The vectors of Icosians ring
icosians.pdf | |
File Size: | 24 kb |
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icosians2.pdf | |
File Size: | 145 kb |
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The 9-dimensional lattice which has 1728 vectors norm 6.
_a3_^3_lattice.pdf | |
File Size: | 88 kb |
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The 12 -dimensional lattices with Icosahedron.
8238238.pdf | |
File Size: | 203 kb |
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12dim_lattices.pdf | |
File Size: | 300 kb |
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12-dimensional lattice
kissingnumber_64.pdf | |
File Size: | 272 kb |
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d12_lattice.pdf | |
File Size: | 273 kb |
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d12_lattice_02.pdf | |
File Size: | 222 kb |
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D6-Lattice
d6lattice.pdf | |
File Size: | 59 kb |
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F4 lattice
f4_geometry.pdf | |
File Size: | 382 kb |
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Group Order 14400
group_order_14400.pdf | |
File Size: | 41 kb |
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Symmetry Group S6
s6.pdf | |
File Size: | 760 kb |
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s6_10.pdf | |
File Size: | 404 kb |
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2^5 * S6
2^5_s6.pdf | |
File Size: | 139 kb |
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G2 function
g2_.pdf | |
File Size: | 843 kb |
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length-12 code, order 384
code_384.pdf | |
File Size: | 807 kb |
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Ternary Golay code
ternary_golay_code.pdf | |
File Size: | 82 kb |
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The code length 11 and its lattice
code_11.pdf | |
File Size: | 410 kb |
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On the Aut of lattices
対称性の数え上げ.pdf | |
File Size: | 162 kb |
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Rhombic triacontahedron
These coordinates are generated by the following vectors
where A is the action of A3.
The Polyhedron in D5
This polyhedron is the subspace of the lattice D5 generated by the following matrix
and the subspace is generated by
using the orthogonal transformation
the generator matrix can be transformed to
only taking the type of the vectors in the subspace
we obtain the following 18 vectors in the subspace
Connect the points in the relationship whose distance is the root 2 by a line, and transforming by P, we obtain the following figure with 18 vectors in 3 dimensions.
and it has the following Polyhedron with 12 vectors.
The two-dimensional projection of the 18 vectors is as follows
The list of transformations by orthogonal transformation is given below.
By computing the norms, we find that the coordinates of this polyhedron with 12 vertices are actually
The projection of this into two dimensions is as follows.
with coordinates
The generating matrix of the subspace of a 12-dimensional vector space consisting of the direct sum of the coordinates of an arbitrary triangle is
The generating matrix of the subspace of a 12-dimensional vector space consisting of the direct sum of the coordinates of an arbitrary square is
The lattice in 6th dimensions.
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