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Acronym
|
rax
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|
Name
|
rectified hexeract,
rectified dodecapeton
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|
Circumradius
|
sqrt(5/2) = 1.581139
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Inradius
wrt. hix
|
5/sqrt(12) = 1.443376
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Inradius
wrt. rin
|
1/sqrt(2) = 0.707107
|
Lace city
in approx. ASCII-art
|
 ©
|
r Q r -- o3o3o3x4o (rin)
Q Q -- o3o3o3o4q (q-pent)
r Q r -- o3o3o3x4o (rin)
where:
r - o3o3x4o (rit)
Q - o3o3o4q (q-tes)
|
|
+---------------- o3o3o3x4o (rin)
/ +--------- o3o3o3o4q (q-pent)
/ / +-- o3o3o3x4o (rin)
/
x3o3o3o o3o3o3o -- x3o3o3o3o (hix)
x3x3o3o u3o3o3o x3o3o3o -- x3x3o3o3o (tix)
o3x3x3o o3u3o3o x3x3o3o -- o3x3x3o3o (bittix)
o3o3x3x o3o3u3o o3x3x3o -- o3o3x3x3o (alt. bittix)
o3o3o3x o3o3o3u o3o3x3x -- o3o3o3x3x (alt. tix)
o3o3o3o o3o3o3x -- o3o3o3o3x (dual hix)
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Coordinates
|
(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign
|
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Volume
|
719/90 = 7.988889
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|
Surface
|
(714 sqrt(2)+2 sqrt(3))/15 = 67.547506
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Dihedral angles
(at margins)
|
- at pen between hix and rin: arccos[-1/sqrt(6)] = 114.094843°
- at rit between rin and rin: 90°
|
|
Face vector
|
192, 960, 1520, 1120, 444, 76
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Confer
|
- related scaliform:
-
bittixa
- ambification:
-
rerax
- general polytopal classes:
-
Wythoffian polypeta
lace simplices
ambifications
- analogs:
-
rectified hypercube rCn
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External
links
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Incidence matrix according to Dynkin symbol
o3o3o3o3x4o
. . . . . . | 192 ♦ 10 | 20 5 | 20 10 | 10 10 | 2 5
------------+-----+-----+----------+---------+--------+------
. . . . x . | 2 | 960 | 4 1 | 6 4 | 4 6 | 1 4
------------+-----+-----+----------+---------+--------+------
. . . o3x . | 3 | 3 | 1280 * | 3 1 | 3 3 | 1 3
. . . . x4o | 4 | 4 | * 240 ♦ 0 4 | 0 6 | 0 4
------------+-----+-----+----------+---------+--------+------
. . o3o3x . ♦ 4 | 6 | 4 0 | 960 * | 2 1 | 1 2
. . . o3x4o ♦ 12 | 24 | 8 6 | * 160 | 0 3 | 0 3
------------+-----+-----+----------+---------+--------+------
. o3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 384 * | 1 1
. . o3o3x4o ♦ 32 | 96 | 64 24 | 16 8 | * 60 | 0 2
------------+-----+-----+----------+---------+--------+------
o3o3o3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 | 64 *
. o3o3o3x4o ♦ 80 | 320 | 320 80 | 160 40 | 32 10 | * 12
o3o3o3o3x4/3o
. . . . . . | 192 ♦ 10 | 20 5 | 20 10 | 10 10 | 2 5
--------------+-----+-----+----------+---------+--------+------
. . . . x . | 2 | 960 | 4 1 | 6 4 | 4 6 | 1 4
--------------+-----+-----+----------+---------+--------+------
. . . o3x . | 3 | 3 | 1280 * | 3 1 | 3 3 | 1 3
. . . . x4/3o | 4 | 4 | * 240 ♦ 0 4 | 0 6 | 0 4
--------------+-----+-----+----------+---------+--------+------
. . o3o3x . ♦ 4 | 6 | 4 0 | 960 * | 2 1 | 1 2
. . . o3x4/3o ♦ 12 | 24 | 8 6 | * 160 | 0 3 | 0 3
--------------+-----+-----+----------+---------+--------+------
. o3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 384 * | 1 1
. . o3o3x4/3o ♦ 32 | 96 | 64 24 | 16 8 | * 60 | 0 2
--------------+-----+-----+----------+---------+--------+------
o3o3o3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 | 64 *
. o3o3o3x4/3o ♦ 80 | 320 | 320 80 | 160 40 | 32 10 | * 12
x3o3x *b3o3o3o
. . . . . . | 192 | 5 5 | 10 5 10 | 10 10 10 | 10 5 5 | 5 1 1
---------------+-----+---------+-------------+-------------+------------+---------
x . . . . . | 2 | 480 * | 4 1 0 | 4 6 0 | 6 4 0 | 4 1 0
. . x . . . | 2 | * 480 | 0 1 4 | 4 0 6 | 6 0 4 | 4 0 1
---------------+-----+---------+-------------+-------------+------------+---------
x3o . . . . | 3 | 3 0 | 640 * * | 1 3 0 | 3 3 0 | 3 1 0
x . x . . . | 4 | 2 2 | * 240 * ♦ 4 0 0 | 6 0 0 | 4 0 0
. o3x . . . | 3 | 0 3 | * * 640 | 1 0 3 | 3 0 3 | 3 0 1
---------------+-----+---------+-------------+-------------+------------+---------
x3o3x . . . ♦ 12 | 12 12 | 4 6 4 | 160 * * | 3 0 0 | 3 0 0
x3o . *b3o . . ♦ 4 | 6 0 | 4 0 0 | * 480 * | 1 2 0 | 2 1 0
. o3x *b3o . . ♦ 4 | 0 6 | 0 0 4 | * * 480 | 1 0 2 | 2 0 1
---------------+-----+---------+-------------+-------------+------------+---------
x3o3x *b3o . . ♦ 32 | 48 48 | 32 24 32 | 8 8 8 | 60 * * | 2 0 0
x3o . *b3o3o . ♦ 5 | 10 0 | 10 0 0 | 0 5 0 | * 192 * | 1 1 0
. o3x *b3o3o . ♦ 5 | 0 10 | 0 0 10 | 0 0 5 | * * 192 | 1 0 1
---------------+-----+---------+-------------+-------------+------------+---------
x3o3x *b3o3o . ♦ 80 | 160 160 | 160 80 160 | 40 80 80 | 10 16 16 | 12 * *
x3o . *b3o3o3o ♦ 6 | 15 0 | 20 0 0 | 0 15 0 | 0 6 0 | * 32 *
. o3x *b3o3o3o ♦ 6 | 0 15 | 0 0 20 | 0 0 15 | 0 0 6 | * * 32
qo oo3oo3oo3xo4oq&#zx → height = 0
(tegum sum of a q-height rinnip and an equatorial q-pent)
o. o.3o.3o.3o.4o. | 160 * | 8 2 | 12 4 1 8 | 8 6 4 12 | 2 4 6 8 | 1 4 2
.o .o3.o3.o3.o4.o | * 32 | 0 10 | 0 0 5 20 | 0 0 10 20 | 0 0 10 10 | 0 5 2
----------------------+--------+---------+----------------+---------------+--------------+--------
.. .. .. .. x. .. | 2 0 | 640 * | 3 1 0 1 | 3 3 1 3 | 1 3 3 3 | 1 3 1
oo oo3oo3oo3oo4oo&#x | 1 1 | * 320 | 0 0 1 4 | 0 0 4 6 | 0 0 6 4 | 0 4 1
----------------------+--------+---------+----------------+---------------+--------------+--------
.. .. .. o.3x. .. | 3 0 | 3 0 | 640 * * * | 2 1 0 1 | 1 2 1 2 | 1 2 1
.. .. .. .. x.4o. | 4 0 | 4 0 | * 160 * * ♦ 0 3 1 0 | 0 3 3 0 | 1 3 0
qo .. .. .. .. oq&#zx | 2 2 | 0 4 | * * 80 * ♦ 0 0 4 0 | 0 0 6 0 | 0 4 0
.. .. .. .. xo ..&#x | 2 1 | 1 2 | * * * 640 | 0 0 1 3 | 0 0 3 3 | 0 3 1
----------------------+--------+---------+----------------+---------------+--------------+--------
.. .. o.3o.3x. .. ♦ 4 0 | 6 0 | 4 0 0 0 | 320 * * * | 1 1 0 1 | 1 1 1
.. .. .. o.3x.4o. ♦ 12 0 | 24 0 | 8 6 0 0 | * 80 * * | 0 2 1 0 | 1 2 0
qo .. .. .. xo4oq&#zx ♦ 8 4 | 8 16 | 0 2 4 8 | * * 80 * | 0 0 3 0 | 0 3 0
.. .. .. oo3xo ..&#x ♦ 3 1 | 3 3 | 1 0 0 3 | * * * 640 | 0 0 1 2 | 0 2 1
----------------------+--------+---------+----------------+---------------+--------------+--------
.. o.3o.3o.3x. .. ♦ 5 0 | 10 0 | 10 0 0 0 | 5 0 0 0 | 64 * * * | 1 0 1
.. .. o.3o.3x.4o. ♦ 32 0 | 96 0 | 64 24 0 0 | 16 8 0 0 | * 20 * * | 1 1 0
qo .. .. oo3xo4oq&#zx ♦ 24 8 | 48 48 | 16 12 12 48 | 0 2 6 16 | * * 40 * | 0 2 0
.. .. oo3oo3xo ..&#x ♦ 4 1 | 6 4 | 4 0 0 6 | 1 0 0 4 | * * * 320 | 0 1 1
----------------------+--------+---------+----------------+---------------+--------------+--------
.. o.3o.3o.3x.4o. ♦ 80 0 | 320 0 | 320 80 0 0 | 160 40 0 0 | 32 10 0 0 | 2 * *
qo .. oo3oo3xo4oq&#zx ♦ 64 16 | 192 128 | 128 48 32 192 | 32 16 24 128 | 0 2 8 32 | * 10 *
.. oo3oo3oo3xo ..&#x ♦ 5 1 | 10 5 | 10 0 0 10 | 5 0 0 10 | 1 0 0 5 | * * 64
ooo3ooo3ooo3xox4oqo&#xt → both heights = = 1/sqrt(2) = 0.707107
(rin || pseudo q-pent || rin)
o..3o..3o..3o..4o.. | 80 * * | 8 2 0 0 | 12 4 8 1 0 0 0 | 8 6 12 4 0 0 0 | 2 4 8 6 0 0 0 | 1 2 4 0 0
.o.3.o.3.o.3.o.4.o. | * 32 * | 0 5 5 0 | 0 0 10 5 10 0 0 | 0 0 10 10 10 0 0 | 0 0 5 10 5 0 0 | 0 1 5 1 0
..o3..o3..o3..o4..o | * * 80 | 0 0 2 8 | 0 0 0 1 8 12 4 | 0 0 0 4 12 8 6 | 0 0 0 6 8 2 4 | 0 0 4 2 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
... ... ... x.. ... | 2 0 0 | 320 * * * | 3 1 1 0 0 0 0 | 3 3 3 1 0 0 0 | 1 3 3 3 0 0 0 | 1 1 3 0 0
oo.3oo.3oo.3oo.4oo.&#x | 1 1 0 | * 160 * * | 0 0 4 1 0 0 0 | 0 0 6 4 0 0 0 | 0 0 4 6 0 0 0 | 0 1 4 0 0
.oo3.oo3.oo3.oo4.oo&#x | 0 1 1 | * * 160 * | 0 0 0 1 4 0 0 | 0 0 0 4 6 0 0 | 0 0 0 6 4 0 0 | 0 0 4 1 0
... ... ... ..x ... | 0 0 2 | * * * 320 | 0 0 0 0 1 3 1 | 0 0 0 1 3 3 3 | 0 0 0 3 3 1 3 | 0 0 3 1 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
... ... o..3x.. ... | 3 0 0 | 3 0 0 0 | 320 * * * * * * | 2 1 1 0 0 0 0 | 1 2 2 1 0 0 0 | 1 1 2 0 0
... ... ... x..4o.. | 4 0 0 | 4 0 0 0 | * 80 * * * * * ♦ 0 3 0 1 0 0 0 | 0 3 0 3 0 0 0 | 1 0 3 0 0
... ... ... xo. ...&#x | 2 1 0 | 1 2 0 0 | * * 320 * * * * | 0 0 3 1 0 0 0 | 0 0 3 3 0 0 0 | 0 1 3 0 0
... ... ... ... oqo&#xt | 1 2 1 | 0 2 2 0 | * * * 80 * * * ♦ 0 0 0 4 0 0 0 | 0 0 0 6 0 0 0 | 0 0 4 0 0
... ... ... .ox ...&#x | 0 1 2 | 0 0 2 1 | * * * * 320 * * | 0 0 0 1 3 0 0 | 0 0 0 3 3 0 0 | 0 0 3 1 0
... ... ..o3..x ... | 0 0 3 | 0 0 0 3 | * * * * * 320 * | 0 0 0 0 1 2 1 | 0 0 0 1 2 1 2 | 0 0 2 1 1
... ... ... ..x4..o | 0 0 4 | 0 0 0 4 | * * * * * * 80 ♦ 0 0 0 1 0 0 3 | 0 0 0 3 0 0 3 | 0 0 3 0 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
... o..3o..3x.. ... ♦ 4 0 0 | 6 0 0 0 | 4 0 0 0 0 0 0 | 160 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 0
... ... o..3x..4o.. ♦ 12 0 0 | 24 0 0 0 | 8 6 0 0 0 0 0 | * 40 * * * * * | 0 2 0 1 0 0 0 | 1 0 2 0 0
... ... oo.3xo. ...&#x ♦ 3 1 0 | 3 3 0 0 | 1 0 3 0 0 0 0 | * * 320 * * * * | 0 0 2 1 0 0 0 | 0 1 2 0 0
... ... ... xox4oqo&#xt ♦ 4 4 4 | 4 8 8 4 | 0 1 4 4 4 0 1 | * * * 80 * * * | 0 0 0 3 0 0 0 | 0 0 3 0 0
... ... .oo3.ox ...&#x ♦ 0 1 3 | 0 0 3 3 | 0 0 0 0 3 1 0 | * * * * 320 * * | 0 0 0 1 2 0 0 | 0 0 2 1 0
... ..o3..o3..x ... ♦ 0 0 4 | 0 0 0 6 | 0 0 0 0 0 4 0 | * * * * * 160 * | 0 0 0 0 1 1 1 | 0 0 1 1 1
... ... ..o3..x4..o ♦ 0 0 12 | 0 0 0 24 | 0 0 0 0 0 8 6 | * * * * * * 40 | 0 0 0 1 0 0 2 | 0 0 2 0 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
o..3o..3o..3x.. ... ♦ 5 0 0 | 10 0 0 0 | 10 0 0 0 0 0 0 | 5 0 0 0 0 0 0 | 32 * * * * * * | 1 1 0 0 0
... o..3o..3x..4o.. ♦ 32 0 0 | 96 0 0 0 | 64 24 0 0 0 0 0 | 16 8 0 0 0 0 0 | * 10 * * * * * | 1 0 1 0 0
... oo.3oo.3xo. ...&#x ♦ 4 1 0 | 6 4 0 0 | 4 0 6 0 0 0 0 | 1 0 4 0 0 0 0 | * * 160 * * * * | 0 1 1 0 0
... ... ooo3xox4oqo&#xt ♦ 12 8 12 | 24 24 24 24 | 8 6 24 12 24 8 6 | 0 1 8 6 8 0 1 | * * * 40 * * * | 0 0 2 0 0
... .oo3.oo3.ox ...&#x ♦ 0 1 4 | 0 0 4 6 | 0 0 0 0 6 4 0 | 0 0 0 0 4 1 0 | * * * * 160 * * | 0 0 1 1 0
..o3..o3..o3..x ... ♦ 0 0 5 | 0 0 0 10 | 0 0 0 0 0 10 0 | 0 0 0 0 0 5 0 | * * * * * 32 * | 0 0 0 1 1
... ..o3..o3..x4..o ♦ 0 0 32 | 0 0 0 96 | 0 0 0 0 0 64 24 | 0 0 0 0 0 16 8 | * * * * * * 10 | 0 0 1 0 1
------------------------+----------+-----------------+--------------------------+--------------------------+------------------------+-------------
o..3o..3o..3x..4o.. ♦ 80 0 0 | 320 0 0 0 | 320 80 0 0 0 0 0 | 160 40 0 0 0 0 0 | 32 10 0 0 0 0 0 | 1 * * * *
oo.3oo.3oo.3xo. ...&#x ♦ 5 1 0 | 10 5 0 0 | 10 0 10 0 0 0 0 | 5 0 10 0 0 0 0 | 1 0 5 0 0 0 0 | * 32 * * *
... ooo3ooo3xox4oqo&#xt ♦ 32 16 32 | 96 64 64 96 | 64 24 96 32 96 64 24 | 16 8 64 24 64 16 8 | 0 1 16 8 16 0 1 | * * 10 * *
.oo3.oo3.oo3.ox ...&#x ♦ 0 1 5 | 0 0 5 10 | 0 0 0 0 10 10 0 | 0 0 0 0 10 5 0 | 0 0 0 0 5 1 0 | * * * 32 *
..o3..o3..o3..x4..o ♦ 0 0 80 | 0 0 0 320 | 0 0 0 0 0 320 80 | 0 0 0 0 0 160 40 | 0 0 0 0 0 32 10 | * * * * 1