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In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space. T ¯ 9 {\displaystyle {\bar {T}}_{9}} , also (E10)
E9_honeycomb
Quasiregular space-filling tesselation
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
8-cubic honeycomb 8-demicubic honeycomb 521 honeycomb, 251 honeycomb, 152 honeycomb 9-polytope 9-simplex 9-demicube 9-cube 9-orthoplex E9 honeycomb 10-polytope
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
8-cubic honeycomb 8-demicubic honeycomb 521 honeycomb, 251 honeycomb, 152 honeycomb 9-polytope 9-cube 9-demicube 9-orthoplex 9-simplex E9 honeycomb 10-polytope
List_of_mathematical_shapes
Tiling of euclidean or hyperbolic space of three or more dimensions
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of
Honeycomb_(geometry)
Only regular space-filling tessellation of the cube
The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells
Cubic_honeycomb
the cyclotruncated 5-simplex honeycomb or cyclotruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed of 5-simplex
Cyclotruncated 5-simplex honeycomb
Cyclotruncated_5-simplex_honeycomb
In geometry an omnitruncated simplicial honeycomb or omnitruncated n-simplex honeycomb is an n-dimensional uniform tessellation, based on the symmetry
Omnitruncated simplicial honeycomb
Omnitruncated_simplicial_honeycomb
In geometry, the 8-cubic honeycomb or octeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 8-space. It is analogous
8-cubic_honeycomb
Geometric figure
geometry, the 4-simplex honeycomb, 5-cell honeycomb or pentachoric-dispentachoric honeycomb is a space-filling tessellation honeycomb. It is composed of 5-cells
5-cell_honeycomb
four-dimensional Euclidean geometry, the 16-cell honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {3
16-cell_honeycomb
Regular tiling of a two-dimensional space
≈ 0.907 {\textstyle {\frac {\pi }{2{\sqrt {3}}}}\approx 0.907} . The honeycomb theorem states that hexagonal tiling is the best way to divide a surface
Hexagonal_tiling
Spatial tiling of convex uniform polyhedra
cells. Twenty-eight such honeycombs are known: the familiar cubic honeycomb and 7 truncations thereof; the alternated cubic honeycomb and 4 truncations thereof;
Convex_uniform_honeycomb
honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated
Cantitruncated 24-cell honeycomb
Cantitruncated_24-cell_honeycomb
Concept in euclidean geometry
euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {4
Tesseractic_honeycomb
Family of regular honeycombs in geometry
In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensional spaces with the Schläfli symbols {4,3...3,4} and
Hypercubic_honeycomb
honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated
Runcinated_24-cell_honeycomb
Prism with a 3-sided base
prismatic honeycomb, triangular-hexagonal prismatic honeycomb, truncated hexagonal prismatic honeycomb, rhombitriangular-hexagonal prismatic honeycomb, snub
Triangular_prism
Tiling of n-dimensional space
In geometry, the simplicial honeycomb (or n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the A ~ n {\displaystyle {\tilde
Simplicial_honeycomb
Type of uniform space-filling tessellation
The 5-demicube honeycomb (or demipenteractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 5-space. It is constructed
5-demicubic_honeycomb
and uniform honeycombs in 6-space: 6-cubic honeycomb 6-demicubic honeycomb 6-simplex honeycomb Truncated 6-simplex honeycomb 222 honeycomb * Weisstein
Omnitruncated 6-simplex honeycomb
Omnitruncated_6-simplex_honeycomb
honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated
Bitruncated_24-cell_honeycomb
In geometry, the 152 honeycomb is a uniform tessellation of 8-dimensional Euclidean space. It contains 142 and 151 facets, in a birectified 8-simplex
1_52_honeycomb
The 6-cubic honeycomb or hexeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 6-space. It is analogous to the
6-cubic_honeycomb
Tiling of five-dimensional space
In geometry, the 5-cubic honeycomb or penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space. Four 5-cubes
5-cubic_honeycomb
The 7-cubic honeycomb or hepteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 7-space. It is analogous to
7-cubic_honeycomb
Family of regular tessellations in geometry
alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an alternation
Alternated hypercubic honeycomb
Alternated_hypercubic_honeycomb
Geometric figure
cubic honeycomb Regular and uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell
Omnitruncated tesseractic honeycomb
Omnitruncated_tesseractic_honeycomb
7-homeycomb
seven-dimensional Euclidean geometry, the 7-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 7-simplex, rectified
7-simplex_honeycomb
The 8-demicubic honeycomb, or demiocteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 8-space. It is constructed as
8-demicubic_honeycomb
Eight-dimensional geometric tessellation
In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation. It is composed of 241 polytope and 8-simplex facets arranged in
2_51_honeycomb
the birectified 16-cell honeycomb (or runcic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. There
Birectified_16-cell_honeycomb
Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean
24-cell_honeycomb
Geometric object
tessellation (space-filling honeycomb) in 8-space, called the E8 lattice. (A final form was not discovered by Gosset and is called the E9 lattice: 621. It is
Uniform_k_21_polytope
In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space. It can be represented by the Schläfli symbol {3,3,32
2_22_honeycomb
Tessellation in Euclidean geometry
uniform honeycombs in 7-space: 7-cube honeycomb 7-demicube honeycomb 7-simplex honeycomb Truncated 7-simplex honeycomb Omnitruncated 7-simplex honeycomb Coxeter
Quarter_7-cubic_honeycomb
quarter cubic honeycomb, quarter cubic cellulation or bitruncated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean
Quarter_cubic_honeycomb
Regular tiling of the plane
tiling) List of uniform tilings Simplectic honeycomb Tilings of regular polygons Triangular tiling honeycomb Tilings and patterns, p.102-107 "The Lattice
Triangular_tiling
six-dimensional Euclidean geometry, the 6-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 6-simplex, rectified
6-simplex_honeycomb
five-dimensional Euclidean geometry, the 5-simplex honeycomb or hexateric honeycomb is a space-filling tessellation (or honeycomb or pentacomb). Each vertex is shared
5-simplex_honeycomb
Type of uniform tessellation
In geometry, the 521 honeycomb is a uniform tessellation of 8-dimensional Euclidean space. The symbol 521 is from Coxeter, named for the length of the
5_21_honeycomb
Regular tiling of the Euclidean plane
ISBN 978-0-8218-4727-5. Nelson, Roice; Segerman, Henry (2017). "Visualizing hyperbolic honeycombs". Journal of Mathematics and the Arts. 11 (1): 4–39. arXiv:1511.02851
Square_tiling
honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated
Runcinated_16-cell_honeycomb
honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated
Rectified_24-cell_honeycomb
In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol {3,3,3,33,1} and is composed of 321 and 7-simplex facets
3_31_honeycomb
Five dimensional space-filling tessellation
the omnitruncated 5-simplex honeycomb or omnitruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of
Omnitruncated 5-simplex honeycomb
Omnitruncated_5-simplex_honeycomb
honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a bitruncation of a tesseractic honeycomb
Bitruncated tesseractic honeycomb
Bitruncated_tesseractic_honeycomb
geometry, the snub 24-cell honeycomb, or snub icositetrachoric honeycomb is a uniform space-filling tessellation (or honeycomb) by snub 24-cells, 16-cells
Snub_24-cell_honeycomb
eighth-dimensional Euclidean geometry, the 8-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 8-simplex, rectified
8-simplex_honeycomb
3-space honeycomb or 4-polytope = 0 {\displaystyle =0} : Euclidean 3-space honeycomb < 0 {\displaystyle <0} : Hyperbolic 3-space honeycomb These constraints
List_of_regular_polytopes
uniform honeycombs in 5-space: 6-cube honeycomb 6-demicube honeycomb 6-simplex honeycomb Truncated 6-simplex honeycomb Omnitruncated 6-simplex honeycomb Coxeter
Quarter_6-cubic_honeycomb
uniform honeycombs in 8-space: 8-cubic honeycomb 8-demicubic honeycomb 8-simplex honeycomb Truncated 8-simplex honeycomb 521 honeycomb 251 honeycomb 152 honeycomb
Omnitruncated 8-simplex honeycomb
Omnitruncated_8-simplex_honeycomb
honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated
Cantellated_24-cell_honeycomb
cyclotruncated simplicial honeycomb (or cyclotruncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the
Cyclotruncated simplicial honeycomb
Cyclotruncated_simplicial_honeycomb
The 6-demicubic honeycomb or demihexeractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 6-space. It is constructed as
6-demicubic_honeycomb
24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated
Steric_tesseractic_honeycomb
Type of geometric object
8-cubic honeycomb, representing as q{4,36,4}, or qδ9. E ~ 8 {\displaystyle {\tilde {E}}_{8}} 511 forms 521 honeycomb: 251 honeycomb: 152 honeycomb: There
Uniform_9-polytope
In 7-dimensional geometry, 133 is a uniform honeycomb, also given by Schläfli symbol {3,33,3}, and is composed of 132 facets. It is also named
1_33_honeycomb
uniform honeycombs in 8-space: 8-cube honeycomb 8-demicube honeycomb 8-simplex honeycomb Truncated 8-simplex honeycomb Omnitruncated 8-simplex honeycomb Coxeter
Quarter_8-cubic_honeycomb
uniform honeycombs in 4-space: Tesseractic honeycomb Demitesseractic honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell
Truncated tesseractic honeycomb
Truncated_tesseractic_honeycomb
uniform honeycombs in 5-space: 5-cube honeycomb 5-demicube honeycomb 5-simplex honeycomb Truncated 5-simplex honeycomb Omnitruncated 5-simplex honeycomb Coxeter
Quarter_5-cubic_honeycomb
honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated
Truncated_24-cell_honeycomb
Uniform 7-Honeycomb
The 7-demicubic honeycomb, or demihepteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 7-space. It is constructed
7-demicubic_honeycomb
and uniform honeycombs in 7-space: 7-cubic honeycomb 7-demicubic honeycomb 7-simplex honeycomb Truncated 7-simplex honeycomb 331 honeycomb Weisstein, Eric
Omnitruncated 7-simplex honeycomb
Omnitruncated_7-simplex_honeycomb
honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated
Stericated_24-cell_honeycomb
Five-dimensional geometric shape
Ph.D. dissertation under Coxeter, The Theory of Uniform Polytopes and Honeycombs, University of Toronto Non-convex uniform polytopes: 1966: Johnson describes
Uniform_5-polytope
Tessalating shape in four dimensional space
Euclidean geometry, the rectified tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by
Rectified tesseractic honeycomb
Rectified_tesseractic_honeycomb
uniform honeycombs in 4-space: Tesseractic honeycomb 16-cell honeycomb 24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell
Bitruncated_16-cell_honeycomb
24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated
Stericantic tesseractic honeycomb
Stericantic_tesseractic_honeycomb
Uniform space-filling tessellation in Euclidean 4-space
24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb Kaleidoscopes:
Cantitruncated tesseractic honeycomb
Cantitruncated_tesseractic_honeycomb
24-cell honeycomb Rectified 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated
Steriruncic tesseractic honeycomb
Steriruncic_tesseractic_honeycomb
geometry, the truncated 16-cell honeycomb (or cantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It
Truncated_16-cell_honeycomb
Four-dimensional analogue of the tetrahedron
3} and 120-cell {5,3,3} of Euclidean 4-space, and the hexagonal tiling honeycomb {6,3,3} of hyperbolic space. It is one of three {3,3,p} regular 4-polytopes
5-cell
24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb Kaleidoscopes:
Runcitruncated tesseractic honeycomb
Runcitruncated_tesseractic_honeycomb
1968 musical fantasy film by Ken Hughes
(24 May 1967). "Song Writing Team Eschews Gimmicks". Los Angeles Times. p. e9. Jane's, Airship Development, p. 93 Ventry, Lord; Koleśnik, Eugeène M. (1976)
Chitty_Chitty_Bang_Bang
Uniform 6-dimensional polytope
Truncated 5-simplex honeycomb Omnitruncated 5-simplex honeycomb C ~ 5 {\displaystyle {\tilde {C}}_{5}} There are 35 uniform honeycombs, including: Regular
Uniform_6-polytope
quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb. It is given a
Quarter_hypercubic_honeycomb
24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell honeycomb Truncated 5-cell honeycomb Omnitruncated 5-cell honeycomb Kaleidoscopes:
Cantellated tesseractic honeycomb
Cantellated_tesseractic_honeycomb
uniform honeycombs in 4-space: Tesseractic honeycomb Demitesseractic honeycomb 24-cell honeycomb Truncated 24-cell honeycomb Snub 24-cell honeycomb 5-cell
Runcinated tesseractic honeycomb
Runcinated_tesseractic_honeycomb
Vertex-transitive tiling of the plane by regular polygons
Manuscript (1991) N. W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph. D. Dissertation, University of Toronto, 1966 Grünbaum, Branko; Shephard
Uniform_tiling
Battery electric mid-size hatchback
front fascia, the lower section of the front fascia is matched with a honeycomb-shaped grille, the rear taillight bar adopts a wave shape design echoes
BYD_Seal_06_GT
Uniform polytope
2160 demihepteract facets) 152 honeycomb, tessellates Euclidean 8-space (∞ 142 and ∞ demiocteract facets) 162 honeycomb, tessellates hyperbolic 9-space
Uniform_1_k2_polytope
Uniform polytope
Springer, Berlin, 1940 N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966 H.S.M. Coxeter: Regular
Uniform_2_k1_polytope
Region of deformed terrain on Venus
hypothesis for Venusian tectonics". Journal of Geophysical Research. 98 (E9): 17061–17068. Bibcode:1993JGR....9817061T. doi:10.1029/93je01775. Hansen
Tessera_(Venus)
Tablet computer
getting a Honeycomb upgrade in Q2", however an HTC representative subsequently stated "I can confirm that we are working to bring a Honeycomb update to
HTC_Flyer
Convex regular 5-polytope in geometry
Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Klitzing, Richard. "5D uniform polytopes (polytera) with
5-orthoplex
Full phone specifications". GSMArena. "HTC One E9 - Full phone specifications". GSMArena. "HTC One E9+ - Full phone specifications". GSMArena. "HTC One
List_of_Android_smartphones
Uniform 6-polytope
0221) can tessellate 6-dimensional space as the Voronoi cell of the E6* honeycomb lattice (dual of E6 lattice). Birectified 221 polytope Rectified pentacontatetrapeton
1_22_polytope
Benign neoplasm that may arise from the fibroblasts of the periodontal ligaments
the degree of calcification, including a ground-glass or multilocular honeycomb appearance. PsJOF typically affects a slightly older age group than TrJOF
Central_ossifying_fibroma
2010 Android smartphone by HTC
Harman Kardon Edition One (M8) Eye One Mini 2 / One Remix 2015 One A9 One E9 One E9+ One E9s One M8s One M9 / One M9 Prime Camera Edition One M9+ / One M9+
Nexus_One
Uniform polytope
and honeycombs, expressed by Coxeter as 13k series. The next figure is the Euclidean honeycomb 133 and the final is a noncompact hyperbolic honeycomb, 134
1_32_polytope
2014 Android tablet computer by Google and HTC
Harman Kardon Edition One (M8) Eye One Mini 2 / One Remix 2015 One A9 One E9 One E9+ One E9s One M8s One M9 / One M9 Prime Camera Edition One M9+ / One M9+
Nexus_9
Uniform Polytope
Hyperbolic n 3 4 5 6 7 8 9 10 Coxeter group E3=A2A1 E4=A4 E5=D5 E6 E7 E8 E9 = E ~ 8 {\displaystyle {\tilde {E}}_{8}} = E8+ E10 = T ¯ 8 {\displaystyle
2_31_polytope
Uniform 8 dimensional polytope
Hyperbolic n 3 4 5 6 7 8 9 10 Coxeter group E3=A2A1 E4=A4 E5=D5 E6 E7 E8 E9 = E ~ 8 {\displaystyle {\tilde {E}}_{8}} = E8+ E10 = T ¯ 8 {\displaystyle
1_42_polytope
Uniform polytope in 8 dimensional geometry
Hyperbolic n 3 4 5 6 7 8 9 10 Coxeter group E3=A2A1 E4=A4 E5=D5 E6 E7 E8 E9 = E ~ 8 {\displaystyle {\tilde {E}}_{8}} = E8+ E10 = T ¯ 8 {\displaystyle
2_41_polytope
Uniform polychoron
Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The
Rectified_5-cell
Uniform 6-polytope
221. This polytope can tessellate Euclidean 6-space, forming the 222 honeycomb with this Coxeter-Dynkin diagram: . The regular complex polygon 3{3}3{3}3
2_21_polytope
Tablet computer made by HTC
September 2011 Introductory price $849.99 Operating system Android 3.1 (Honeycomb) with HTC Sense UI CPU 1.5 GHz Qualcomm Snapdragon Memory 1 GB DDR2 RAM
HTC_Jetstream
Uniform 7-dimensional polytope
and orthoplexes. It is in a dimensional series of uniform polytopes and honeycombs, expressed by Coxeter as 3k1 series. (A degenerate 4-dimensional case
3_21_polytope
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