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Acronym
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sirhin
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Name
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small rhombihemipenteract,
cantellated demipenteract,
runcic penteract
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Circumradius
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sqrt(21/8) = 1.620185
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Lace city
in approx. ASCII-art
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x3o3o x3x3o o3x3x o3o3x -- x3o3o *b3x (rit)
x3x3o u3o3x x3o3u o3x3x -- x3x3o *b3o (gyro thex)
o3x3x x3o3u u3o3x x3x3o -- o3x3x *b3o (thex)
o3o3x o3x3x x3x3o x3o3o -- o3o3x *b3x (gyro rit)
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o3o3x o3x3x x3x3o x3o3o -- x3o3o *b3x (rit)
o3x3o o3u3o x3x3x o3u3o o3x3x -- x3x3o *b3o (gyro thex)
x3x3o u3o3x x3o3u o3x3x -- o3x3x *b3o (thex)
x3o3x uo3oo3ou- x3o3x -- o3o3x *b3x (gyro rit)
&#zx
\ \ \ \ \
\ \ \ \ +-- o3x3o3o (rap)
\ \ \ +--------- o3x3x3o (deca)
\ \ +---------------- x3o3x3x (prip)
\ +----------------------- uo3oo3ou3xo&#zx
+------------------------------ x3o3x3o (srip)
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Coordinates
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(3/sqrt(8), 3/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8)) & all permutations, all even changes of sign
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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)
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- at oct between rap and srip: arccos(-3/5) = 126.869898°
- at tet between rap and rit: arccos(-1/sqrt(5)) = 116.565051°
- at co between rit and srip: arccos(-1/sqrt(5)) = 116.565051°
- at trip between srip and srip: arccos(-1/5) = 101.536959°
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Face vector
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160, 720, 880, 360, 42
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Confer
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- related segmentotera:
-
ritag thex
thexa
teta tuttip
rapadeca
deca aprip
tutcupa toe
- general polytopal classes:
-
Wythoffian polytera
lace simplices
partial Stott expansions
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External
links
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As abstract polytope sirhin is isomorphic to its (Grünbaumian) isomorph, thereby replacing some prograde by retrograde triangles,
co by 2thah, resp. rit by 2tho+24{4} and srip by pinnip+5 2thah.
Incidence matrix according to Dynkin symbol
x3o3o *b3x3o
. . . . . | 160 | 3 6 | 3 6 6 3 | 1 6 3 2 3 | 2 3 1
-------------+-----+---------+-----------------+----------------+---------
x . . . . | 2 | 240 * | 2 2 0 0 | 1 4 1 0 0 | 2 2 0
. . . x . | 2 | * 480 | 0 1 2 1 | 0 2 1 1 2 | 1 2 1
-------------+-----+---------+-----------------+----------------+---------
x3o . . . | 3 | 3 0 | 160 * * * | 1 2 0 0 0 | 2 1 0
x . . x . | 4 | 2 2 | * 240 * * | 0 2 1 0 0 | 1 2 0
. o . *b3x . | 3 | 0 3 | * * 320 * | 0 1 0 1 1 | 1 1 1
. . . x3o | 3 | 0 3 | * * * 160 | 0 0 1 0 2 | 0 2 1
-------------+-----+---------+-----------------+----------------+---------
x3o3o . . ♦ 4 | 6 0 | 4 0 0 0 | 40 * * * * | 2 0 0
x3o . *b3x . ♦ 12 | 12 12 | 4 6 4 0 | * 80 * * * | 1 1 0
x . . x3o ♦ 6 | 3 6 | 0 3 0 2 | * * 80 * * | 0 2 0
. o3o *b3x . ♦ 4 | 0 6 | 0 0 4 0 | * * * 80 * | 1 0 1
. o . *b3x3o ♦ 6 | 0 12 | 0 0 4 4 | * * * * 80 | 0 1 1
-------------+-----+---------+-----------------+----------------+---------
x3o3o *b3x . ♦ 32 | 48 48 | 32 24 32 0 | 8 8 0 8 0 | 10 * *
x3o . *b3x3o ♦ 30 | 30 60 | 10 30 20 20 | 0 5 10 0 5 | * 16 *
. o3o *b3x3o ♦ 10 | 0 30 | 0 0 20 10 | 0 0 0 5 5 | * * 16
x3o3/2o *b3x3o
. . . . . | 160 | 3 6 | 3 6 6 3 | 1 6 3 2 3 | 2 3 1
---------------+-----+---------+-----------------+----------------+---------
x . . . . | 2 | 240 * | 2 2 0 0 | 1 4 1 0 0 | 2 2 0
. . . x . | 2 | * 480 | 0 1 2 1 | 0 2 1 1 2 | 1 2 1
---------------+-----+---------+-----------------+----------------+---------
x3o . . . | 3 | 3 0 | 160 * * * | 1 2 0 0 0 | 2 1 0
x . . x . | 4 | 2 2 | * 240 * * | 0 2 1 0 0 | 1 2 0
. o . *b3x . | 3 | 0 3 | * * 320 * | 0 1 0 1 1 | 1 1 1
. . . x3o | 3 | 0 3 | * * * 160 | 0 0 1 0 2 | 0 2 1
---------------+-----+---------+-----------------+----------------+---------
x3o3/2o . . ♦ 4 | 6 0 | 4 0 0 0 | 40 * * * * | 2 0 0
x3o . *b3x . ♦ 12 | 12 12 | 4 6 4 0 | * 80 * * * | 1 1 0
x . . x3o ♦ 6 | 3 6 | 0 3 0 2 | * * 80 * * | 0 2 0
. o3/2o *b3x . ♦ 4 | 0 6 | 0 0 4 0 | * * * 80 * | 1 0 1
. o . *b3x3o ♦ 6 | 0 12 | 0 0 4 4 | * * * * 80 | 0 1 1
---------------+-----+---------+-----------------+----------------+---------
x3o3/2o *b3x . ♦ 32 | 48 48 | 32 24 32 0 | 8 8 0 8 0 | 10 * *
x3o . *b3x3o ♦ 30 | 30 60 | 10 30 20 20 | 0 5 10 0 5 | * 16 *
. o3/2o *b3x3o ♦ 10 | 0 30 | 0 0 20 10 | 0 0 0 5 5 | * * 16
x3o3o *b3x3/2o
. . . . . | 160 | 3 6 | 3 6 6 3 | 1 6 3 2 3 | 2 3 1
---------------+-----+---------+-----------------+----------------+---------
x . . . . | 2 | 240 * | 2 2 0 0 | 1 4 1 0 0 | 2 2 0
. . . x . | 2 | * 480 | 0 1 2 1 | 0 2 1 1 2 | 1 2 1
---------------+-----+---------+-----------------+----------------+---------
x3o . . . | 3 | 3 0 | 160 * * * | 1 2 0 0 0 | 2 1 0
x . . x . | 4 | 2 2 | * 240 * * | 0 2 1 0 0 | 1 2 0
. o . *b3x . | 3 | 0 3 | * * 320 * | 0 1 0 1 1 | 1 1 1
. . . x3/2o | 3 | 0 3 | * * * 160 | 0 0 1 0 2 | 0 2 1
---------------+-----+---------+-----------------+----------------+---------
x3o3o . . ♦ 4 | 6 0 | 4 0 0 0 | 40 * * * * | 2 0 0
x3o . *b3x . ♦ 12 | 12 12 | 4 6 4 0 | * 80 * * * | 1 1 0
x . . x3/2o ♦ 6 | 3 6 | 0 3 0 2 | * * 80 * * | 0 2 0
. o3o *b3x . ♦ 4 | 0 6 | 0 0 4 0 | * * * 80 * | 1 0 1
. o . *b3x3/2o ♦ 6 | 0 12 | 0 0 4 4 | * * * * 80 | 0 1 1
---------------+-----+---------+-----------------+----------------+---------
x3o3o *b3x . ♦ 32 | 48 48 | 32 24 32 0 | 8 8 0 8 0 | 10 * *
x3o . *b3x3/2o ♦ 30 | 30 60 | 10 30 20 20 | 0 5 10 0 5 | * 16 *
. o3o *b3x3/2o ♦ 10 | 0 30 | 0 0 20 10 | 0 0 0 5 5 | * * 16
o3x3o3o4s
demi( . . . . . ) | 160 | 6 3 | 3 6 6 3 | 3 2 3 1 6 | 1 2 3
------------------+-----+---------+-----------------+----------------+---------
demi( . x . . . ) | 2 | 480 * | 1 2 1 0 | 2 1 1 0 2 | 1 1 2
. . . o4s | 2 | * 240 | 0 0 2 2 | 0 0 1 1 4 | 0 2 2
------------------+-----+---------+-----------------+----------------+---------
demi( o3x . . . ) | 3 | 3 0 | 160 * * * | 2 0 1 0 0 | 1 0 2
demi( . x3o . . ) | 3 | 3 0 | * 320 * * | 1 1 0 0 1 | 1 1 1
. x 2 o4s | 4 | 2 2 | * * 240 * | 0 0 1 0 2 | 0 1 2
sefa( . . o3o4s ) | 3 | 0 3 | * * * 160 | 0 0 0 1 2 | 0 2 1
------------------+-----+---------+-----------------+----------------+---------
demi( o3x3o . . ) ♦ 6 | 12 0 | 4 4 0 0 | 80 * * * * | 1 0 1
demi( . x3o3o . ) ♦ 4 | 6 0 | 0 4 0 0 | * 80 * * * | 1 1 0
o3x 2 o4s ♦ 6 | 6 3 | 2 0 3 0 | * * 80 * * | 0 0 2
. . o3o4s ♦ 4 | 0 6 | 0 0 0 4 | * * * 40 * | 0 2 0
sefa( . x3o3o4s ) ♦ 12 | 12 12 | 0 4 6 4 | * * * * 80 | 0 1 1
------------------+-----+---------+-----------------+----------------+---------
demi( o3x3o3o . ) ♦ 10 | 30 0 | 10 20 0 0 | 5 5 0 0 0 | 16 * *
. x3o3o4s ♦ 32 | 48 48 | 0 32 24 32 | 0 8 0 8 8 | * 10 *
sefa( o3x3o3o4s ) ♦ 30 | 60 30 | 20 20 30 10 | 5 0 10 0 5 | * * 16
starting figure: o3x3o3o4x
xxoo3oxxo3ooxx *b3xoox&#xt → all heights = 1/sqrt(2) = 0.707107
(rit || gyro thex || thex || gyro rit)
o...3o...3o... *b3o... & | 64 * | 3 3 3 0 0 0 | 3 3 3 3 3 3 0 0 0 0 | 1 3 1 3 3 1 3 0 0 0 | 1 1 3 1
.o..3.o..3.o.. *b3.o.. & | * 96 | 0 0 2 1 4 2 | 0 0 0 2 1 1 2 2 3 4 | 0 0 0 6 1 2 2 1 1 2 | 0 2 3 1
-----------------------------+-------+---------------------+--------------------------------+-------------------------------+----------
x... .... .... .... & | 2 0 | 96 * * * * * | 2 1 0 1 0 0 0 0 0 0 | 1 2 0 2 1 0 0 0 0 0 | 1 1 2 0
.... .... .... x... & | 2 0 | * 96 * * * * | 0 1 2 0 0 1 0 0 0 0 | 0 2 1 0 1 0 2 0 0 0 | 1 0 2 1
oo..3oo..3oo.. *b3oo..&#x & | 1 1 | * * 192 * * * | 0 0 0 1 2 1 0 0 0 0 | 0 0 0 2 1 1 2 0 0 0 | 0 1 2 1
.x.. .... .... .... & | 0 2 | * * * 48 * * | 0 0 0 2 0 0 0 0 2 0 | 0 0 0 4 1 0 0 0 1 0 | 0 2 2 0
.... .x.. .... .... & | 0 2 | * * * * 192 * | 0 0 0 0 1 0 1 1 0 1 | 0 0 0 2 0 1 1 1 0 1 | 0 1 2 1
.oo.3.oo.3.oo. *b3.oo.&#x | 0 2 | * * * * * 96 | 0 0 0 0 0 0 0 0 2 2 | 0 0 0 4 0 0 0 0 1 1 | 0 2 2 0
-----------------------------+-------+---------------------+--------------------------------+-------------------------------+----------
x...3o... .... .... & | 3 0 | 3 0 0 0 0 0 | 64 * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0
x... .... .... x... & | 4 0 | 2 2 0 0 0 0 | * 48 * * * * * * * * | 0 2 0 0 1 0 0 0 0 0 | 1 0 2 0
.... o... .... *b3x... & | 3 0 | 0 3 0 0 0 0 | * * 64 * * * * * * * | 0 1 1 0 0 0 1 0 0 0 | 1 0 1 1
xx.. .... .... ....&#x & | 2 2 | 1 0 2 1 0 0 | * * * 96 * * * * * * | 0 0 0 2 1 0 0 0 0 0 | 0 1 2 0
.... ox.. .... ....&#x & | 1 2 | 0 0 2 0 1 0 | * * * * 192 * * * * * | 0 0 0 1 0 1 1 0 0 0 | 0 1 1 1
.... .... .... xo..&#x & | 2 1 | 0 1 2 0 0 0 | * * * * * 96 * * * * | 0 0 0 0 1 0 2 0 0 0 | 0 0 2 1
.... .x..3.o.. .... & | 0 3 | 0 0 0 0 3 0 | * * * * * * 64 * * * | 0 0 0 1 0 1 0 1 0 0 | 0 1 1 1
.... .x.. .... *b3.o.. & | 0 3 | 0 0 0 0 3 0 | * * * * * * * 64 * * | 0 0 0 0 0 0 1 1 0 1 | 0 0 2 1
.xo. .... .... ....&#x & | 0 3 | 0 0 0 1 0 2 | * * * * * * * * 96 * | 0 0 0 2 0 0 0 0 1 0 | 0 2 1 0
.... .xx. .... ....&#x | 0 4 | 0 0 0 0 2 2 | * * * * * * * * * 96 | 0 0 0 2 0 0 0 0 0 1 | 0 1 2 0
-----------------------------+-------+---------------------+--------------------------------+-------------------------------+----------
x...3o...3o... .... & ♦ 4 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 | 16 * * * * * * * * * | 1 1 0 0
x...3o... .... *b3x... & ♦ 12 0 | 12 12 0 0 0 0 | 4 6 4 0 0 0 0 0 0 0 | * 16 * * * * * * * * | 1 0 1 0
.... o...3o... *b3x... & ♦ 4 0 | 0 6 0 0 0 0 | 0 0 4 0 0 0 0 0 0 0 | * * 16 * * * * * * * | 1 0 0 1
xxo.3oxx. .... ....&#xt & ♦ 3 9 | 3 0 6 3 6 6 | 1 0 0 3 3 0 1 0 3 3 | * * * 64 * * * * * * | 0 1 1 0
xx.. .... .... xo..&#x & ♦ 4 2 | 2 2 4 1 0 0 | 0 1 0 2 0 2 0 0 0 0 | * * * * 48 * * * * * | 0 0 2 0
.... ox..3oo.. ....&#x & ♦ 1 3 | 0 0 3 0 3 0 | 0 0 0 0 3 0 1 0 0 0 | * * * * * 64 * * * * | 0 1 0 1
.... ox.. .... *b3xo..&#x & ♦ 3 3 | 0 3 6 0 3 0 | 0 0 1 0 3 3 0 1 0 0 | * * * * * * 64 * * * | 0 0 1 1
.... .x..3.o.. *b3.o.. & ♦ 0 6 | 0 0 0 0 12 0 | 0 0 0 0 0 0 4 4 0 0 | * * * * * * * 16 * * | 0 0 1 1
.xo. .... .ox. ....&#x ♦ 0 4 | 0 0 0 2 0 4 | 0 0 0 0 0 0 0 0 4 0 | * * * * * * * * 24 * | 0 2 0 0
.... .xx. .... *b3.oo.&#x ♦ 0 6 | 0 0 0 0 6 3 | 0 0 0 0 0 0 0 2 0 3 | * * * * * * * * * 32 | 0 0 2 0
-----------------------------+-------+---------------------+--------------------------------+-------------------------------+----------
x...3o...3o... *b3x... & ♦ 32 0 | 48 48 0 0 0 0 | 32 24 32 0 0 0 0 0 0 0 | 8 8 8 0 0 0 0 0 0 0 | 2 * * *
xxoo3oxxo3ooxx ....&#xt ♦ 8 24 | 12 0 24 12 24 24 | 8 0 0 12 24 0 8 0 24 12 | 2 0 0 8 0 8 0 0 6 0 | * 8 * *
xxo.3oxx. .... *b3xoo.&#xt & ♦ 12 18 | 12 12 24 6 24 12 | 4 6 4 12 12 12 4 8 6 12 | 0 1 0 4 6 0 4 1 0 4 | * * 16 *
.... ox..3oo.. *b3xo..&#x & ♦ 4 6 | 0 6 12 0 12 0 | 0 0 4 0 12 6 4 4 0 0 | 0 0 1 0 0 4 4 1 0 0 | * * * 16