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Acronym
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codify (alt.: hexgyi, trihexdip)
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Name
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tetracontaocta-diminished dischiliahectohexaconta-myriaheptachiliadiacosioctaconta-zetton,
hexadacachoron gyro-icositetrachoronism,
tegum sum of 3 pairwise bigyrated hexadecachoron duoprisms,
tri-hexadecachoron-duoprism
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Circumradius
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1
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Lace hyper city
in approx. ASCII-art
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N
|
_E---------_O
O----------E |
| | | |
| | | |
| | | |
| _O-------|-_E
E----------O
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N
/ \\
/ | \ \
/ _ - N_ \
/ _ - | | -_\
N _ _ - N
\ -_| _ + /
\ N /
\ \ | /
\\ /
N
|
_O---------_E
E----------O |
| | | |
| | | |
| | | |
| _E-------|-_O
O----------E
|
N
|
i.e. the vertex positions of an 1/q-ico
where:
N = o3o3o *b3x (hex)
E = x3o3o *b3o (gyro hex)
O = o3o3x *b3o (alt. gyro hex)
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Face vector
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192, 4224, 29184, 86784, 124464, 84672, 23808, 1968
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Confer
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- uniform relative:
-
fy
hocto
hexdip
- related segmentozetta:
-
hexal hesa
- general polytopal classes:
-
scaliform
gyro-icositetrachoronism
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External
links
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This polyzetton originated from a representation of fy within its D4 × D4 subsymmetry by Krieger in 2018.
In fact it is obtained therefrom by eliminating the vertex subset of 2 mutually perpendicular vertex inscribed icoes.
The remainder then happens to be a tegum sum of 3 pairwise bigyrated hexdips,
which, as Klitzing pointed out, obviously will be a scaliform polyzetton.
The tegum sum of E-tethex and gyro-dual O-tethex, as being required in
second and fourth layer of the above lace hyper city, clearly is nothing but a single hesa each.
Thence, in combination those form a hesa alterprism, which thereby is nothing but an inscribed hocto.
Incidence matrix according to Dynkin symbol
xoo3ooo3oxo *b3oox xoo3ooo3oxo *f3oox&#zx → all heights = 0
(tegum sum of 3 pairwise bigyrated hexdips)
o..3o..3o.. *b3o.. o..3o..3o.. *f3o.. & | 192 | 12 32 | 24 288 144 | 16 256 96 288 1152 | 2 64 80 480 480 720 1440 | 16 144 192 216 1152 144 864 | 112 24 240 224 336 36 | 16 12 88
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
x.. ... ... ... ... ... ... ... & | 2 | 1152 * | 4 16 0 | 4 32 8 24 48 | 1 16 16 64 48 48 96 | 8 28 32 48 128 12 72 | 24 12 52 32 40 6 | 4 7 20
oo.3oo.3oo. *b3oo. oo.3oo.3oo. *f3oo.&#x & | 2 | * 3072 | 0 12 9 | 0 12 6 18 90 | 0 6 4 36 42 72 144 | 2 12 18 30 132 18 108 | 12 6 42 30 48 9 | 2 6 18
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
x..3o.. ... ... ... ... ... ... & | 3 | 3 0 | 1536 * * | 2 8 0 0 0 | 1 8 8 12 12 0 0 | 8 12 8 24 24 0 0 | 10 12 24 8 6 0 | 2 6 9
xo. ... ... ... ... ... ... ...&#x & | 3 | 1 2 | * 18432 * | 0 2 1 3 6 | 0 2 1 9 6 9 18 | 1 4 6 9 26 3 18 | 5 3 14 8 11 3 | 1 4 7
ooo3ooo3ooo *b3ooo ooo3ooo3ooo *f3ooo&#x | 3 | 0 3 | * * 9216 ♦ 0 0 0 0 12 | 0 0 0 0 6 12 24 | 0 0 0 6 24 4 24 | 0 2 12 6 12 4 | 0 4 6
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
x..3o..3o.. ... ... ... ... ... & ♦ 4 | 6 0 | 4 0 0 | 768 * * * * | 1 4 4 0 0 0 0 | 8 6 0 12 0 0 0 | 4 12 12 0 0 0 | 1 6 4
xo.3oo. ... ... ... ... ... ...&#x & ♦ 4 | 3 3 | 1 3 0 | * 12288 * * * | 0 1 1 3 3 0 0 | 1 3 3 6 9 0 0 | 4 3 9 4 3 0 | 1 3 5
xo. ... ox. ... ... ... ... ...&#x & ♦ 4 | 2 4 | 0 4 0 | * * 4608 * * | 0 2 0 0 0 6 0 | 1 0 0 6 0 3 6 | 0 3 6 0 2 3 | 0 4 2
xo. ... ... ... ... ... ox. ...&#x & ♦ 4 | 2 4 | 0 4 0 | * * * 13824 * | 0 0 0 4 0 0 4 | 0 2 4 0 8 0 4 | 4 0 4 4 4 1 | 1 2 4
xoo ... ... ... ... ... ... ...&#x & ♦ 4 | 1 5 | 0 2 2 | * * * * 55296 | 0 0 0 0 1 2 4 | 0 0 0 2 6 1 6 | 0 1 5 2 4 2 | 0 3 3
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
x..3o..3o.. *b3o.. ... ... ... ... & ♦ 8 | 24 0 | 32 0 0 | 16 0 0 0 0 | 48 * * * * * * ♦ 8 0 0 0 0 0 0 | 0 12 0 0 0 0 | 0 6 0
xo.3oo.3ox. ... ... ... ... ...&#x & ♦ 8 | 12 12 | 8 24 0 | 2 8 6 0 0 | * 1536 * * * * * | 1 0 0 3 0 0 0 | 0 3 3 0 0 0 | 0 3 1
xo.3oo. ... *b3oo. ... ... ... ...&#x & ♦ 5 | 6 4 | 4 6 0 | 1 4 0 0 0 | * * 3072 * * * * | 1 3 0 3 0 0 0 | 3 3 6 0 0 0 | 1 3 3
xo.3oo. ... ... ... ... ox. ...&#x & ♦ 5 | 4 6 | 1 9 0 | 0 2 0 3 0 | * * * 18432 * * * | 0 1 2 0 2 0 0 | 3 0 2 2 1 0 | 1 1 3
xoo3ooo ... ... ... ... ... ...&#x & ♦ 5 | 3 7 | 1 6 3 | 0 2 0 0 3 | * * * * 18432 * * | 0 0 0 2 4 0 0 | 0 1 4 2 2 0 | 0 2 3
xoo ... oxo ... ... ... ... ...&#x & ♦ 5 | 2 8 | 0 6 4 | 0 0 1 0 4 | * * * * * 27648 * | 0 0 0 1 0 1 2 | 0 1 2 0 1 2 | 0 3 1
xoo ... ... ... ... ... oxo ...&#x & ♦ 5 | 2 8 | 0 6 4 | 0 0 0 1 4 | * * * * * * 55296 | 0 0 0 0 2 0 2 | 0 0 2 1 2 1 | 0 2 2
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
xo.3oo.3ox. *b3oo. ... ... ... ...&#x & ♦ 16 | 48 32 | 64 96 0 | 32 64 24 0 0 | 2 8 16 0 0 0 0 | 192 * * * * * * | 0 3 0 0 0 0 | 0 3 0
xo.3oo. ... *b3oo. ... ... ox. ...&#x & ♦ 6 | 7 8 | 4 16 0 | 1 8 0 6 0 | 0 0 2 4 0 0 0 | * 4608 * * * * * | 2 0 2 0 0 0 | 1 1 2
xo.3oo. ... ... ... oo.3ox. ...&#x & ♦ 6 | 6 9 | 2 18 0 | 0 6 0 9 0 | 0 0 0 6 0 0 0 | * * 6144 * * * * | 2 0 0 1 0 0 | 1 0 2
xoo3ooo3oxo ... ... ... ... ...&#x & ♦ 9 | 12 20 | 8 36 12 | 2 16 6 0 24 | 0 1 2 0 8 6 0 | * * * 4608 * * * | 0 1 2 0 0 0 | 0 2 1
xoo3ooo ... ... ... ... oxo ...&#x & ♦ 6 | 4 11 | 1 13 6 | 0 3 0 3 9 | 0 0 0 1 2 0 3 | * * * * 36864 * * | 0 0 1 1 1 0 | 0 1 2
xoo ... oxo oox ... ... ... ...&#x & ♦ 6 | 3 12 | 0 12 8 | 0 0 3 0 12 | 0 0 0 0 0 6 0 | * * * * * 4608 * | 0 1 0 0 0 2 | 0 3 0
xoo ... oxo ... ... ... ... oox&#x & ♦ 6 | 3 12 | 0 12 8 | 0 0 1 2 12 | 0 0 0 0 0 2 4 | * * * * * * 27648 | 0 0 1 0 1 1 | 0 2 1
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
xo.3oo. ... *b3oo. ... oo.3ox. ...&#x & ♦ 7 | 9 12 | 5 30 0 | 1 16 0 18 0 | 0 0 3 18 0 0 0 | 0 3 4 0 0 0 0 | 3072 * * * * * | 1 0 1
xoo3ooo3oxo *b3oox ... ... ... ...&#x & ♦ 24 | 72 96 | 96 288 96 | 48 192 72 0 288 | 3 24 48 0 96 144 0 | 3 0 0 24 0 24 0 | * 192 * * * * | 0 2 0
xoo3ooo3oxo ... ... ... ... oox&#x & ♦ 10 | 13 28 | 8 56 24 | 2 24 6 12 60 | 0 1 4 8 16 12 24 | 0 2 0 2 8 0 6 | * * 4608 * * * | 0 1 1
xoo3ooo ... ... ... ooo3oxo ...&#x & ♦ 7 | 6 15 | 2 24 9 | 0 8 0 9 18 | 0 0 0 6 6 0 9 | 0 0 1 0 6 0 0 | * * * 6144 * * | 0 0 2
xoo3ooo ... ... ... ... oxo oox&#x & ♦ 7 | 5 16 | 1 22 12 | 0 4 1 6 24 | 0 0 0 2 4 3 12 | 0 0 0 0 4 0 3 | * * * * 9216 * | 0 1 1
xoo ... oxo oox xoo ... oxo oox&#zx ♦ 12 | 12 48 | 0 96 64 | 0 0 24 24 192 | 0 0 0 0 0 96 96 | 0 0 0 0 0 16 48 | * * * * * 576 | 0 2 0
--------------------------------------------+-----+-----------+-----------------+----------------------------+--------------------------------------+-------------------------------------+-----------------------------+------------
xo.3oo. ... *b3oo. ... oo.3ox. *f3oo.&#x & ♦ 8 | 12 16 | 8 48 0 | 2 32 0 36 0 | 0 0 8 48 0 0 0 | 0 12 16 0 0 0 0 | 8 0 0 0 0 0 | 384 * *
xoo3ooo3oxo *b3oox xoo ... oxo oox&#zx & ♦ 48 | 168 384 | 192 1536 768 | 96 768 384 576 3456 | 6 96 192 384 768 1728 2304 | 12 96 0 192 768 288 1152 | 0 8 96 0 192 24 | * 48 *
xoo3ooo3oxo ... ... ooo ... *f3oox&#x & ♦ 11 | 15 36 | 9 84 36 | 2 40 6 36 108 | 0 1 6 36 36 18 72 | 0 6 8 3 48 0 18 | 2 0 3 8 6 0 | * * 1536
o(xo)o(xo)o3o(oo)x(oo)o3o(ox)o(ox)o o(xo)o(ox)o3o(oo)o(oo)o3o(ox)o(xo)o *e3x(oo)x(oo)x&#xt → all heights = 1/sqrt(8) = 0.353553
(hex || pseudo gyro hesa || pseudo octhex || pseudo alt. gyro hesa || hex)
...