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Regular polytope whose 2D form is a pentagon
complete family of dodecahedral pentagonal polytopes are: Line segment, { } Pentagon, {5} Dodecahedron, {5, 3} (12 pentagonal faces) 120-cell, {5, 3, 3} (120
Pentagonal_polytope
Shape with five sides
echinoderms with a pentagonal shape. A Ho-Mg-Zn icosahedral quasicrystal formed as a pentagonal dodecahedron. The faces are true regular pentagons. A pyritohedral
Pentagon
rhombicosidodecahedron Pentagonal bipyramid Pentagonal cupola Pentagonal gyrobicupola Pentagonal gyrocupolarotunda Pentagonal orthobicupola Pentagonal orthobirotunda
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Geometric object with flat sides
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any
Polytope
Four-dimensional analogues of the regular polyhedra in three dimensions
In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular
Regular_4-polytope
Polyhedron with 12 faces
self-intersecting equilateral pentagonal faces. A tetartoid (also tetragonal pentagonal dodecahedron, pentagon-tritetrahedron, and tetrahedric pentagon dodecahedron)
Dodecahedron
Polyhedron with four faces
tetrahedron of the cube is an example of a Heronian tetrahedron. Every regular polytope, including the regular tetrahedron, has its characteristic orthoscheme
Tetrahedron
Solid with twenty equal triangular faces
can be constructed from a pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points
Regular_icosahedron
Regular polytope dual to the hypercube in any number of dimensions
In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean
Cross-polytope
Four-dimensional geometric object with flat sides
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure
4-polytope
rhombicosidodecahedron Pentagonal bipyramid Pentagonal cupola Pentagonal gyrobicupola Pentagonal gyrocupolarotunda Pentagonal orthobicupola Pentagonal orthobirotunda
List_of_mathematical_shapes
Uniform 4-polytope bounded by 320 cells
antiprism or pentagonal double antiprismoid is a uniform 4-polytope (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and
Grand_antiprism
5-dimensional hypercube
deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the
5-cube
5-dimensional geometric object
geometry, a five-dimensional polytope (or 5-polytope or polyteron) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which
5-polytope
Regular star 4-polytope with 600 faces
only regular n-dimensional star polytopes which are derived by performing stellational operations on the pentagonal polytope which has simplectic faces. It
Grand_600-cell
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 Gosset
4_21_polytope
Four-dimensional analog of the dodecahedron
dodecahedron has 12 pentagonal facets, with 3 around each vertex, the dodecaplex has 120 dodecahedral facets, with 3 around each edge. Its dual polytope is the 600-cell
120-cell
Equiangular and equilateral polygon
Polyhedra? Branko Grünbaum (2003), Fig. 3 Regular polytopes, p.95 Coxeter, The Densities of the Regular Polytopes II, 1932, p.53 Lee, Hwa Young; "Origami-Constructible
Regular_polygon
Four-dimensional analogue of the cube
labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope. The construction
Tesseract
Convex polytope, the n-dimensional analogue of a square and a cube
measure polytope (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes. The
Hypercube
regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. There is only one polytope of
List_of_regular_polytopes
6-dimensional hypercube
being a 6-dimensional polytope constructed from 12 regular facets. Acronym: ax It is a part of an infinite family of polytopes, called hypercubes. The
6-cube
Four-dimensional analog of the octahedron
convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described
16-cell
Kepler–Poinsot polyhedron
analogue, by attempting to stellate the n-dimensional pentagonal polytope (which has pentagonal polytope faces and simplex vertex figures) until it can no
Great_stellated_dodecahedron
Type of geometrical object
geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge. A
Uniform_10-polytope
Class of 4-dimensional polytopes
In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra
Uniform_4-polytope
Type of uniform 4-polytope in four-dimensional geography
3-5 duoprism - - 3 pentagonal prisms, 5 triangular prisms 4-5 duoprism - - 4 pentagonal prisms, 5 cubes 5-5 duoprism - - 10 pentagonal prisms 3-6 duoprism
Prismatic_uniform_4-polytope
4D geometry item
and one pentagon. The cantitruncated 600-cell is a uniform 4-polytope. It is composed of 1440 cells: 120 truncated icosahedra, 720 pentagonal prisms and
Cantellated_120-cell
Polytope with highest degree of symmetry
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In
Regular_polytope
Regular 5-polytope
five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed
5-demicube
Skew polygon derived from a polytope
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one
Petrie_polygon
Four-dimensional analogue of the tetrahedron
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells
5-cell
9-dimensional hypercube
nine-dimensional polytope constructed with 18 regular facets. It was given acronym enne by J. Bowers. It is a part of an infinite family of polytopes, called hypercubes
9-cube
Uniform 7-dimensional polytope
In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. It was discovered by Thorold Gosset
3_21_polytope
10-dimensional hypercube
as a 10 dimensional polytope, constructed from 20 regular facets. Acronym: deker It is a part of an infinite family of polytopes, called hypercubes. The
10-cube
Plane figure bounded by line segments
single plane. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. There are many more generalizations of polygons
Polygon
7-dimensional hypercube
called a regular tetradeca-7-tope or tetradecaexon, being a 7 dimensional polytope constructed from 14 regular facets. This configuration matrix represents
7-cube
Uniform 6-polytope
122 polytope is a uniform polytope, constructed from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named
1_22_polytope
Isogonal polytope with uniform facets
In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. Here, "vertex-transitive" means
Uniform_polytope
6-dimensional geometry, there are 39 uniform polytopes with E6 symmetry. The two simplest forms are the 221 and 122 polytopes, composed of 27 and 72 vertices respectively
E6_polytope
4-D shape
vertices. A pentagonal antiprismatic prism or pentagonal antiduoprism is a convex uniform 4-polytope. It is formed as two parallel pentagonal antiprisms
Uniform_antiprismatic_prism
Uniform polytope in 8 dimensional geometry
In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 241, describing its
2_41_polytope
geometry, there are 255 uniform polytopes with E8 symmetry. The three simplest forms are the 421, 241, and 142 polytopes, composed of 240, 2160 and 17280
E8_polytope
8-dimensional hypercube
hexadecazetton, being an 8-dimensional polytope constructed from 16 regular facets. It is a part of an infinite family of polytopes, called hypercubes. The dual
8-cube
Five-dimensional geometric shape
5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope facets
Uniform_5-polytope
Solid with 2 parallel n-gonal bases connected by n parallelograms
Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids. Like many basic
Prism_(geometry)
Generalization of a polytope in real space
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension
Complex_polytope
In 8-dimensional geometry, there are 135 uniform polytopes with A8 symmetry. There is one self-dual regular form, the 8-simplex with 9 vertices. Each
A8_polytope
Convex regular 5-polytope in geometry
In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron
5-orthoplex
In 7-dimensional geometry, there are 128 uniform polytopes with B7 symmetry. There are two regular forms, the 7-orthoplex, and 8-cube with 14 and 128
B7_polytope
Regular object in four dimensional geometry
regular polytopes made of triangles and squares that exist in four dimensions except the regular 5-cell, but none of the pentagonal polytopes. The geometric
24-cell
Solid with eight equal triangular faces
segments. More generally, every cross-polytope and its dual, hypercube, in any higher-dimensional space are Hanner polytope. The polyhedral compounds, in which
Regular_octahedron
Shape with four equal sides and angles
truncated square is an octagon. The square belongs to a family of regular polytopes that includes the cube in three dimensions and the hypercubes in higher
Square
stacked polytope (it has a small gap between the first and last tetrahedron). However, the similar-looking pentagonal bipyramid is not a stacked polytope, because
Stacked_polytope
Shape with three equal sides
of Numbers. Springer-Verlag. Coxeter, H. S. M. Coxeter (1948). Regular Polytopes (1 ed.). London: Methuen & Co. LTD. OCLC 4766401. Zbl 0031.06502. Cromwell
Equilateral_triangle
Uniform Polytope
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 231, describing its bifurcating Coxeter-Dynkin
2_31_polytope
Four-dimensional geometric objects
In 4-dimensional geometry, there are 15 uniform polytopes with H4 symmetry. Two of these, the 120-cell and 600-cell, are regular. Each can be visualized
H4_polytope
In 6-dimensional geometry, there are 64 uniform polytopes with B6 symmetry. There are two regular forms, the 6-orthoplex, and 6-cube with 12 and 64 vertices
B6_polytope
Uniform polytopes with D8 symmetry
In 8-dimensional geometry, there are 191 uniform polytopes with D8 symmetry, of which 64 are unique and 127 are shared with the B8 symmetry. There is
D8_polytope
6-dimensional geometric object
six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets. A 6-polytope is a closed six-dimensional figure
6-polytope
Group of polytopes
In 8-dimensional geometry, there are 255 uniform polytopes with B8 symmetry (to which this article adds for illustration the 8-demicube as an alternation
B8_polytope
replacing the simplicial cells of the 600-cell with icosahedral pentagonal polytope cells, it could be seen as a four-dimensional analogue of the great
Icosahedral_120-cell
In 6-dimensional geometry, there are 35 uniform polytopes with A6 symmetry. There is one self-dual regular form, the 6-simplex with 7 vertices. Each can
A6_polytope
figure of the 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
Rectified_600-cell
In 5-dimensional geometry, there are 31 uniform polytopes with B5 symmetry. There are two regular forms, the 5-orthoplex, and 5-cube with 10 and 32 vertices
B5_polytope
Shape with six sides
for these higher dimensional regular, uniform and dual polyhedra and polytopes, shown in these skew orthogonal projections: A principal diagonal of a
Hexagon
Polytope constructed from alternation of a hypercube
(also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled
Demihypercube
Type of 7-polytope
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. It has 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5-cell
7-simplex
Seven-dimensional geometric object
7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets. A uniform 7-polytope is
Uniform_7-polytope
Uniform 8 dimensional polytope
In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 142, describing its
1_42_polytope
hecatonicosachoron is a uniform 4-polytope. It is composed of 2640 cells: 120 rhombicosidodecahedron, 600 truncated tetrahedra, 720 pentagonal prisms, and 1200 hexagonal
Runcinated_120-cells
Regular 5-polytope
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and
5-simplex
In 7-dimensional geometry, there are 71 uniform polytopes with A7 symmetry. There is one self-dual regular form, the 7-simplex with 8 vertices. Each can
A7_polytope
Uniform 6-polytope
In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset
2_21_polytope
In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube. There are 9 rectifications
Rectified_9-cubes
Uniform 6-polytope
In geometry, a 6-simplex is a self-dual regular 6-polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and
6-simplex
Uniform 7-polytope
In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. It is
7-demicube
Polyhedron with eight triangular faces
Johnson solid, obtained by removing three pentagonal pyramids from a regular icosahedron, resulting in three pentagonal and five triangular faces. Heptagonal
Octahedron
Multi-dimensional generalization of triangle
dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point
Simplex
Polytope contained by 7-polytope facets
eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets, each 6-polytope ridge being shared by exactly two 7-polytope facets. A
Uniform_8-polytope
Four-dimensional analog of the icosahedron
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known
600-cell
In 6-dimensional geometry, there are 47 uniform polytopes with D6 symmetry, of which 16 are unique and 31 are shared with the B6 symmetry. There are two
D6_polytope
In 4-dimensional geometry, there are 15 uniform 4-polytopes with B4 symmetry. There are two regular forms, the tesseract and 16-cell, with 16 and 8 vertices
B4_polytope
In 7-dimensional geometry, there are 95 uniform polytopes with D7 symmetry; 32 are unique, and 63 are shared with the B7 symmetry. There are two regular
D7_polytope
Uniform 6-polytope
6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called
6-demicube
Uniform 6-dimensional polytope
uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete
Uniform_6-polytope
In 5-dimensional geometry, there are 23 uniform polytopes with D5 symmetry, 8 are unique, and 15 are shared with the B5 symmetry. There are two special
D5_polytope
Uniform 10-polytope
uniform 10-polytope, constructed from the 10-cube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called
10-demicube
In 5-dimensional geometry, there are 19 uniform polytopes with A5 symmetry. There is one self-dual regular form, the 5-simplex with 6 vertices. Each can
A5_polytope
Solid with 12 equal pentagonal faces
regular dodecahedron or pentagonal dodecahedron is a dodecahedron (a polyhedron with 12 faces) composed of regular pentagonal faces, three meeting at
Regular_dodecahedron
Kepler–Poinsot polyhedron
composed of 12 pentagonal faces (six pairs of parallel pentagons), intersecting each other making a pentagrammic path, with five pentagons meeting at each
Great_dodecahedron
geometry, the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells. Five tetrahedra
Snub_24-cell
Convex polytope of parenthesizations
In mathematics, an associahedron Kn is an (n − 2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening
Associahedron
In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube. Runcinated demihexeract Runcinated
Steric_6-cubes
seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex. There
Stericated_7-orthoplexes
Uniform polytope
In geometry, 1k2 polytope is a uniform polytope in n dimensions (n = k + 4) constructed from the En Coxeter group. The family was named by their Coxeter
Uniform_1_k2_polytope
Uniform polychoron
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge
Rectified_5-cell
In 4-dimensional geometry, there are 9 uniform polytopes with A4 symmetry. There is one self-dual regular form, the 5-cell with 5 vertices. A4 symmetry
A4_polytope
10-pointed star polygon
compound of 120-cell and 600-cell; that is, the compound of two pentagonal polytopes in their respective dual positions. {10/4} can be seen as the two-dimensional
Decagram_(geometry)
Isogonal polyhedron with regular faces
polyhedron is a 2-dimensional abstract polytope with a non-degenerate 3-dimensional realization. Here an abstract polytope is a poset of its "faces" satisfying
Uniform_polyhedron
PENTAGONAL POLYTOPE
PENTAGONAL POLYTOPE
PENTAGONAL POLYTOPE
PENTAGONAL POLYTOPE
Male
English
Fortress
Girl/Female
Indian
Someone Special
Boy/Male
Latin
Dark skinned.
Girl/Female
German, Swedish
Bright Angle
Girl/Female
Indian
Dedicated
Boy/Male
English
Surname and place name.
Boy/Male
Tamil
Devotee
Boy/Male
English
Famed; famous.
Girl/Female
Hindu, Indian
Laugh Love
Female
Hebrew
(×ֲבִיטַל) Hebrew name ABIYTAL means "my father is dew." In the bible, this is the name of one of David's wives.Â
PENTAGONAL POLYTOPE
PENTAGONAL POLYTOPE
PENTAGONAL POLYTOPE
PENTAGONAL POLYTOPE
PENTAGONAL POLYTOPE
n. pl.
A class of Echinodermata including the true starfishes. The rays vary in number and always have ambulacral grooves below. The body is star-shaped or pentagonal.
n.
A pentagon.
a.
Of or pertaining to plants of the order Pentagyna; having five styles.
a.
Heptagonal.
n.
A plane figure having five angles, and, consequently, five sides; any figure having five angles.
adv.
In the form of a pentagon; with five angles.
n.
The pentagonal dodecahedron, a common form of pyrite.
a.
Having seven angles or sides.
a.
Pentagonal.
a.
Having five corners or angles.