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Two tetrahedra joined by one face
A triangular bipyramid is a hexahedron, a polyhedron with six triangular faces. It is constructed by attaching two tetrahedra face-to-face. The same shape
Triangular_bipyramid
Triangular prism capped with tetrahedra
The elongated triangular bipyramid or elongated triangular dipyramid is a polyhedron constructed from a triangular prism by attaching two regular tetrahedra
Elongated triangular bipyramid
Elongated_triangular_bipyramid
Molecular structure with atoms at the center and vertices of a triangular bipyramid
trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular bipyramid. This is one
Trigonal bipyramidal molecular geometry
Trigonal_bipyramidal_molecular_geometry
Polyhedron formed by joining mirroring pyramids base-to-base
the base, for an n-gonal base forming n triangular faces in addition to the base face. An n-gonal bipyramid thus has 2n faces, 3n edges, and n + 2 vertices
Bipyramid
Two pentagonal pyramids fused base-to-base
A pentagonal bipyramid or pentagonal dipyramid is a polyhedron with ten triangular faces. It is constructed by attaching two pentagonal pyramids to each
Pentagonal_bipyramid
Prism with a 3-sided base
is a bipyramid, a polyhedron formed by fusing two pyramids base-to-base. In the case of a triangular prism, its dual is a triangular bipyramid, both
Triangular_prism
Convex polyhedron with 16 triangular faces
In geometry, the gyroelongated square bipyramid is a polyhedron with 16 triangular faces. it can be constructed from a square antiprism by attaching two
Gyroelongated square bipyramid
Gyroelongated_square_bipyramid
Polyhedron; 2 hexagonal pyramids joined base-to-base
A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices
Hexagonal_bipyramid
Polyhedron formed by capping an antiprism with pyramids
triangular faces, which are known as deltahedra: the gyroelongated square bipyramid and regular icosahedron. For a gyroelongated triangular bipyramid
Gyroelongated_bipyramid
Polyhedron made of equilateral triangles
of which can be considered the base. triangular bipyramid, regular octahedron, and pentagonal bipyramid; bipyramids with six, eight, and ten equilateral
Deltahedron
Convex polyhedron with regular faces
triangle faces. J12 Triangular bipyramid J13 Pentagonal bipyramid J17 Gyroelongated square bipyramid J51 Triaugmented triangular prism J84 Snub disphenoid
Johnson_solid
pairs of tetrahedra existing in the alternated gaps (instead of a triangular bipyramid). There are 1 + 3 + 1 = 5 edges meeting at a vertex, 3 hexagonal
Triangular prismatic honeycomb
Triangular_prismatic_honeycomb
Modular origami module
reconnected on the underside, resulting in two triangular pyramids joined at the base, a triangular bipyramid. A popular intermediate model is the triakis
Sonobe
hexecontahedron Bipyramid Triangular bipyramid, Pentagonal bipyramid, Hexagonal bipyramid, Heptagonal bipyramid, Octagonal bipyramid, Decagonal bipyramid Trapezohedron
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Polyhedron created by truncating a triangular bipyramid
truncated triangular bipyramid; however, that term is ambiguous, as it may also refer to polyhedra formed by truncating all five vertices of a triangular bipyramid
Triangular_bifrustum
Polyhedron formed by capping a prism with pyramids
elongated bipyramids that are Johnson solids: Elongated triangular bipyramid (J14), Elongated square bipyramid (J15), and Elongated pentagonal bipyramid (J16)
Elongated_bipyramid
Polyhedron with eight triangular faces
octahedron all of whose faces are quadrilaterals. Triangular bifrustum: The dual of an elongated triangular bipyramid (a Johnson solid), this can be realized with
Octahedron
Four-dimensional shape
tetrahedra, creating 8 tetrahedral cells, 16 triangular faces, 14 edges, and 6 vertices. A tetrahedral bipyramid can be seen as two tetrahedral pyramids augmented
Tetrahedral_bipyramid
Solid with four equal triangular faces
elongated triangular bipyramid are constructed by attaching one and two regular tetrahedra onto the bases of a triangular prism; the triangular bipyramid is
Regular_tetrahedron
Solid with eight equal triangular faces
faces are isosceles triangles, the regular octahedron becomes a square bipyramid. The regular octahedron is an example of many classifications as deltahedron
Regular_octahedron
Convex polytope of parenthesizations
Fullerene of fourteen carbon atoms C14" under "b) Base-truncated triangular bipyramid (Fig. 16)" a K5 polyhedron Loday, Jean-Louis (2012), "Dichotomy of
Associahedron
Fundamental color in color mixing
(a German mathematician, physicist, and astronomer) described a triangular bipyramid with red, yellow and blue at the 3 vertices in the same plane, white
Primary_color
Convex polyhedron with 12 triangular faces
snubification. The snub disphenoid may also be constructed from a triangular bipyramid, by cutting its two edges along the apices. These apices can be pushed
Snub_disphenoid
Truncated trapezohedron with a 3-sided base
In geometry, the truncated triangular trapezohedron is the first in an infinite series of truncated trapezohedra. It has 6 pentagon and 2 triangle faces
Truncated triangular trapezohedron
Truncated_triangular_trapezohedron
Four-dimensional analog of the icosahedron
the long diameter of a face-bonded pair of tetrahedral cells (a triangular bipyramid), and passes through the center of the shared face. As there are
600-cell
Square orthobicupola Square pyramid Triangular bipyramid Triangular cupola Triangular hebesphenorotunda Triangular orthobicupola Triaugmented dodecahedron
List_of_mathematical_shapes
Triangular prism capped with a tetrahedron
has the same connectivity as the original solid. Elongated triangular bipyramid – Triangular prism capped with tetrahedra Rajwade, A. R. (2001). Convex
Elongated_triangular_pyramid
Polytope made by turning a polytope's facets into pyramids
graph, the Kleetope of the triangular bipyramid, has six vertices added in the Kleetope construction and only five in the bipyramid from which it was formed
Kleetope
Shape with three equal sides
icosahedron, triangular bipyramid, pentagonal bipyramid, snub disphenoid, triaugmented triangular prism, and gyroelongated square bipyramid). The last five
Equilateral_triangle
solids, as well as dihedral symmetry families including the pyramids, bipyramids, prisms, antiprisms, and trapezohedrons. Notes: Polyhedra with different
List of small polyhedra by vertex count
List_of_small_polyhedra_by_vertex_count
4-D object; direct sum of a cube and a segment
pyramids, creating 12 square pyramidal cells, 30 triangular faces, 28 edges, and 10 vertices. A cubical bipyramid can be seen as two cubic pyramids augmented
Cubical_bipyramid
Solid with twenty equal triangular faces
names called bicapped pentagonal antiprism, or gyroelongated pentagonal bipyramid due to its construction process through gyroelongation—polyhedra construction
Regular_icosahedron
Shape with three sides
deltahedra. Antiprisms have alternating triangles on their sides. Pyramids and bipyramids are polyhedra with polygonal bases and triangles for lateral faces; the
Triangle
Arrangement of points on a sphere
regular tetrahedron. For N = 5, electrons reside at the vertices of a triangular bipyramid. For N = 6, electrons reside at vertices of a regular octahedron
Thomson_problem
Polyhedron with 6 faces
Image Name Triangular bipyramid Pentagonal pyramid Doubly truncated tetrahedron Features 5 vertices 9 edges 6 triangles 6 vertices 10 edges 4 triangles
Hexahedron
3D shape obtained by revolving a rhombus about one of its axes of symmetry
bipyramids: Bipyramid name Digonal bipyramid Triangular bipyramid Square bipyramid Pentagonal bipyramid Hexagonal bipyramid ... Apeirogonal bipyramid
Bicone
Cartesian product of two polytopes
D2d symmetry) but cannot be made uniform. The vertex figure is a triangular bipyramid. Like the duoantiprisms as alternated duoprisms, there is a set of
Duoprism
Cube capped by two square pyramids
In geometry, the elongated square bipyramid (or elongated octahedron) is the polyhedron constructed by attaching two equilateral square pyramids onto
Elongated_square_bipyramid
Polyhedron made by joining two identical frusta at their bases
symmetry, and also as a bipyramid with the two polar vertices truncated. They are duals to the family of elongated bipyramids. For a regular n-gonal bifrustum
Bifrustum
Polyhedron with regular congruent polygons as faces
congruent to the triangular sides), or the shape formed by joining two tetrahedra together (since although all faces of that triangular bipyramid would be equilateral
Regular_polyhedron
Number of stacked spheres in a pyramid
two consecutive triangular numbers. If a tetrahedron is reflected across one of its faces, the two copies form a triangular bipyramid. The square pyramidal
Square_pyramidal_number
Type of diamond that has not been cut
naturally occurring shapes, including octahedral (eight-sided bipyramid), cubic, and triangular (most commonly macles). A diamond or rough diamond can also
Rough_diamond
4-D polytope; direct sum of an icosahedron and a segment
tetrahedra, creating 40 tetrahedral cells, 80 triangular faces, 54 edges, and 14 vertices. An icosahedral bipyramid can be seen as two icosahedral pyramids
Icosahedral_bipyramid
Field of mathematics dealing with three-dimensional Euclidean spaces
two bases square antiprism Bipyramid A polyhedron comprising an n-sided polygonal center with two apexes. triangular bipyramid Trapezohedron A polyhedron
Solid_geometry
Convex polyhedron with 14 triangle faces
icosahedron, pentagonal bipyramid, snub disphenoid, and gyroelongated square bipyramid. The dual polyhedron of the triaugmented triangular prism has a face for
Triaugmented_triangular_prism
Construction in group theory
Geometrically, this can be visualized as the rotation group of the triangular bipyramid, which is isomorphic to the dihedral group of the triangle D3 ≅ S3;
Projective_linear_group
Polyhedron with 6 congruent rhombus faces
since a square is a special case of a rhombus. A gyroelongated triangular bipyramid constructed with equilateral triangles can also be seen as a trigonal
Trigonal_trapezohedron
16th Johnson solid; pentagonal prism capped by pyramids
In geometry, the elongated pentagonal bipyramid or bicapped pentagonal prism is a polyhedron constructed by attaching two pentagonal pyramids onto the
Elongated pentagonal bipyramid
Elongated_pentagonal_bipyramid
Concept in three-dimensional geometry
approximant structure packs denser than this double lattice of triangular bipyramids when tetrahedra are slightly rounded (the Minkowski sum of a tetrahedron
Tetrahedron_packing
Type of polyhedron
In geometry, a rectified prism (also rectified bipyramid) is one of an infinite set of polyhedra, constructed as a rectification of an n-gonal prism,
Rectified_prism
conic Triangle group Triangle inequality Triangular bipyramid Triangular prism Triangular pyramid Triangular tiling Triangulation Trilinear coordinates
List_of_triangle_topics
polytopes in dimension three: tetrahedron square pyramid triangular prism triangular bipyramid The following list of projectively unique 4-polytopes was
Projectively_unique_polytope
Spatial tiling of convex uniform polyhedra
is the cubic, shown above.) The vertex figure of each is an irregular bipyramid whose faces are isosceles triangles. There are only 3 unique honeycombs
Convex_uniform_honeycomb
Materials made only out of carbon
of eight carbon atoms, with the shape of an elongated triangular bipyramid—a six-atom triangular prism with two more atoms above and below its bases. Protomene:
Allotropes_of_carbon
Conic solid with a polygonal base
the apex and the (n − 1)-dimensional hyperplane containing the base A. Bipyramid Cajori, Florian (1991), History of Mathematics (5th ed.), American Mathematical
Pyramid_(geometry)
Four-dimensional analogue of the tetrahedron
The A2 Coxeter plane projection of the regular 5-cell is that of a triangular bipyramid (two tetrahedra joined face-to-face) with the two opposite vertices
5-cell
Polyhedron with 20 faces
19 triangular faces and a 19-gon base A prism with 18 lateral faces and 2 18-gon bases An antiprism with a nine-sided polygonal base A bipyramid with
Icosahedron
Convex polyhedron whose faces are almost regular polygons
Tetratetrahedron, triangulated tetrahedron Augmented triangular cupola Triangulated truncated triangular bipyramid Edge-contracted icosahedron Hexagonal prism
Near-miss_Johnson_solid
Polyhedron with 12 faces
the center of their base, the bipyramid has D6h symmetry of order 24. Like any other bipyramids, the hexagonal bipyramid is face-transitive and the dual
Dodecahedron
American mathematician
solution of the 5-electron case of J. J. Thomson's 1904 problem: The triangular bipyramid is the configuration of 5 electrons on the sphere that minimizes
Richard Schwartz (mathematician)
Richard_Schwartz_(mathematician)
Convex polyhedron that fills space isohedrally
Catoptric cells Faces 4 5 6 8 12 Type Tetrahedra Square pyramid Triangular bipyramid Cube Octahedron Rhombic dodecahedron Images 1/48 (1) 1/24 (2) 1/12
Stereohedron
Any of 4 regular star polyhedra
dodecahedron: constructed from a great dodecahedron with twenty asymmetric triangular bipyramids, attaching to the hollow between the wedges. John Conway introduces
Kepler–Poinsot_polyhedron
Geometric operation on a regular polytope
notation eP3 eA4 eaO = eaC eaI = eaD Polyhedra to be expanded Triangular prism or triangular bipyramid Square antiprism or tetragonal trapezohedron Cuboctahedron
Cantellation_(geometry)
Space-filling tessellation
ditrigonal trapezoprisms). Its vertex figure is a C2v-symmetric triangular bipyramid. This honeycomb can then be alternated to produce another nonuniform
Bitruncated_cubic_honeycomb
Quasiregular space-filling tesselation
the voids create triangular bipyramids which can be divided into pairs of tetrahedra of this honeycomb. This honeycomb with bipyramids is called a
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
Isogonal polyhedron with regular faces
hexagonal bipyramid and alternately colored triangles on a sphere: There are 16 fundamental triangles, visible in the faces of the octagonal bipyramid and alternately
Uniform_polyhedron
Four-dimensional geometrical object
C2v symmetry), and 240 vertices. Its vertex figure is an irregular triangular bipyramid. Vertex figure This polychoron can then be alternated to produce
Runcinated_5-cell
Only regular space-filling tessellation of the cube
tetragonal disphenoids) from the cubes, and two tetrahedra from the triangular bipyramids. Wikimedia Commons has media related to Cubic honeycomb. Architectonic
Cubic_honeycomb
Tiling of hyperbolic 3-space by uniform polyhedra
exists as Vinberg polytope fundamental domains, including these triangular bipyramid fundamental domains (double tetrahedra) as rank 5 graphs including
Uniform honeycombs in hyperbolic space
Uniform_honeycombs_in_hyperbolic_space
nonzero sign and three points with the other sign represents the triangular bipyramid. In general, the number of distinct Gale diagrams with n = d + 2
Gale_diagram
configuration, or for masses forming a triangular bipyramid, with the three masses in the central triangle of the bipyramid also forming a central configuration
Central_configuration
Polyhedron with 9 faces
attaching an equilateral square pyramid to the face of a cube. Elongated triangular bipyramid: a Johnson solid with six equilateral triangles and three squares
Enneahedron
symmetry), and 2304 vertices. Its vertex figure is an irregular triangular bipyramid. Vertex figure This polychoron can then be alternated to produce
Runcinated_24-cells
Uniform Euclidean 3D tessellations and their duals
(Cantellated cubic honeycomb) Wedge Quarter oblate octahedrille irr. Triangular bipyramid , , J16 A3 W2 G28 t1,2δ4 bc [[4,3,4]] Truncated octahedrille (Bitruncated
Architectonic and catoptric tessellation
Architectonic_and_catoptric_tessellation
Polytope whose facets are all simplices
polyhedron, the polytope contains only triangular faces of any type. These polyhedra include bipyramids, gyroelongated bipyramids, deltahedra (wherein the faces
Simplicial_polytope
Polyhedron made by truncating one end of a trapezohedron
to form half of a hexagram. Elongated pyramid Gyroelongated bipyramid Elongated bipyramid Gyroelongated pyramid "Chestahedron Geometry". The Art & Science
Diminished_trapezohedron
a Blind polytope. Two copies can be augmented to make an icosahedral bipyramid which is also a Blind Polytope. The regular 600-cell has icosahedral pyramids
Icosahedral_pyramid
Two tetrahedra crossing each other
whether the triangular faces of the two crossing tetrahedra are considered as faces themselves or whether they are subdivided into smaller triangular faces
Stellated_octahedron
4-D polyhedral pyramid
is a Blind polytope. Two copies can be augmented to make an octahedral bipyramid which is also a Blind polytope. The regular 16-cell has octahedral pyramids
Octahedral_pyramid
Topics referred to by the same term
Navy Chanel J12, a Swiss-made watch County Route J12 (California) Triangular bipyramid, a Johnson solid (J12) Marlboro Pike Line, a bus route in the Washington
J12
Topics referred to by the same term
numbered J14, a bus route in Chicago Bacterial pneumonia Elongated triangular bipyramid, a Johnson solid (J14) This disambiguation page lists articles associated
J14
7-coordinate molecular geometry
heptacoordinate transition metal complexes, along with the pentagonal bipyramid and the capped trigonal prism. Examples of the capped octahedral molecular
Capped octahedral molecular geometry
Capped_octahedral_molecular_geometry
Geometric prism
triangular prisms. Octahedral dyadic prism (Norman W. Johnson) Ope (Jonathan Bowers, for octahedral prism) Triangular antiprismatic prism Triangular antiprismatic
Octahedral_prism
Four-dimensional analog of the octahedron
is bounded by 16 cells, all of which are regular tetrahedra. It has 32 triangular faces, 24 edges, and 8 vertices. The 24 edges bound 6 orthogonal central
16-cell
Uniform 4-polytope bounded by 320 cells
tetrahedra with two new regular tetrahedra (representing a non-corealmic triangular bipyramid) created at the deleted vertices. This is the only uniform solution
Grand_antiprism
Spherical polyhedron composed of lunes
lune into two spherical triangles creates an n {\displaystyle n} -gonal bipyramid, which represents the dihedral symmetry D n h {\displaystyle D_{nh}}
Hosohedron
honeycomb walls are removed, joining pairs of square pyramids into square bipyramids (octahedra). Its vertex and edge framework is identical to the hexakis
Tetragonal disphenoid honeycomb
Tetragonal_disphenoid_honeycomb
Polyhedron formed by capping an antiprism with a pyramid
constructed allowing for isosceles triangles. Gyroelongated bipyramid Elongated bipyramid Elongated pyramid Diminished trapezohedron Rajwade, A. R. (2001)
Gyroelongated_pyramid
Chemical compound
to carbonium ions, or those five hydrogen atoms are arranged in a triangular bipyramid structure around the nitrogen atom. A compound that is similar to
Nitrogen_pentahydride
Polyhedron formed by capping a prism with a pyramid
can be constructed with isosceles triangles. Gyroelongated bipyramid Elongated bipyramid Gyroelongated pyramid Diminished trapezohedron Norman W. Johnson
Elongated_pyramid
Prism with a 6-sided base
across a horizontal plane. The dual of a hexagonal prism is a hexagonal bipyramid, both of which have the same three-dimensional symmetry group. As in most
Hexagonal_prism
Polyhedron with 14 faces
pentagons) Tetradecahedra having at least one irregular face: Heptagonal bipyramid (14 triangles) (see Dipyramid) Heptagonal trapezohedron (14 kites) (see
Tetradecahedron
Space-filling polyhedron with 8 faces
polyhedron Elongated square bipyramid, a space-filling Johnson solid Trapezo-rhombic dodecahedron, a space-filling dual of triangular orthobicupola Rich, Anthony
Elongated_gyrobifastigium
Solid with 2 parallel n-gonal bases connected by n parallelograms
joining faces are rectangular. The dual of a right n-prism is a right n-bipyramid. A right prism (with rectangular sides) with regular n-gon bases has Schläfli
Prism_(geometry)
Pyramid with a pentagon base
{\displaystyle J_{11}} , a pentagonal bipyramid J 13 {\displaystyle J_{13}} , an elongated pentagonal bipyramid J 16 {\displaystyle J_{16}} , an augmented
Pentagonal_pyramid
Uniform polychoron
24-cell, this shape and its dual (a polytope with ten vertices and ten triangular bipyramid facets) was one of the first 2-simple 2-simplicial 4-polytopes known
Rectified_5-cell
Discrete subgroup in geometry
the regular pentagon, heptagon, and nonagon and the equilateral triangular bipyramid. Włodzimierz Kuperberg and Greg Kuperberg showed that all convex
Double_lattice
pentagonal bipyramid is not a stacked polytope, because if it is formed by gluing tetrahedra together, the last tetrahedron will be glued to two triangular faces
Stacked_polytope
Uniform 4-polytope
has 6 polyhedral cells: 2 tetrahedra connected by 4 triangular prisms. It has 14 faces: 8 triangular and 6 square. It has 16 edges and 8 vertices. It is
Tetrahedral_prism
Pyramid with a square base
elongated square bipyramid J 15 {\displaystyle J_{15}} , gyroelongated square bipyramid J 17 {\displaystyle J_{17}} , augmented triangular prism J 49 {\displaystyle
Square_pyramid
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