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A semiregular space is a topological space whose regular open sets (sets that equal the interiors of their closures) form a base for the topology. Every
Semiregular_space
Topological space that is homeomorphic to a metric space
(but not Hausdorff). It is also a T1 locally regular space but not a semiregular space. The long line is locally metrizable but not metrizable; in a sense
Metrizable_space
Variously-defined concept in geometry
In geometry, the term semiregular polyhedron (or semiregular polytope) is used variously by different authors. In its original definition, it is a polyhedron
Semiregular_polyhedron
Isogonal polytope with regular facets
as The Semiregular Polytopes of the Hyperspaces which included a wider definition. In three-dimensional space and below, the terms semiregular polytope
Semiregular_polytope
Geometric object
example the 5-ic semiregular figure. The sequence as identified by Gosset ends as an infinite tessellation (space-filling honeycomb) in 8-space, called the
Uniform_k_21_polytope
Geometric space with five dimensions
five-dimensional (5D) space is a mathematical or physical space that has five independent dimensions. In physics and geometry, such a space extends the familiar
Five-dimensional_space
Example of topological space
regular open sets, it is an example of a semiregular space that is not regular. In terms of compactness, the space R2 ⊔ {0*}, along with the double origin
Double_origin_topology
Basic subset of a topological space
{\displaystyle X} . A topological space for which there exists a base consisting of regular open sets is called a semiregular space. A subset of X {\displaystyle
Open_set
List of concrete topologies and topological spaces
Hausdorff (but not Hausdorff). It is also a T1 locally regular space but not a semiregular space. Prüfer manifold − A Hausdorff 2-dimensional real analytic
List_of_topologies
U=\operatorname {Int} (X\setminus U).} Regular space – Property of topological space Semiregular space Separation axiom – Axioms in topology defining
Regular_open_set
Property of topological space
the regular space X. This property is actually weaker than regularity; a topological space whose regular open sets form a base is semiregular. Munkres,
Regular_space
Subdivision of the plane into polygons that are all regular
eight additional tilings possible, known as Archimedean, uniform or semiregular tilings. Note that there are two mirror image (enantiomorphic or chiral)
Euclidean tilings by convex regular polygons
Euclidean_tilings_by_convex_regular_polygons
Prism with a 3-sided base
triangular prism is a right prism. A right triangular prism may be both semiregular and uniform. The triangular prism can be used as the core of constructing
Triangular_prism
Isogonal polyhedron with regular faces
and 11 semiregular—the non-convex star polyhedra as in 4 Kepler–Poinsot polyhedra and 53 uniform star polyhedra—14 quasiregular and 39 semiregular. There
Uniform_polyhedron
Polytope in 8-dimensional geometry
In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group. It was discovered by Thorold
4_21_polytope
Four-dimensional analogue of the cube
Mathematical Association of America. p. 219. Elte, E. L. (2005). The Semiregular Polytopes of the Hyperspaces. Groningen: University of Groningen. ISBN 1-4181-7968-X
Tesseract
Covering by shapes without overlaps or gaps
regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner
Tessellation
Polytope constructed from alternation of a hypercube
the regular and semiregular figures in n-dimensions above three. He called it a 5-ic semi-regular. It also exists within the semiregular k21 polytope family
Demihypercube
Semiregular tiling of the Euclidean plane
geometry, the snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are four triangles and one hexagon
Snub_trihexagonal_tiling
Uniform tiling of the Euclidean plane
In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane. There are one square, one hexagon, and one
Truncated_trihexagonal_tiling
Red supergiant star in the constellation Orion
the second brightest in its constellation. It is a distinctly reddish, semiregular variable star whose apparent magnitude, varying between +0.0 and +1.6
Betelgeuse
Semiregular tiling of the Euclidean plane
In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one triangle, two squares, and one hexagon on each
Rhombitrihexagonal_tiling
Topics referred to by the same term
2nd and 3rd Reidemeister moves only Regular space (or T 3 {\displaystyle T_{3}} ) space, a topological space in which a point and a closed set can be separated
Regular
and semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight semiregular tilings in the plane. The semiregular tilings
List of Euclidean uniform tilings
List_of_Euclidean_uniform_tilings
5-dimensional geometric object
Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900 A. Boole Stott (1910). "Geometrical deduction of semiregular from regular
5-polytope
Uniform polychoron
2-simple 2-simplicial polytopes have been constructed. It is one of three semiregular 4-polytopes made of two or more cells which are Platonic solids, discovered
Rectified_5-cell
English lawyer and mathematician (1869–1962)
mathematician. In mathematics, he is noted for discovering and classifying the semiregular polytopes in dimensions four and higher, and for his generalization of
Thorold_Gosset
Convex polytope, the n-dimensional analogue of a square and a cube
2006.10.002. Elte, E. L. (1912). "IV, Five dimensional semiregular polytope". The Semiregular Polytopes of the Hyperspaces. Netherlands: University of
Hypercube
Natural number
important is T ~ 9 {\displaystyle {\tilde {T}}_{9}} : it contains the final semiregular hyperbolic honeycomb 621 made of only regular facets and the 521 Euclidean
72_(number)
Regular tiling of the hyperbolic plane
hyperbolic tiling is related to a semiregular infinite skew polyhedron with the same vertex figure in Euclidean 3-space. John H. Conway, Heidi Burgiel,
Order-5_square_tiling
Class of 4-dimensional polytopes
Boole Stott, in her publication Geometrical deduction of semiregular from regular polytopes and space fillings, expanded the definition by also allowing Archimedean
Uniform_4-polytope
{Cl} _{X}A\right)\right)} Semiregular A space is semiregular if the regular open sets form a base. Separable A space is separable if it has a countable
Glossary_of_general_topology
Semiregular tiling of the plane
In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex
Elongated_triangular_tiling
Uniform 6-dimensional polytope
semiregular polytopes: (Various definitions before Coxeter's uniform category) 1900: Thorold Gosset enumerated the list of nonprismatic semiregular convex
Uniform_6-polytope
Convex uniform 7-polytope in seven-dimensional geometry
Coxeter-Dynkin diagram, shown as . E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S1 7. Rectified octaexon (Acronym: roc) (Jonathan
Rectified_7-simplexes
Uniform Polytope
tessellation of 7-dimensional space, 331. E. L. Elte named it V126 (for its 126 vertices) in his 1912 listing of semiregular polytopes. It was called 231
2_31_polytope
Regular 5-polytope
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices
5-demicube
Star in the constellation Scutum
Majoris and IRC +10420. It has some emission-lines and is classified as a semiregular variable with an approximate pulsation period of 740 days. Based on an
UY_Scuti
Semiregular tiling of a plane
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons (12-sides) and one triangle on each
Truncated_hexagonal_tiling
Semiregular tiling of the plane
In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. Its Schläfli
Snub_square_tiling
Semiregular tiling
In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex
Truncated_square_tiling
Spatial tiling of convex uniform polyhedra
list of semiregular convex polytopes with regular cells (Platonic solids) in his publication On the Regular and Semi-Regular Figures in Space of n Dimensions
Convex_uniform_honeycomb
Euclidean tilings using 2 or more regular polygon faces
1987: Ghyka lists 10 of them with 2 or 3 vertex types, calling them semiregular polymorph partitions. Steinhaus gives 5 examples of non-homogeneous tessellations
Demiregular_tiling
Type of uniform tiling in geometry
In geometry, the snub hexaoctagonal tiling is a semiregular tiling of the hyperbolic plane. There are three triangles, one hexagon, and one octagon on
Snub_hexaoctagonal_tiling
Uniform 6-polytope
the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named as V72 (for its 72 vertices). Its Coxeter symbol is
1_22_polytope
Italian physician and entomologist
list of 25 convex uniform honeycombs in 1905 (the space-filling tessellations of regular and semiregular polyhedra). This was the most complete list published
Alfredo_Andreini
Prism with a 6-sided base
perpendicular to the base. If faces are all regular, the hexagonal prism is a semiregular polyhedron—more generally, a uniform polyhedron—and the fourth in an
Hexagonal_prism
Semiregular tiling of the hyperbolic plane
In geometry, the truncated triheptagonal tiling is a semiregular tiling of the hyperbolic plane. There is one square, one hexagon, and one tetradecagon
Truncated triheptagonal tiling
Truncated_triheptagonal_tiling
Geometric tiling
In geometry, the rhombitriheptagonal tiling is a semiregular tiling of the hyperbolic plane. At each vertex of the tiling there is one triangle and one
Rhombitriheptagonal_tiling
Uniform polytope
Lodewijk Elte named it V576 (for its 576 vertices) in his 1912 listing of semiregular polytopes. Coxeter called it 132 for its bifurcating Coxeter-Dynkin diagram
1_32_polytope
Semi-regular arrangement of squares, decagons, and dodecagons
In geometry, the truncated tetrahexagonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one decagon, and one dodecagon
Truncated pentahexagonal tiling
Truncated_pentahexagonal_tiling
Group of irregular uniform polytopes
and semi-regular figures in space of n dimensions". Messenger of Mathematics. 29: 43–48. Elte, E. L. (2006), The Semiregular Polytopes of the Hyperspaces
Gosset–Elte_figures
Concept in mathematics
In geometry, the truncated octagonal tiling is a semiregular tiling of the hyperbolic plane. There is one triangle and two hexakaidecagons on each vertex
Truncated_octagonal_tiling
types of vertices. The 1-uniform tiling include 3 regular tilings, and 8 semiregular tilings. A 1-uniform tiling can be defined by its vertex configuration
List_of_k-uniform_tilings
Isogonal polytope with uniform facets
lengths of edges. This is a generalization of the older category of semiregular polytopes, but also includes the regular polytopes. Further, star regular
Uniform_polytope
semiregolari e sulle corrispondenti reti correlative (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets)". Mem. Società
Triangular prismatic honeycomb
Triangular_prismatic_honeycomb
Type of polyhedron with many holes
Stott, Alicia Boole (1910). "Geometrical deduction of semiregular from regular polytopes and space fillings". Amst. Ak. Versl. 19: 3–8. Gevay, G.; Schulte
Leonardo_polyhedron
Five-dimensional geometric shape
semiregular polytopes: (Various definitions before Coxeter's uniform category) 1900: Thorold Gosset enumerated the list of nonprismatic semiregular convex
Uniform_5-polytope
Axioms in topology defining notions of "separation"
in strength. The KC space property is strictly[citation needed] stronger than the weak Hausdorff space property. X is semiregular if the regular open
Separation_axiom
Semiregular variable star in the constellation Grus
Pi1 Gruis (π1 Gruis) is a semiregular variable star in the constellation Grus around 590 light-years from Earth. It forms a close double star with π2
Pi1_Gruis
Star in the constellation Libra
which places it in the red giant stage of its evolution. This is a semiregular variable star with a single pulsation period of 20 days. It shows small
Sigma_Librae
Only regular space-filling tessellation of the cube
space-fillings) A. Andreini, Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative (On the regular and semiregular nets
Cubic_honeycomb
Semiregular tiling of the hyperbolic plane
triangular tiling, sometimes called the hyperbolic soccerball, is a semiregular tiling of the hyperbolic plane. There are two hexagons and one heptagon
Truncated order-7 triangular tiling
Truncated_order-7_triangular_tiling
Natural number
There are also a total of 32 uniform colorings to the 11 regular and semiregular tilings. There are 32 three-dimensional crystallographic point groups
32_(number)
Geometric object
uniform prismatic polychora, which are Cartesian products of a regular or semiregular polyhedron and a line segment. There are eighteen convex uniform prisms
Spherinder
white dwarfs List of red dwarfs List of notable variable stars List of semiregular variable stars List of stars that have unusual dimming periods List of
Lists_of_stars
its circumsphere to form a uniform honeycomb in spherical space. It represents a semiregular honeycomb as defined by all regular cells, although from the
Hyperbolic tetrahedral-octahedral honeycomb
Hyperbolic_tetrahedral-octahedral_honeycomb
Natural number
and hyperbolic 3-space: 75 is the total number of non-prismatic uniform polyhedra, which incorporate regular polyhedra, semiregular polyhedra, and star
151_(number)
Variable star in the constellation Cepheus
SS Cephei is a semiregular variable star in the constellation Cepheus. It is of spectral type M5III, and has an estimated temperature of about 3,700 K
SS_Cephei
Uniform 7-dimensional polytope
Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900 Elte, E.L. (2006). The Semiregular Polytopes of the Hyperspaces
3_21_polytope
Open cluster in Scorpius
with its blue neighbours in photographs. BM Scorpii, is classed as a semiregular variable star, its brightness varying from magnitude +5.5 to magnitude
Butterfly_Cluster
its circumsphere to form a uniform honeycomb in spherical space. It represents a semiregular honeycomb as defined by all regular cells, although from the
Tetrahedral-triangular tiling honeycomb
Tetrahedral-triangular_tiling_honeycomb
Constellation straddling the celestial equator
end of its life. It is the second-brightest star in Orion, and is a semiregular variable star. It serves as the right shoulder of the hunter (assuming
Orion_(constellation)
Overview of the scientific field of astronomy
Cephei variable PV Telescopii variable Long Period and Semiregular Mira variable Semiregular variable Slow irregular variable Other RV Tauri variable
Outline_of_astronomy
Catalan solid with 12 faces
1017/CBO9780511569371, ISBN 978-0-521-54325-5, MR 0730208 (The thirteen semiregular convex polyhedra and their duals, Page 19, Rhombic dodecahedron) The
Rhombic_dodecahedron
Natural number
figure). The sphere in particular circumscribes all the above regular and semiregular polyhedra (as a fundamental property); all of these solids also have
37_(number)
geometry, the alternated hexagonal tiling honeycomb, h{6,3,3}, or , is a semiregular tessellation with tetrahedron and triangular tiling cells arranged in
Alternated hexagonal tiling honeycomb
Alternated_hexagonal_tiling_honeycomb
Canadian actress
members of the Toronto branch of The Second City comedy troupe and was a semiregular on SCTV. She was in the original Toronto production of Godspell. In 2005
Jayne_Eastwood
Constellation in the northern celestial hemisphere
is Lambda Ursae Minoris, a red giant of spectral type M1III. It is a semiregular variable varying between magnitudes 6.35 and 6.45. The northerly nature
Ursa_Minor
Solid with 10 faces
is also known as an anticube. If all its faces are regular, it is a semiregular polyhedron or uniform polyhedron. A nonuniform D4-symmetric variant is
Square_antiprism
Regular tiling of hyperbolic 3-space
honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol {4,3,5}, it has five
Order-5_cubic_honeycomb
cell centers of the 8-simplex. E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S1 8. It is also called 06,1 for its branching
Rectified_8-simplexes
Semiregular tiling of the hyperbolic plane
In geometry, the triheptagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 heptagonal tiling. There are two
Triheptagonal_tiling
Variable star in the constellation Scorpius
V915 Scorpii (HR 6392, HD 155603) is a hypergiant and semiregular variable star, located 1,718 parsecs (5,600 ly) away in the constellation Scorpius.
V915_Scorpii
Red supergiant star in the constellation Cepheus
obsolete class of the Mu Cephei variables. It is now considered to be a semiregular variable of type SRc. Its apparent brightness varies erratically between
Mu_Cephei
Wenninger Polyhedron Models: W001-W119 1–18: 5 convex regular and 13 convex semiregular 20–22, 41: 4 non-convex regular 19–66: Special 48 stellations/compounds
List_of_uniform_polyhedra
American actor, comedian and jazz drummer (1927–2011)
was also a regular performer on The ABC Comedy Hour in 1972. He was a semiregular on The Flip Wilson Show and co-host of The Joey Bishop Show. His last
Charlie_Callas
Solid with 2 parallel n-gonal bases connected by n parallelograms
prism. A regular prism is a prism with regular bases. A uniform prism or semiregular prism is a right prism with regular bases and all edges of the same length
Prism_(geometry)
Natural number
completely fill a plane vertex. Eleven of these belong to regular and semiregular tilings, while 6 of these (3.7.42, 3.8.24, 3.9.18, 3.10.15, 4.5.20, and
17_(number)
Isogonal honeycomb of uniform polytope facets
semiregolari e sulle corrispondenti reti correlative (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società
Uniform_honeycomb
discovered by Thorold Gosset with his 1900 paper of semiregular polytopes. It is not semiregular by Gosset's definition of regular facets, but all of
Snub_24-cell_honeycomb
Vertex-transitive tiling of the plane by regular polygons
These symmetry groups create 3 regular tilings, and 7 semiregular ones. A number of the semiregular tilings are repeated from different symmetry constructors
Uniform_tiling
Star in the constellation Hydra
of M1 III. It is currently on the asymptotic giant branch, and is a semiregular variable that undergoes changes in luminosity according to three pulsation
Phi2_Hydrae
Transformations induced by a mathematical group
corresponding to the action is injective. The action is called free (or semiregular or fixed-point free) if the statement that g ⋅ x = x {\displaystyle g\cdot
Group_action
Star in the constellation Cancer
M3 IIIa, currently on the asymptotic giant branch. It is classified as a semiregular variable star of type SRb and its brightness varies from magnitude +5
27_Cancri
rectified 600-cell is a uniform pentagonal prism. It is one of three semiregular 4-polytopes made of two or more cells which are Platonic solids, discovered
Rectified_600-cell
Uniform 6-polytope
Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900 Elte, E. L. (1912), The Semiregular Polytopes of the Hyperspaces
2_21_polytope
Notation for a polyhedron's vertex figure
5/2. Semiregular polyhedra have vertex configurations with positive angle defect. NOTE: The vertex figure can represent a regular or semiregular tiling
Vertex_configuration
American series of comedy short films
character of Stymie's sister "Buckwheat", although Thomas was male. Semiregular actors such as Jackie Lynn Taylor, Marianne Edwards, and Leonard Kibrick
Our_Gang
Star in the constellation Crux
; et al. (May 2004). "Multiwavelength diameters of nearby Miras and semiregular variables". Monthly Notices of the Royal Astronomical Society. 350 (1):
Gacrux
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