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Acronym
|
rin
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Name
|
rectified penteract,
equatorial cross-section of nit-first brox
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Field of sections
|
 ©
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Circumradius
|
sqrt(2) = 1.414214
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Inradius
wrt. pen
|
sqrt(8/5) = 1.264911
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Inradius
wrt. rit
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1/sqrt(2) = 0.707107
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Vertex figure
|
 ©  ©
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Lace city
in approx. ASCII-art
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o3x4o o3o4q o3x4o -- o3o3x4o (rit)
o3o4q o3o4q -- o3o3o4q (q-tes)
o3x4o o3o4q o3x4o -- o3o3x4o (rit)
|
+---------- o3o3x4o (rit)
/ +------ o3o3o4q (q-tes)
/ / +- o3o3x4o (rit)
/
x3o3o o3o3o -- x3o3o3o (pen)
x3x3o u3o3o x3o3o -- x3x3o3o (tip)
o3x3x o3u3o x3x3o -- o3x3x3o (deca)
o3o3x o3o3u o3x3x -- o3o3x3x (alt. tip)
o3o3o o3o3x -- o3o3o3x (dual pen)
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Coordinates
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(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign
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Volume
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119 sqrt(2)/30 = 5.609714
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Surface
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(115+sqrt(5))/3 = 39.078689
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General of army
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(is itself convex)
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Colonel of regiment
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(is itself locally convex
– uniform polyteral members:
& others)
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Dihedral angles
(at margins)
|
- at tet between pen and rit: arccos[-1/sqrt(5)] = 116.565051°
- at co between rit and rit: 90°
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Face vector
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80, 320, 400, 200, 42
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Confer
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- related segmentotera:
-
pennatip
tipadeca
- ambification:
-
rerin
- ambification pre-image:
-
pent
- general polytopal classes:
-
Wythoffian polytera
lace simplices
partial Stott expansions
- analogs:
-
rectified hypercube rCn
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External
links
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Incidence matrix according to Dynkin symbol
o3o3o3x4o
. . . . . | 80 ♦ 8 | 12 4 | 8 6 | 2 4
----------+----+-----+--------+--------+------
. . . x . | 2 | 320 | 3 1 | 3 3 | 1 3
----------+----+-----+--------+--------+------
. . o3x . | 3 | 3 | 320 * | 2 1 | 1 2
. . . x4o | 4 | 4 | * 80 | 0 3 | 0 3
----------+----+-----+--------+--------+------
. o3o3x . ♦ 4 | 6 | 4 0 | 160 * | 1 1
. . o3x4o ♦ 12 | 24 | 8 6 | * 40 | 0 2
----------+----+-----+--------+--------+------
o3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 32 *
. o3o3x4o ♦ 32 | 96 | 64 24 | 16 8 | * 10
o3o3o3x4/3o
. . . . . | 80 ♦ 8 | 12 4 | 8 6 | 2 4
------------+----+-----+--------+--------+------
. . . x . | 2 | 320 | 3 1 | 3 3 | 1 3
------------+----+-----+--------+--------+------
. . o3x . | 3 | 3 | 320 * | 2 1 | 1 2
. . . x4/3o | 4 | 4 | * 80 | 0 3 | 0 3
------------+----+-----+--------+--------+------
. o3o3x . ♦ 4 | 6 | 4 0 | 160 * | 1 1
. . o3x4/3o ♦ 12 | 24 | 8 6 | * 40 | 0 2
------------+----+-----+--------+--------+------
o3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 32 *
. o3o3x4/3o ♦ 32 | 96 | 64 24 | 16 8 | * 10
x3o3x *b3o3o
. . . . . | 80 ♦ 4 4 | 6 4 6 | 6 4 4 | 4 1 1
-------------+----+---------+------------+----------+---------
x . . . . | 2 | 160 * | 3 1 0 | 3 3 0 | 3 1 0
. . x . . | 2 | * 160 | 0 1 3 | 3 0 3 | 3 0 1
-------------+----+---------+------------+----------+---------
x3o . . . | 3 | 3 0 | 160 * * | 1 2 0 | 2 1 0
x . x . . | 4 | 2 2 | * 80 * | 3 0 0 | 3 0 0
. o3x . . | 3 | 0 3 | * * 160 | 1 0 2 | 2 0 1
-------------+----+---------+------------+----------+---------
x3o3x . . ♦ 12 | 12 12 | 4 6 4 | 40 * * | 2 0 0
x3o . *b3o . ♦ 4 | 6 0 | 4 0 0 | * 80 * | 1 1 0
. o3x *b3o . ♦ 4 | 0 6 | 0 0 4 | * * 80 | 1 0 1
-------------+----+---------+------------+----------+---------
x3o3x *b3o . ♦ 32 | 48 48 | 32 24 32 | 8 8 8 | 10 * *
x3o . *b3o3o ♦ 5 | 10 0 | 10 0 0 | 0 5 0 | * 16 *
. o3x *b3o3o ♦ 5 | 0 10 | 0 0 10 | 0 0 5 | * * 16
o3o3o3x4s
demi( . . . . . ) | 80 ♦ 4 4 | 6 4 6 | 4 6 4 | 1 4 1
------------------+----+---------+------------+----------+---------
demi( . . . x . ) | 2 | 160 * | 3 1 0 | 3 3 0 | 1 3 0
sefa( . . . x4s ) | 2 | * 160 | 0 1 3 | 0 3 3 | 0 3 1
------------------+----+---------+------------+----------+---------
demi( . . o3x . ) | 3 | 3 0 | 160 * * | 2 1 0 | 1 2 0
. . . x4s ♦ 4 | 2 2 | * 80 * | 0 3 0 | 0 3 0
sefa( . . o3x4s ) | 3 | 0 3 | * * 160 | 0 1 2 | 0 2 1
------------------+----+---------+------------+----------+---------
demi( . o3o3x . ) ♦ 4 | 6 0 | 4 0 0 | 80 * * | 1 1 0
. . o3x4s ♦ 12 | 12 12 | 4 6 4 | * 40 * | 0 2 0
sefa( . o3o3x4s ) ♦ 4 | 0 6 | 0 0 4 | * * 80 | 0 1 1
------------------+----+---------+------------+----------+---------
demi( o3o3o3x . ) ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 16 * *
. o3o3x4s ♦ 32 | 48 48 | 32 24 32 | 8 8 8 | * 10 *
sefa( o3o3o3x4s ) ♦ 5 | 0 10 | 0 0 10 | 0 0 5 | * * 16
starting figure: o3o3o3x4x
qo oo3oo3xo4oq&#zx → height = 0
(tegum sum of a q-height rittip and an equatorial q-tes)
o. o.3o.3o.4o. | 64 * ♦ 6 2 | 6 3 1 6 | 2 3 3 6 | 1 3 2
.o .o3.o3.o4.o | * 16 ♦ 0 8 | 0 0 4 12 | 0 0 6 8 | 0 4 2
-------------------+-------+---------+---------------+--------------+-------
.. .. .. x. .. | 2 0 | 192 * | 2 1 0 1 | 1 2 1 2 | 1 2 1
oo oo3oo3oo4oo&#x | 1 1 | * 128 | 0 0 1 3 | 0 0 3 3 | 0 3 1
-------------------+-------+---------+---------------+--------------+-------
.. .. o.3x. .. | 3 0 | 3 0 | 128 * * * | 1 1 0 1 | 1 1 1
.. .. .. x.4o. | 4 0 | 4 0 | * 48 * * | 0 2 1 0 | 1 2 0
qo .. .. .. oq&#zx | 2 2 | 0 4 | * * 32 * | 0 0 3 0 | 0 3 0
.. .. .. xo ..&#x | 2 1 | 1 2 | * * * 192 | 0 0 1 2 | 0 2 1
-------------------+-------+---------+---------------+--------------+-------
.. o.3o.3x. .. ♦ 4 0 | 6 0 | 4 0 0 0 | 32 * * * | 1 0 1
.. .. o.3x.4o. ♦ 12 0 | 24 0 | 8 6 0 0 | * 16 * * | 1 1 0
qo .. .. xo4oq&#zx ♦ 8 4 | 8 16 | 0 2 4 8 | * * 24 * | 0 2 0
.. .. oo3xo ..&#x ♦ 3 1 | 3 3 | 1 0 0 3 | * * * 128 | 0 1 1
-------------------+-------+---------+---------------+--------------+-------
.. o.3o.3x.4o. ♦ 32 0 | 96 0 | 64 24 0 0 | 16 8 0 0 | 2 * *
qo .. oo3xo4oq&#zx ♦ 24 8 | 48 48 | 16 12 12 48 | 0 2 6 16 | * 8 *
.. oo3oo3xo ..&#x ♦ 4 1 | 6 4 | 4 0 0 6 | 1 0 0 4 | * * 32
ooo3ooo3xox4oqo&#xt → both heights = 1/sqrt(2) = 0.707107
(rit || pseudo q-tes || rit)
o..3o..3o..4o.. | 32 * * ♦ 6 2 0 0 | 6 3 6 1 0 0 0 | 2 3 6 3 0 0 0 | 1 2 3 0 0
.o.3.o.3.o.4.o. | * 16 * ♦ 0 4 4 0 | 0 0 6 4 6 0 0 | 0 0 4 6 4 0 0 | 0 1 4 1 0
..o3..o3..o4..o | * * 32 ♦ 0 0 2 6 | 0 0 0 1 6 6 3 | 0 0 0 3 6 2 3 | 0 0 3 2 1
--------------------+----------+-------------+----------------------+--------------------+------------
... ... x.. ... | 2 0 0 | 96 * * * | 2 1 1 0 0 0 0 | 1 2 2 1 0 0 0 | 1 1 2 0 0
oo.3oo.3oo.4oo.&#x | 1 1 0 | * 64 * * | 0 0 3 1 0 0 0 | 0 0 3 3 0 0 0 | 0 1 3 0 0
.oo3.oo3.oo4.oo&#x | 0 1 1 | * * 64 * | 0 0 0 1 3 0 0 | 0 0 0 3 3 0 0 | 0 0 3 1 0
... ... ..x ... | 0 0 2 | * * * 96 | 0 0 0 0 1 2 1 | 0 0 0 1 2 1 2 | 0 0 2 1 1
--------------------+----------+-------------+----------------------+--------------------+------------
... o..3x.. ... | 3 0 0 | 3 0 0 0 | 64 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 0
... ... x..4o.. | 4 0 0 | 4 0 0 0 | * 24 * * * * * | 0 2 0 1 0 0 0 | 1 0 2 0 0
... ... xo. ...&#x | 2 1 0 | 1 2 0 0 | * * 96 * * * * | 0 0 2 1 0 0 0 | 0 1 2 0 0
... ... ... oqo&#x | 1 2 1 | 0 2 2 0 | * * * 32 * * * | 0 0 0 3 0 0 0 | 0 0 3 0 0
... ... .ox ...&#x | 0 1 2 | 0 0 2 1 | * * * * 96 * * | 0 0 0 1 2 0 0 | 0 0 2 1 0
... ..o3..x ... | 0 0 3 | 0 0 0 3 | * * * * * 64 * | 0 0 0 0 1 1 1 | 0 0 1 1 1
... ... ..x4..o | 0 0 4 | 0 0 0 4 | * * * * * * 24 | 0 0 0 1 0 0 2 | 0 0 2 0 1
--------------------+----------+-------------+----------------------+--------------------+------------
o..3o..3x.. ... ♦ 4 0 0 | 6 0 0 0 | 4 0 0 0 0 0 0 | 16 * * * * * * | 1 1 0 0 0
... o..3x..4o.. ♦ 12 0 0 | 24 0 0 0 | 8 6 0 0 0 0 0 | * 8 * * * * * | 1 0 1 0 0
... oo.3xo. ...&#x ♦ 3 1 0 | 3 3 0 0 | 1 0 3 0 0 0 0 | * * 64 * * * * | 0 1 1 0 0
... ... xox4oqo&#xt ♦ 4 4 4 | 4 8 8 4 | 0 1 4 4 4 0 1 | * * * 24 * * * | 0 0 2 0 0
... .oo3.ox ...&#x ♦ 0 1 3 | 0 0 3 3 | 0 0 0 0 3 1 0 | * * * * 64 * * | 0 0 1 1 0
..o3..o3..x ... ♦ 0 0 4 | 0 0 0 6 | 0 0 0 0 0 4 0 | * * * * * 16 * | 0 0 0 1 1
... ..o3..x4..o ♦ 0 0 12 | 0 0 0 24 | 0 0 0 0 0 8 6 | * * * * * * 8 | 0 0 1 0 1
--------------------+----------+-------------+----------------------+--------------------+------------
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 | 1 * * * *
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 | * 16 * * *
... ooo3xox4oqo&#xt ♦ 12 8 12 | 24 24 24 24 | 8 6 24 12 24 8 6 | 0 1 8 6 8 0 1 | * * 8 * *
.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 | * * * 16 *
..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 | * * * * 1
xxooo3oxxoo3ooxxo3oooxx&#xt → all heights = sqrt(2/5) = 0.632456
(pen || pseudo tip || pseudo deca || pseudo inv tip || dual pen)
o....3o....3o....3o.... & | 10 * * ♦ 4 4 0 0 0 0 | 6 4 6 0 0 0 0 0 | 4 6 4 0 0 0 0 | 1 1 4 0
.o...3.o...3.o...3.o... & | * 40 * ♦ 0 1 1 3 3 0 | 0 1 3 3 3 3 3 0 | 0 3 3 1 3 3 1 | 0 1 4 1
..o..3..o..3..o..3..o.. | * * 30 ♦ 0 0 0 0 4 4 | 0 0 0 0 2 4 8 2 | 0 2 0 0 4 4 4 | 0 0 4 2
------------------------------+----------+--------------------+--------------------------+----------------------+-----------
x.... ..... ..... ..... & | 2 0 0 | 20 * * * * * | 3 1 0 0 0 0 0 0 | 3 3 0 0 0 0 0 | 1 0 3 0
oo...3oo...3oo...3oo...&#x & | 1 1 0 | * 40 * * * * | 0 1 3 0 0 0 0 0 | 0 3 3 0 0 0 0 | 0 1 3 0
.x... ..... ..... ..... & | 0 2 0 | * * 20 * * * | 0 1 0 0 3 0 0 0 | 0 3 0 0 3 0 0 | 0 0 3 1
..... .x... ..... ..... & | 0 2 0 | * * * 60 * * | 0 0 1 2 0 1 0 0 | 0 1 2 1 0 2 0 | 0 1 3 0
.oo..3.oo..3.oo..3.oo..&#x & | 0 1 1 | * * * * 120 * | 0 0 0 0 1 1 2 0 | 0 1 0 0 2 2 1 | 0 0 3 1
..... ..x.. ..... ..... & | 0 0 2 | * * * * * 60 | 0 0 0 0 0 1 2 1 | 0 1 0 0 1 2 2 | 0 0 3 1
------------------------------+----------+--------------------+--------------------------+----------------------+-----------
x....3o.... ..... ..... & | 3 0 0 | 3 0 0 0 0 0 | 20 * * * * * * * | 2 1 0 0 0 0 0 | 1 0 2 0
xx... ..... ..... .....&#x & | 2 2 0 | 1 2 1 0 0 0 | * 20 * * * * * * | 0 3 0 0 0 0 0 | 0 0 3 0
..... ox... ..... .....&#x & | 1 2 0 | 0 2 0 1 0 0 | * * 60 * * * * * | 0 1 2 0 0 0 0 | 0 1 2 0
..... .x...3.o... ..... & | 0 3 0 | 0 0 0 3 0 0 | * * * 40 * * * * | 0 0 1 1 0 1 0 | 0 1 2 0
.xo.. ..... ..... .....&#x & | 0 2 1 | 0 0 1 0 2 0 | * * * * 60 * * * | 0 1 0 0 2 0 0 | 0 0 2 1
..... .xx.. ..... .....&#x & | 0 2 2 | 0 0 0 1 2 1 | * * * * * 60 * * | 0 1 0 0 0 2 0 | 0 0 3 0
..... ..... .ox.. .....&#x & | 0 1 2 | 0 0 0 0 2 1 | * * * * * * 120 * | 0 0 0 0 1 1 1 | 0 0 2 1
..o..3..x.. ..... ..... & | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * 20 | 0 1 0 0 0 0 2 | 0 0 2 1
------------------------------+----------+--------------------+--------------------------+----------------------+-----------
x....3o....3o.... ..... & ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 | 10 * * * * * * | 1 0 1 0
xxo..3oxx.. ..... .....&#xt & ♦ 3 6 3 | 3 6 3 3 6 3 | 1 3 3 0 3 3 0 1 | * 20 * * * * * | 0 0 2 0
..... ox...3oo... .....&#x & ♦ 1 3 0 | 0 3 0 3 0 0 | 0 0 3 1 0 0 0 0 | * * 40 * * * * | 0 1 1 0
..... .x...3.o...3.o... & ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 4 0 0 0 0 | * * * 10 * * * | 0 1 1 0
.xo.. ..... .ox.. .....&#x & ♦ 0 2 2 | 0 0 1 0 4 1 | 0 0 0 0 2 0 2 0 | * * * * 60 * * | 0 0 1 1
..... .xxo.3.oxx. .....&#xt ♦ 0 6 6 | 0 0 0 6 12 6 | 0 0 0 2 0 6 6 0 | * * * * * 20 * | 0 0 2 0
..... ..... .ox..3.oo..&#x & ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 3 1 | * * * * * * 40 | 0 0 1 1
------------------------------+----------+--------------------+--------------------------+----------------------+-----------
x....3o....3o....3o.... & ♦ 5 0 0 | 10 0 0 0 0 0 | 10 0 0 0 0 0 0 0 | 5 0 0 0 0 0 0 | 2 * * *
..... ox...3oo...3oo...&#x & ♦ 1 4 0 | 0 4 0 6 0 0 | 0 0 6 4 0 0 0 0 | 0 0 4 1 0 0 0 | * 10 * *
xxoo.3oxxo.3ooxx. .....&#xt & ♦ 4 16 12 | 6 12 6 18 36 18 | 4 6 12 8 12 18 24 4 | 1 4 4 1 6 4 4 | * * 10 *
.xo.. ..... .ox..3.oo..&#x & ♦ 0 2 3 | 0 0 1 0 6 3 | 0 0 0 0 3 0 6 1 | 0 0 0 0 3 0 2 | * * * 20