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Extending the elements of a polytope to form a new figure
In geometry, stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in n dimensions
Stellation
Catalan solid with 12 faces
dodecahedron, one of which is the Bilinski dodecahedron. There are some stellations of the rhombic dodecahedron, one of which is the Escher's solid. The
Rhombic_dodecahedron
Solid with twenty equal triangular faces
icosahedron, including its 59 stellations. The great dodecahedron, one of the Kepler–Poinsot polyhedra, is constructed by either stellation of the regular dodecahedron
Regular_icosahedron
Group of stars on the celestial sphere
A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived pattern or outline, typically representing an animal
Constellation
Self-intersecting polyhedron with 12 faces
first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation of
First stellation of the rhombic dodecahedron
First_stellation_of_the_rhombic_dodecahedron
Any of 4 regular star polyhedra
both regular icosahedron and regular dodecahedron, an operation named stellation. This operation results in four different polyhedra: Great dodecahedron:
Kepler–Poinsot_polyhedron
of stellation to a polyhedron extends its faces (or edges and planes) until they generate new vertices that bound a newly formed figure. Stellation represents
List of polyhedral stellations
List_of_polyhedral_stellations
Kepler-Poinsot polyhedron with 20 faces
icosahedron" ("Uniform polyhedron") at MathWorld. Weisstein, Eric W. "Fifteen stellations of the icosahedron". MathWorld. Uniform polyhedra and duals
Great_icosahedron
Natural number
fully supported stellations generated by an icosahedron. The seventeenth prime number is 59, which is equal to the total number of stellations of the icosahedron
17_(number)
Outermost stellation of the icosahedron
In geometry, the complete, final stellation of the icosahedron, or echidnahedron is the outermost stellation of the icosahedron, and is "complete" and
Final stellation of the icosahedron
Final_stellation_of_the_icosahedron
Polyhedron with 20 faces
Kepler–Poinsot polyhedron. Both have icosahedral symmetry. There are 59 stellations of a regular icosahedron (including the original icosahedron itself)
Icosahedron
Natural number
deltahedra. The stella octangula, or eight-pointed star, is the only stellation with octahedral symmetry. It has eight triangular faces alongside eight
8
Book on stellations of the regular icosahedron by H. S. M. Coxeter and colleagues
Coxeter, P. Du Val, H. T. Flather, and J. F. Petrie. It enumerates certain stellations of the regular convex or Platonic icosahedron, according to a set of
The_Fifty-Nine_Icosahedra
Removing parts of a polytope without creating new vertices
of polyhedra. Faceting is the reciprocal or dual process to stellation. For every stellation of some convex polytope, there exists a dual faceting of the
Faceting
Flat-sided three-dimensional shape
the Platonic solids by a process called stellation. Most stellations are not regular. The study of stellations of the Platonic solids was given a big push
Polyhedron
Topics referred to by the same term
Fifty-Nine Icosahedra a book by H. S. M. Coxeter, and others it enumerates stellations of the regular icosahedron, 59th (disambiguation) Fifty-Niner This disambiguation
59
Polyhedral compound
In geometry, this polyhedron can be seen as either a polyhedral stellation or a compound. It can be seen as the compound of an icosahedron and dodecahedron
Compound of dodecahedron and icosahedron
Compound_of_dodecahedron_and_icosahedron
In geometry, a stellation diagram or stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other
Stellation_diagram
3D geometric shape
In geometry, a rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry
Rhombic_hexecontahedron
Polyhedral compound
form pentagrams, which are the stellations of the pentagonal faces of the dodecahedron. It is one of the stellations of the rhombic triacontahedron.
Compound_of_five_cubes
Polyhedral compound
5-cells. The stellated octahedron is constructed by a stellation of the regular octahedron. In a stellation, the faces of the underlying polyhedron are extended
Stellated_octahedron
Regular non-convex polygon
also be obtained as a sequence of stellations of a convex regular core polygon. Constructions based on stellation also allow regular polygonal compounds
Star_polygon
Polyhedral compound
one of the five regular polyhedron compounds, and can also be seen as a stellation. It was first described by Edmund Hess in 1876. It is unique among the
Compound_of_five_octahedra
Polyhedron with 12 faces
There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120
Dodecahedron
Regular Schläfli-Hess 4-polytope with 600 vertices
in the name. The great grand stellated 120-cell is the final regular stellation of the 120-cell, and is the only Schläfli-Hess polychoron to have the
Great grand stellated 120-cell
Great_grand_stellated_120-cell
Lithograph print by M. C. Escher
one on the left is a compound of three cubes. The one on the right is a stellation of a rhombic dodecahedron (or a compound of three non-regular octahedra)
Waterfall_(M._C._Escher)
Characters of the Tron film series
dodecahedron and icosahedron and the small triambic icosahedron, the first stellation of the icosahedron. When it answers "yes", it changes into a yellow octahedron
List of Tron (franchise) characters
List_of_Tron_(franchise)_characters
and stellation groupings. back to top back to top back to top List of uniform polyhedra The Fifty-Nine Icosahedra List of polyhedral stellations Wenninger
List of Wenninger polyhedron models
List_of_Wenninger_polyhedron_models
Natural number
number is sixty-one, with which it comprises a twin prime. There are 59 stellations of the regular icosahedron. Fifty-nine is: The "59-minute rule" is an
59_(number)
Kepler–Poinsot polyhedron
pentagonal pyramids onto each of its faces, known as the first stellation. The second stellation appears when 30 wedges are attached to it. Given a great dodecahedron
Great_dodecahedron
86°37′28″W / 34.73500°N 86.62444°W / 34.73500; -86.62444 Con†Stellation (also written as Con*Stellation) was an annual general-interest science fiction convention
Con†Stellation
Catalan solid with 30 faces
tiling. The rhombic triacontahedron has 227 fully supported stellations. One of the stellations of the rhombic triacontahedron is the compound of five cubes
Rhombic_triacontahedron
Solid with 12 equal pentagonal faces
Goldberg polyhedron. The stellations of the regular dodecahedron make up three of the four Kepler–Poinsot polyhedra. The first stellation of a regular dodecahedron
Regular_dodecahedron
Kepler–Poinsot polyhedron
regular dodecahedron, as well as being a stellation of a (smaller) dodecahedron. It is the only dodecahedral stellation with this property, apart from the dodecahedron
Great_stellated_dodecahedron
Quadrilateral with sides of equal length
with 30 intersecting rhombic faces. The rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic
Rhombus
Natural number
has 92 vertices. On the other hand, as a simple polyhedron, the final stellation of the icosahedron has 92 vertices. There are 92 Johnson solids. 92 is
92_(number)
Polyhedron with some pattern of nonconvexity
classes are the stellations of convex polyhedra and their duals, the facettings of the dual polyhedra. For example, the complete stellation of the icosahedron
Star_polyhedron
Topics referred to by the same term
hip hop/rock band Con†Stellation, an annual general-interest science fiction convention held in Huntsville, Alabama ConStellation, the 41st World Science
Constellation (disambiguation)
Constellation_(disambiguation)
Polyhedron with regular congruent polygons as faces
solids by a process called stellation. The reciprocal process to stellation is called facetting (or faceting). Every stellation of one polyhedron is dual
Regular_polyhedron
Natural number
Lie algebra. In the third dimension, there are a total of sixty-three stellations generated with icosahedral symmetry I h {\displaystyle \mathrm {I_{h}}
63_(number)
Four-dimensional analogues of the regular polyhedra in three dimensions
adds a grand modifier. Conway offered these operational definitions: stellation – replaces edges with longer edges in same lines. (Example: a pentagon
Regular_4-polytope
dual uniform polyhedra. The exterior surface also represents the De2f2 stellation of the icosahedron. These figures can be differentiated by marking which
Great_triambic_icosahedron
Natural number
produces 187 distinct stellations. It is the smallest Catalan solid, dual to the truncated tetrahedron, which only has 9 distinct stellations. 187 (disambiguation)
187_(number)
Natural number between 89 and 91
icosahedron, a near-miss Johnson solid. On the other hand, the final stellation of the icosahedron has 90 edges. It also has 92 vertices like the rhombic
90_(number)
Topics referred to by the same term
2000 box set Salival The stellated octahedron, a polyhedral compound and stellation named "merkaba" by some contemporary mystics Markaba (Arabic: مركبا),
Merkabah_(disambiguation)
disconnected plane figures as still being faces) coincides with the first (B) stellation of the icosahedron. If instead, after removing the surrounded parts of
Small_triambic_icosahedron
Polyhedral compound
and octahedron is a polyhedron which can be seen as either a polyhedral stellation or a compound. The 14 Cartesian coordinates of the vertices of the compound
Compound of cube and octahedron
Compound_of_cube_and_octahedron
Two polyhedral compounds with the same name
dodecahedron: one is a dual compound and a stellation of the great icosidodecahedron, the other is a stellation of the icosidodecahedron. It can be seen
Compound of great icosahedron and great stellated dodecahedron
Compound_of_great_icosahedron_and_great_stellated_dodecahedron
Five-pointed star polygon
pentagon; see details of the construction. It can also be constructed as a stellation of a pentagon, by extending the edges of a pentagon until the lines intersect
Pentagram
Polyhedron with 60 faces
suggested these figures are members of a new class of stellation polyhedra, called stellation to infinity. However, he also acknowledged that strictly
Great_dirhombicosidodecacron
Nine-pointed star polygon
Enneagram Enneagrams shown as sequential stellations Edges and vertices 9 Symmetry group Dihedral (D9) Internal angle (degrees) 100° {9/2} 20° {9/4}
Enneagram_(geometry)
41st Worldcon (1983)
The 41st World Science Fiction Convention (Worldcon), also known as ConStellation, was held on 1–5 September 1983 at the Baltimore Convention Center in
41st World Science Fiction Convention
41st_World_Science_Fiction_Convention
3D shape made of polyhedra sharing a common center
of the compound. This polyhedron can be used as the core for a set of stellations. A regular polyhedral compound can be defined as a compound which, like
Polytope_compound
Concave polyhedron
represents the Ef1g1 stellation of the icosahedron. It appears in Magnus Wenninger's book Polyhedron Models as model 28, the third stellation of icosahedron
Excavated_dodecahedron
Compound polyhedron
five regular polyhedral compounds. This compound polyhedron is also a stellation of the regular icosahedron. It was first described by Edmund Hess in 1876
Compound_of_five_tetrahedra
13 polyhedra; duals of the Archimedean solids
solid. Diudea (2018), p. 39. Wenninger (1983), p. 1, Basic notions about stellation and duality. Diudea (2018), p. 39 Heil & Martini (1993), p. 352 Cundy
Catalan_solid
Zimmermann), ran CP/M-86, MS-DOS, and UCSD Pascal Motorola 6809 – The Mill, by Stellation Two, ran OS-9 Level One. AP10 by IBS running FLEX Motorola 68008 – mc
Apple_II_processor_cards
Star polygon with 7 sides
"Children's Books Are Important". Grünbaum–Rigby configuration Star polygon Stellation § Stellating polygons List of regular polytopes § Two-dimensional regular
Heptagram
Kepler-Poinsot polyhedron
forms a degenerate uniform compound figure. It is the second of four stellations of the dodecahedron (including the original dodecahedron itself). The
Small_stellated_dodecahedron
Feature of a polyhedron, polytope, etc.
form the faces of a new polyhedron; this is the reciprocal process to stellation and may also be applied to higher-dimensional polytopes. In polyhedral
Facet_(geometry)
1983 film directed by Philip Kaufman
Yeager, Gordon Cooper, Scott Glenn and Dennis Quaid appeared in 1983 at ConStellation, the 41st World Science Fiction Convention in Baltimore. The Right Stuff
The_Right_Stuff_(film)
convex semiregular 20–22, 41: 4 non-convex regular 19–66: Special 48 stellations/compounds (Nonregulars not given on this list) 67–109: 43 non-convex
List_of_uniform_polyhedra
Archimedean solid with 32 faces
rotunda. An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices
Icosidodecahedron
Uniform star polyhedron with 204 faces
suggested these figures are members of a new class of stellation polyhedra, called stellation to infinity. However, he also acknowledged that strictly
Great disnub dirhombidodecahedron
Great_disnub_dirhombidodecahedron
3D graphics software
polyhedra. Operations which can be performed on these polyhedra include stellation, faceting, augmentation, dualization (also called "reciprocation"), creating
Stella_(software)
the United States was 331,449,281 in 2020. Mathematics: 358,833,097 stellations of the rhombic triacontahedron. Mathematics: There are 406,425,600 possible
Orders_of_magnitude_(numbers)
Polyhedral compound
regular polyhedral compounds. This polyhedron can be seen as either a stellation of the icosahedron or a compound. This compound was first described by
Compound_of_ten_tetrahedra
Polyhedral mechanical puzzle toy
dodecahedron 2×2×2 cube form of Yoshimoto Cube STL model of the first stellation of the rhombic dodecahedron decomposed into pyramids and half-cubes Rubik's
Yoshimoto_Cube
Catalan solid with 24 kite faces
24 faces of a dyakis dodecahedron. The great triakis octahedron is a stellation of the deltoidal icositetrahedron. Tetrakis hexahedron, another 24-face
Deltoidal_icositetrahedron
German geometer (1860–1934)
Teubner, 1900). The shapes first studied in this book include the final stellation of the icosahedron and the compound of three octahedra, made famous by
Max_Brückner
Polyhedron with 14 faces
{8/3} octagrams. Even though the stellated truncated hexahedron is a stellation of the truncated hexahedron, its core is a regular octahedron. It shares
Stellated truncated hexahedron
Stellated_truncated_hexahedron
Solid with eight equal triangular faces
and this compound—called the stella octangula—is its first and only stellation. Correspondingly, a regular octahedron is the result of cutting off from
Regular_octahedron
Polytope or tiling whose vertices are identical
2-uniform). This tiling is made of equilateral triangle and regular hexagonal faces. 2-isogonal 9/4 enneagram (face of the final stellation of the icosahedron)
Isogonal_figure
Regular star 4-polytope with 600 faces
turn is also analogous to the pentagram); all of these are the final stellations of the n-dimensional "dodecahedral-type" pentagonal polytope. It has
Grand_600-cell
Topics referred to by the same term
Stellate trichomes (hairs) Stellate wounds from lacerations or incisions Stellation, a geometric process of extending a polygon or polyhedron This disambiguation
Stellate
German mathematician (1843–1903)
Stellation diagrams (1876) On the right are those of the compound of five cubes and its dual.
Edmund_Hess
Pyramid with a pentagon base
each pentagonal face, similar to the small stellated dodecahedron by stellation, and a regular icosahedron constructed from a pentagonal antiprism by
Pentagonal_pyramid
Any of the five regular polyhedra
polyhedra. These all have icosahedral symmetry and may be obtained as stellations of the dodecahedron and the icosahedron. The next most regular convex
Platonic_solid
Star polygon with 12 vertices
series by Bryn Donovan The twelve tribes of Nauru on the national flag. Stellation Star polygon List of regular polytopes and compounds γραμμή, Henry George
Dodecagram
Polyhedron with 22 faces
Wenninger suggested these figures are members of a new class of stellation figures, called stellation to infinity. However, he also suggested that strictly speaking
Great_dodecahemicosahedron
Complicated polygon
eight other regular star 4-polytopes. It may also be seen as the first stellation of the 120-cell. In this sense it could be seen as analogous to the three-dimensional
Small_stellated_120-cell
Polyhedron resulting from the snub operation
convex, non-uniform) Bipyramids (infinite) Pyramids (infinite) Stellations Stellations Polyhedral compounds (5 regular) Deltahedra (Deltahedra, equilateral
Snub_polyhedron
Catalan solid with 48 faces
symmetry group with order 2,3,n mirrors at each triangle face vertex. First stellation of rhombic dodecahedron Disdyakis triacontahedron Kisrhombille tiling
Disdyakis_dodecahedron
speaking {n/m} = {n/(n − m)}) and m and n are coprime (as such, all stellations of a polygon with a prime number of sides will be regular stars). Symbols
List_of_regular_polytopes
Polyhedron with 7 faces
Wenninger suggested these figures are members of a new class of stellation figures, called "stellation to infinity". However, he also suggested that strictly speaking
Tetrahemihexahedron
Catalan solid with 12 faces
triakis tetrahedron. Truncated triakis tetrahedron Smith, Anthony (1965), "Stellations of the Triakis Tetrahedron", The Mathematical Gazette, 49 (368): 135–143
Triakis_tetrahedron
Star polyhedron
Wenninger suggested these figures are members of a new class of stellation figures, called stellation to infinity. However, he also suggested that strictly speaking
Small_icosihemidodecacron
Catalan solid with 60 faces
the triples of coplanar isosceles triangles form the faces of the first stellation of the icosahedron. Yet another non-convex form, with golden isosceles
Triakis_icosahedron
convex, non-uniform) Bipyramids (infinite) Pyramids (infinite) Stellations Stellations Polyhedral compounds (5 regular) Deltahedra (Deltahedra, equilateral
List of uniform polyhedra by vertex figure
List_of_uniform_polyhedra_by_vertex_figure
Uniform star polyhedron with 12 faces
Wenninger suggested these figures are members of a new class of stellation figures, called stellation to infinity. However, Wenninger also suggested that strictly
Octahemioctahedron
Topics referred to by the same term
may refer to: W42 (nuclear warhead) Fallston Airport, in Maryland Final stellation of the icosahedron Shibetsu Station, in Hokkaido, Japan W42, a Toyota
W42
Polyhedron associated with another by swapping vertices for faces
Self-dual graph Self-dual polygon Wenninger (1983), "Basic notions about stellation and duality", p. 1. Grünbaum (2003) Cundy & Rollett (1961), 3.2 Duality
Dual_polyhedron
convex, non-uniform) Bipyramids (infinite) Pyramids (infinite) Stellations Stellations Polyhedral compounds (5 regular) Deltahedra (Deltahedra, equilateral
List of uniform polyhedra by spherical triangle
List_of_uniform_polyhedra_by_spherical_triangle
Polyhedral compound
to each face of the central cube. Thus, the compound can be seen as a stellation of the tetrakis hexahedron. A different form of the tetrakis hexahedron
Compound_of_three_octahedra
Class of musical pitch sets
and confusingly overlapped with the Euler–Fokker genus, the subsequent stellation of Wilson's combination product sets (CPS) are outside of that Genus.
Hexany
Polyhedron with 30 faces
Wenninger suggested these figures are members of a new class of stellation figures, called stellation to infinity. However, he also suggested that strictly speaking
Small_dodecahemicosacron
Uniform star polyhedron whose faces intersect its center
Wenninger suggested these figures are members of a new class of stellation figures, called stellation to infinity. However, he also suggested that strictly speaking
Hemipolyhedron
11-pointed star polygon
connected by edges. These same four forms can also be considered as stellations of a regular hendecagon. Since 11 is prime, all hendecagrams are star
Hendecagram
Polyhedron with 30 faces
Wenninger suggested these figures are members of a new class of stellation figures, called stellation to infinity. However, he also suggested that strictly speaking
Great_dodecahemidodecacron
Physical manifestation of a geometric shape
simpler related polyhedron used as a colour guide. Complex models, such as stellations, can have hundreds of polygons in their nets. Recent computer graphics
Polyhedron_model
STELLATION
STELLATION
STELLATION
STELLATION
Surname or Lastname
English
English : variant spelling of Adams.
Surname or Lastname
English
English : unexplained; possibly a variant spelling of Butt.
Boy/Male
Hindu
Supreme being
Girl/Female
American, Australian, Chinese, Danish, French, Hawaiian, Hebrew, Latin, Swedish
Star of the Sea; Beautiful; Mary means Bitter and Belle means Beautiful; Beloved; God is My Oath; Blend of Mary and Belle
Boy/Male
Welsh Shakespearean
Pure.
Male
Swiss
, addition.
Boy/Male
Hindu, Indian
Base for Something
Boy/Male
Hindu
Large eared Lord
Girl/Female
Gujarati, Hindu, Indian, Telugu, Traditional
Goddess Lakshmi
Girl/Female
Arabic French English Latin
Perfection.
STELLATION
STELLATION
STELLATION
STELLATION
STELLATION
n.
Radiation of light.