 0 0 | * * * 24 * * * * ♦ 0 1 0 4 0 1 0 0 | 0 4 0 4 4 0 0 | 0 4 0 4 0
..... ..x.. ..... ..... | 0 0 2 0 0 | * * * * 96 * * * | 0 0 1 1 2 0 1 0 | 0 1 2 2 1 2 0 | 0 2 1 2 0
..oo.3..oo.3..oo.4..oo.&#x | 0 0 1 1 0 | * * * * * 48 * * | 0 0 0 0 0 1 4 0 | 0 0 0 0 4 4 0 | 0 0 1 4 0
...oo3...oo3...oo4...oo&#x | 0 0 0 1 1 | * * * * * * 8 * ♦ 0 0 0 0 0 6 0 0 | 0 0 0 0 12 0 0 | 0 0 0 8 0
....x ..... ..... ..... | 0 0 0 0 2 | * * * * * * * 24 | 0 0 0 0 0 1 0 4 | 0 0 0 0 4 0 4 | 0 0 0 4 1
----------------------------+------------+-----------------------+-------------------------+----------------------+------------
x....3o.... ..... ..... | 3 0 0 0 0 | 3 0 0 0 0 0 0 0 | 32 * * * * * * * | 2 1 0 0 0 0 0 | 1 2 0 0 0
xux.. ..... ..... .....&#xt | 2 2 2 0 0 | 1 2 2 1 0 0 0 0 | * 24 * * * * * * | 0 4 0 0 0 0 0 | 0 4 0 0 0
..... .ox.. ..... .....&#x | 0 1 2 0 0 | 0 0 2 0 1 0 0 0 | * * 96 * * * * * | 0 1 2 0 0 0 0 | 0 2 1 0 0
..x..3..x.. ..... ..... | 0 0 6 0 0 | 0 0 0 3 3 0 0 0 | * * * 32 * * * * | 0 1 0 2 1 0 0 | 0 2 0 2 0
..... ..x..3..o.. ..... | 0 0 3 0 0 | 0 0 0 0 3 0 0 0 | * * * * 64 * * * | 0 0 1 1 0 1 0 | 0 1 1 1 0
..xux ..... ..... .....&#xt | 0 0 2 2 2 | 0 0 0 1 0 2 2 1 | * * * * * 24 * * | 0 0 0 0 4 0 0 | 0 0 0 4 0
..... ..xo. ..... .....&#xt | 0 0 2 1 0 | 0 0 0 0 1 2 0 0 | * * * * * * 96 * | 0 0 0 0 1 2 0 | 0 0 1 2 0
....x3....o ..... ..... | 0 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * 32 | 0 0 0 0 1 0 2 | 0 0 0 2 1
----------------------------+------------+-----------------------+-------------------------+----------------------+------------
x....3o....3o.... ..... ♦ 4 0 0 0 0 | 6 0 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 | 16 * * * * * * | 1 1 0 0 0
xux..3oox.. ..... .....&#xt ♦ 3 3 6 0 0 | 3 3 6 3 3 0 0 0 | 1 3 3 1 0 0 0 0 | * 32 * * * * * | 0 2 0 0 0
..... .ox..3.oo.. .....&#x ♦ 0 1 3 0 0 | 0 0 3 0 3 0 0 0 | 0 0 3 0 1 0 0 0 | * * 64 * * * * | 0 1 1 0 0
..x..3..x..3..o.. ..... ♦ 0 0 12 0 0 | 0 0 0 6 12 0 0 0 | 0 0 0 4 4 0 0 0 | * * * 16 * * * | 0 1 0 1 0
..xux3..xoo ..... .....&#xt ♦ 0 0 6 3 3 | 0 0 0 3 3 6 3 3 | 0 0 0 1 0 3 3 1 | * * * * 32 * * | 0 0 0 2 0
..... ..xo.3..oo. .....&#x ♦ 0 0 3 1 0 | 0 0 0 0 3 3 0 0 | 0 0 0 0 1 0 3 0 | * * * * * 64 * | 0 0 1 1 0
....x3....o3....o ..... ♦ 0 0 0 0 4 | 0 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 4 | * * * * * * 16 | 0 0 0 1 1
----------------------------+------------+-----------------------+-------------------------+----------------------+------------
x....3o....3o....4o.... ♦ 8 0 0 0 0 | 24 0 0 0 0 0 0 0 | 32 0 0 0 0 0 0 0 | 16 0 0 0 0 0 0 | 1 * * * *
xux..3oox..3ooo.. .....&#xt ♦ 4 4 12 0 0 | 6 4 12 6 12 0 0 0 | 4 6 12 4 4 0 0 0 | 1 4 4 1 0 0 0 | * 16 * * *
..... .oxo.3.ooo.4.ooo.&#xt ♦ 0 1 6 1 0 | 0 0 6 0 12 6 0 0 | 0 0 12 0 8 0 12 0 | 0 0 8 0 0 8 0 | * * 8 * *
..xux3..xoo3..ooo .....&#xt ♦ 0 0 12 4 4 | 0 0 0 6 12 12 4 6 | 0 0 0 4 4 6 12 4 | 0 0 0 1 4 4 1 | * * * 16 *
....x3....o3....o4....o ♦ 0 0 0 0 8 | 0 0 0 0 0 0 0 24 | 0 0 0 0 0 0 0 32 | 0 0 0 0 0 0 16 | * * * * 1
or
o....3o....3o....4o.... & | 16 * * | 6 1 0 0 0 | 12 6 0 0 0 | 8 12 0 0 | 1 8 0
.o...3.o...3.o...4.o... & | * 16 * | 0 1 6 0 0 | 0 6 12 0 0 | 0 12 8 0 | 0 8 1
..o..3..o..3..o..4..o.. | * * 48 | 0 0 2 1 4 | 0 2 8 4 4 | 0 8 8 4 | 0 8 1
------------------------------+----------+----------------+-----------------+--------------+-------
x.... ..... ..... ..... & | 2 0 0 | 48 * * * * | 4 1 0 0 0 | 4 4 0 0 | 1 4 0
oo...3oo...3oo...4oo...&#x & | 1 1 0 | * 16 * * * ♦ 0 6 0 0 0 | 0 12 0 0 | 0 8 0
.oo..3.oo..3.oo..4.oo..&#x & | 0 1 1 | * * 96 * * | 0 1 4 0 0 | 0 4 4 0 | 0 4 1
..x.. ..... ..... ..... | 0 0 2 | * * * 24 * ♦ 0 2 0 4 0 | 0 8 0 4 | 0 8 0
..... ..x.. ..... ..... | 0 0 2 | * * * * 96 | 0 0 2 1 2 | 0 2 4 2 | 0 4 1
------------------------------+----------+----------------+-----------------+--------------+-------
x....3o.... ..... ..... & | 3 0 0 | 3 0 0 0 0 | 64 * * * * | 2 1 0 0 | 1 2 0
xux.. ..... ..... .....&#xt & | 2 2 2 | 1 2 2 1 0 | * 48 * * * | 0 4 0 0 | 0 4 0
..... .ox.. ..... .....&#x & | 0 1 2 | 0 0 2 0 1 | * * 192 * * | 0 1 2 0 | 0 2 1
..x..3..x.. ..... ..... | 0 0 6 | 0 0 0 3 3 | * * * 32 * | 0 2 0 2 | 0 4 0
..... ..x..3..o.. ..... | 0 0 3 | 0 0 0 0 3 | * * * * 64 | 0 0 2 1 | 0 2 1
------------------------------+----------+----------------+-----------------+--------------+-------
x....3o....3o.... ..... & ♦ 4 0 0 | 6 0 0 0 0 | 4 0 0 0 0 | 32 * * * | 1 1 0
xux..3oox.. ..... .....&#xt & ♦ 3 3 6 | 3 3 6 3 3 | 1 3 3 1 0 | * 64 * * | 0 2 0
..... .ox..3.oo.. .....&#x & ♦ 0 1 3 | 0 0 3 0 3 | 0 0 3 0 1 | * * 128 * | 0 1 1
..x..3..x..3..o.. ..... ♦ 0 0 12 | 0 0 0 6 12 | 0 0 0 4 4 | * * * 16 | 0 2 0
------------------------------+----------+----------------+-----------------+--------------+-------
x....3o....3o....4o.... & ♦ 8 0 0 | 24 0 0 0 0 | 32 0 0 0 0 | 16 0 0 0 | 2 * *
xux..3oox..3ooo.. .....&#xt & ♦ 4 4 12 | 6 4 12 6 12 | 4 6 12 4 4 | 1 4 4 1 | * 32 *
..... .oxo.3.ooo.4.ooo.&#xt ♦ 0 2 6 | 0 0 12 0 12 | 0 0 24 0 8 | 0 0 16 0 | * * 8
Qqo xux3oox3ooo4ooo&#zxt
o.. o..3o..3o..4o.. | 16 * * | 6 1 0 0 0 | 12 6 0 0 0 | 8 12 0 0 | 1 8 0
.o. .o.3.o.3.o.4.o. | * 16 * | 0 1 6 0 0 | 0 6 12 0 0 | 0 12 8 0 | 0 8 1
..o ..o3..o3..o4..o | * * 48 | 0 0 2 1 4 | 0 2 8 4 4 | 0 8 8 4 | 0 8 1
-------------------------+----------+----------------+-----------------+--------------+-------
... x.. ... ... ... | 2 0 0 | 48 * * * * | 4 1 0 0 0 | 4 4 0 0 | 1 4 0
oo. oo.3oo.3oo.4oo.&#x | 1 1 0 | * 16 * * * ♦ 0 6 0 0 0 | 0 12 0 0 | 0 8 0
.oo .oo3.oo3.oo4.oo&#x | 0 1 1 | * * 96 * * | 0 1 4 0 0 | 0 4 4 0 | 0 4 1
... ..x ... ... ... | 0 0 2 | * * * 24 * ♦ 0 2 0 4 0 | 0 8 0 4 | 0 8 0
... ... ..x ... ... | 0 0 2 | * * * * 96 | 0 0 2 1 2 | 0 2 4 2 | 0 4 1
-------------------------+----------+----------------+-----------------+--------------+-------
... x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 | 64 * * * * | 2 1 0 0 | 1 2 0
... xux ... ... ...&#xt | 2 2 2 | 1 2 2 1 0 | * 48 * * * | 0 4 0 0 | 0 4 0
... ... .ox ... ...&#x | 0 1 2 | 0 0 2 0 1 | * * 192 * * | 0 1 2 0 | 0 2 1
... ..x3..x ... ... | 0 0 6 | 0 0 0 3 3 | * * * 32 * | 0 2 0 2 | 0 4 0
... ... ..x3..o ... | 0 0 3 | 0 0 0 0 3 | * * * * 64 | 0 0 2 1 | 0 2 1
-------------------------+----------+----------------+-----------------+--------------+-------
... x..3o..3o.. ... ♦ 4 0 0 | 6 0 0 0 0 | 4 0 0 0 0 | 32 * * * | 1 1 0
... xux3oox ... ...&#xt ♦ 3 3 6 | 3 3 6 3 3 | 1 3 3 1 0 | * 64 * * | 0 2 0
... ... .ox3.oo ...&#x ♦ 0 1 3 | 0 0 3 0 3 | 0 0 3 0 1 | * * 128 * | 0 1 1
... ..x3..x3..o ... ♦ 0 0 12 | 0 0 0 6 12 | 0 0 0 4 4 | * * * 16 | 0 2 0
-------------------------+----------+----------------+-----------------+--------------+-------
... x..3o..3o..4o.. ♦ 8 0 0 | 24 0 0 0 0 | 32 0 0 0 0 | 16 0 0 0 | 2 * *
... xux3oox3ooo ...&#xt ♦ 4 4 12 | 6 4 12 6 12 | 4 6 12 4 4 | 1 4 4 1 | * 32 *
.qo ... .ox3.oo4.oo&#zx ♦ 0 2 6 | 0 0 12 0 12 | 0 0 24 0 8 | 0 0 16 0 | * * 8