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Polyhedron with four faces
3-orthoscheme is not a disphenoid, because its opposite edges are not of equal length. It is not possible to construct a disphenoid with right triangle or
Tetrahedron
Tetrahedron whose faces are all congruent
In geometry, a disphenoid (from Greek sphenoeides 'wedgelike') is a tetrahedron whose four faces are congruent acute-angled triangles. It can also be described
Disphenoid
Convex polyhedron with 12 triangular faces
In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid.
Snub_disphenoid
The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of identical tetragonal disphenoidal
Tetragonal disphenoid honeycomb
Tetragonal_disphenoid_honeycomb
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
Polyhedron with 12 faces
one pentagon, and one decagon. It is C5v symmetry of order 10. Snub disphenoid: both Johnson solid and deltahedron, consisting of twelve equilateral
Dodecahedron
Polyhedron made of equilateral triangles
a triangular prism, such that it has fourteen triangular faces. snub disphenoid, with twelve triangular faces, constructed by involving two regular hexagons
Deltahedron
Only regular space-filling tessellation of the cube
called a disphenoid tetrahedral honeycomb. Although a regular tetrahedron can not tessellate space alone, this dual has identical disphenoid tetrahedron
Cubic_honeycomb
Four-sided polygon
The (red) side edges of tetragonal disphenoid represent a regular zig-zag skew quadrilateral.
Quadrilateral
Space-filling tessellation
called a disphenoid tetrahedral honeycomb. Although a regular tetrahedron can not tessellate space alone, this dual has identical disphenoid tetrahedron
Bitruncated_cubic_honeycomb
parabidiminished rhombicosidodecahedron, tridiminished rhombicosidodecahedron, snub disphenoid, snub square antiprism, sphenocorona, sphenomegacorona, hebesphenomegacorona
List_of_Johnson_solids
Pentagonal orthocupolarotunda Pentagonal pyramid Pentagonal rotunda Snub disphenoid Snub square antiprism Sphenocorona Sphenomegacorona Square cupola Square
List_of_mathematical_shapes
N-dimensional gradient noise function
of the triangular tiling, but whereas 3D Simplex uses the tetragonal disphenoid honeycomb, 3D OpenSimplex uses the tetrahedral-octahedral honeycomb. OpenSimplex
OpenSimplex_noise
Space-filling polyhedron with 8 faces
pitches. The elongated gyrobifastigium is the dual polyhedron of a snub disphenoid,[citation needed] one of 92 Johnson solids, sharing the same three-dimensional
Elongated_gyrobifastigium
Construction for n-dimensional noise functions
tiling in the 3D case of the function is an orientation of the tetragonal disphenoid honeycomb. Simplex noise is useful for computer graphics applications
Simplex_noise
Shape with three equal sides
the 92 Johnson solids (triangular bipyramid, pentagonal bipyramid, snub disphenoid, triaugmented triangular prism, and gyroelongated square bipyramid). More
Equilateral_triangle
Copper iron sulfide mineral
may have iridescent purplish tarnish. Crystal habit Predominantly the disphenoid and resembles a tetrahedron, commonly massive, and sometimes botryoidal
Chalcopyrite
Topics referred to by the same term
tetrahedral and octahedral cells Tetragonal disphenoid honeycomb - Uniform dual honeycomb with tetragonal disphenoid cells Phyllic disphenoidal honeycomb -
Tetrahedral_honeycomb
honeycomb, , has truncated hexagonal tiling cells, with a tetragonal disphenoid vertex figure. The cantellated triangular tiling honeycomb, , has rhombitrihexagonal
Triangular_tiling_honeycomb
Operation in topology
The join of two line segments is homeomorphic to a solid tetrahedron or disphenoid, illustrated in the figure above right (m=n=1). The join of a point and
Join_(topology)
Electron counting rules
Octahedron 7 Pentagonal bipyramid 8 D2d (trigonal) dodecahedron (snub disphenoid) 9 Tricapped trigonal prism 10 Bicapped square antiprismatic molecular
Polyhedral skeletal electron pair theory
Polyhedral_skeletal_electron_pair_theory
Quasiregular space-filling tesselation
all four A3 lattices, and is identical to the vertex arrangement of the disphenoid tetrahedral honeycomb, dual honeycomb of the uniform bitruncated cubic
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
(geometry), hemi-octahedron, hemi-dodecahedron, hemi-icosahedron Tetrahedron Disphenoid Pentahedron Square pyramid, Triangular prism Hexahedron Parallelepiped
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
ligands are arranged around a central atom defining the vertices of a snub disphenoid (also known as a trigonal dodecahedron). This shape has D2d symmetry and
Dodecahedral molecular geometry
Dodecahedral_molecular_geometry
Convex polyhedron with regular faces
Snub polyhedra 84 Snub disphenoid 85 Snub square antiprism
Johnson_solid
Uniform Euclidean 3D tessellations and their duals
octahedrille (Bitruncated cubic honeycomb) Tetragonal disphenoid Oblate tetrahedrille Tetragonal disphenoid J17 A18 W13 G25 t0,1,2δ4 nc [4,3,4] n-tCO-trille
Architectonic and catoptric tessellation
Architectonic_and_catoptric_tessellation
Isohedral and isogonal polyhedron
that is, the five Platonic solids and the four Kepler–Poinsot polyhedra. Disphenoid tetrahedra. Crown polyhedra, also known as stephanoid polyhedra. A variety
Noble_polyhedron
Regular tiling of hyperbolic 3-space
dodecahedral honeycomb, , has truncated icosahedron cells, with a tetragonal disphenoid vertex figure. The cantellated order-5 dodecahedral honeycomb, , has
Order-5 dodecahedral honeycomb
Order-5_dodecahedral_honeycomb
Archimedean solid with 8 faces
version of the truncated tetrahedron, interpreted as a truncated tetragonal disphenoid with its three-dimensional symmetry group as the dihedral group D 2 d
Truncated_tetrahedron
tetragonal disphenoid (v:4; e:2+4; f:4) Rhombic disphenoid (v:4; e:2+2+2; f:4) Digonal disphenoid (v:2+2; e:4+1+1; f:2+2) Phyllic disphenoid (v:2+2; e:2+2+1+1;
Configuration_(polytope)
Polytope whose facets are all simplices
4-polytope 4-simplex, 16-cell, 600-cell Dual convex uniform honeycombs: Disphenoid tetrahedral honeycomb Dual of cantitruncated cubic honeycomb Dual of omnitruncated
Simplicial_polytope
Marked objects for finding random numbers
faces: any multiple of 4 (so that a facet faces up), starting from 8 Disphenoids, an infinite set of tetrahedra made from congruent non-regular triangles:
Dice
Notation for polytopes and tessellations
can be represented as ( ) ∨ { } = ( ) ∨ [( ) ∨ ( )]. In 3D: A digonal disphenoid can be represented as { } ∨ { } = [( ) ∨ ( )] ∨ [( ) ∨ ( )]. A p-gonal
Schläfli_symbol
Triakis tetrahedron Elongated triangular bipyramid Gyrobifastigium Snub disphenoid Biaugmented triangular prism 9 Triangular cupola Triaugmented triangular
List of small polyhedra by vertex count
List_of_small_polyhedra_by_vertex_count
Three-dimensional geometric shape
polyhedron connecting six tetrahedra (or disphenoids) on opposite edges into a cycle. If the faces of the disphenoids are equilateral triangles, it can be
Kaleidocycle
Four-dimensional geometric object with flat sides
convex dual uniform honeycombs, including: Rhombic dodecahedral honeycomb Disphenoid tetrahedral honeycomb Others: Weaire–Phelan structure periodic space-filling
4-polytope
Regular paracompact honeycomb
has truncated tetrahedron and hexagonal tiling cells, with a digonal disphenoid vertex figure. The cantellated hexagonal tiling honeycomb, t0,2{6,3,3}
Hexagonal_tiling_honeycomb
It is also known as the cyclic polytope C(6,4). It has 9 tetragonal disphenoid cells, 18 triangular faces, 15 edges, and 6 vertices. It can be seen in
3-3_duoprism
Tetrahedron where all pairs of opposite edges are perpendicular
and s = 1 2 ( a + b + c ) {\displaystyle s={\tfrac {1}{2}}(a+b+c)} . Disphenoid Trirectangular tetrahedron Court, N. A. (October 1934), "Notes on the
Orthocentric_tetrahedron
Solid with eight equal triangular faces
three polyhedra with this property are the pentagonal dipyramid, the snub disphenoid, and an irregular polyhedron with 12 vertices and 20 triangular faces
Regular_octahedron
Polyhedron sliced by a plane into other polyhedra
parabidiminished rhombicosidodecahedron, tridiminished rhombicosidodecahedron, snub disphenoid, snub square antiprism, sphenocorona, sphenomegacorona, hebesphenomegacorona
Composite_polyhedron
Polyhedron formed by joining mirroring pyramids base-to-base
and merging these into four congruent isosceles triangles makes it a disphenoid; for z > 1, it is concave. If the 2n-gon base is both isotoxal in-out
Bipyramid
Polyhedron resulting from the snub operation
parabireplenished great icosahedron. Two Johnson solids are snub polyhedra: the snub disphenoid and the snub square antiprism. Neither is chiral. Coxeter, Harold Scott
Snub_polyhedron
Solid with 10 faces
replacing both squares of a square antiprism with a square pyramid. The snub disphenoid (J84) is another deltahedron, constructed by replacing the two squares
Square_antiprism
Honeycomb made from unique polyhedrons
honeycomb, constructed from truncated icosidodecahedron cells, in a rhombic disphenoid vertex figure. It has a Coxeter diagram . Perspective view from center
Dodecahedral-icosahedral honeycomb
Dodecahedral-icosahedral_honeycomb
Graph with equal-size maximal independent sets
graphs of the regular octahedron, the pentagonal dipyramid, the snub disphenoid, and an irregular polyhedron (a nonconvex deltahedron) with 12 vertices
Well-covered_graph
Generalisation of dice with identical faces
Convex Coplanar Nonconvex 4 V33 Platonic tetrahedron tetragonal disphenoid rhombic disphenoid Td, [3,3], (*332) D2d, [2+,2], (2*) D2, [2,2]+, (222) 24 4 4
Isohedral_figure
Regular tiling of hyperbolic 3-space
honeycomb, t1,2{3,5,3}, , has truncated dodecahedron cells with a tetragonal disphenoid vertex figure. The cantellated icosahedral honeycomb, t0,2{3,5,3}, , has
Icosahedral_honeycomb
Two pentagonal pyramids fused base-to-base
four-connected simplicial graphs like the regular octahedron, the snub disphenoid, and an irregular polyhedron with twelve vertices and twenty triangular
Pentagonal_bipyramid
Cartesian product of two polytopes
Faces pq squares, p q-gons, q p-gons Edges 2pq Vertices pq Vertex figure disphenoid Symmetry [p,2,q], order 4pq Dual p-q duopyramid Properties convex, vertex-uniform
Duoprism
Polytope constructed from two orthogonal polytopes
polychoron Schläfli symbol {p} + {q} Coxeter diagram Cells pq digonal disphenoids Faces 2pq triangles Edges pq+p+q Vertices p+q Vertex figures p-gonal
Duopyramid
has hexagonal tiling and truncated icosahedron facets, with a digonal disphenoid vertex figure. The cantellated order-5 hexagonal tiling honeycomb, t0
Order-5 hexagonal tiling honeycomb
Order-5_hexagonal_tiling_honeycomb
truncated trihexagonal tiling and dodecagonal prism cells, with a phyllic disphenoid vertex figure. The alternated order-6 hexagonal tiling honeycomb is a
Order-6 hexagonal tiling honeycomb
Order-6_hexagonal_tiling_honeycomb
Polytope constructed from alternation of a hypercube
be stretched with different lengths in n-axes of symmetry. The rhombic disphenoid is the three-dimensional example as alternated cuboid. It has three sets
Demihypercube
Edge-joined polygon with multiple principle shapes
tetrahedron gyroelongated square bipyramid (J17) 37 tetrahedron snub disphenoid (J84) Cube tetramonohedron Cube 1x1x7 and 1x3x3 cuboids cube non-regular
Common_net
Polygonal chain whose vertices are not all coplanar
The red edges of this tetragonal disphenoid represent a regular zig-zag skew quadrilateral.
Skew_polygon
Classification system for symmetry groups in geometry
[2+,4], relating the symmetry of the regular tetrahedron and tetragonal disphenoid. For rank 3 Coxeter groups, [p,3], there is a trionic subgroup [p,3⅄]
Coxeter_notation
cells: 48 cubes, 144 square antiprisms, 288 tetrahedra (as tetragonal disphenoids), and 384 vertices. Its vertex figure is a hexakis triangular cupola
Truncated_24-cells
dual of a 3-4 duoprism is called a 3-4 duopyramid. It has 12 digonal disphenoid cells, 24 isosceles triangular faces, 12 edges, and 7 vertices. Polytope
3-4_duoprism
Type of tesseract
120 32 {3} 24 {4} 64 {6} Edges 192 Vertices 96 Vertex figure Digonal disphenoid Symmetry group B4, [3,3,4], order 384 D4, [31,1,1], order 192 Properties
Truncated_tesseract
Term used in chemistry
the term generally used, the correct term is "bisdisphenoid" or "snub disphenoid" as this polyhedron is a deltahedron) [Mo(CN)8]4− in K4[Mo(CN)8]·2H2O
Coordination_geometry
Existence of geodesic circles on surfaces
have simple closed geodesics (for instance, the regular tetrahedron and disphenoids have infinitely many closed geodesics, all simple) others do not. In
Theorem of the three geodesics
Theorem_of_the_three_geodesics
Topics referred to by the same term
Class J84, a British locomotive class designed by Thomas Wheatley Snub disphenoid (Johnson solid J84) South Observatory (obsevatory code J84), Clanfield
J84
Space-filling tessellation
tetrahedra, and each adjoined to the adjacent truncated tetrahedral cells. Disphenoid tetrahedral honeycomb Föppl, L. (1914). "Der Fundamentalbereich des Diamantgitters"
Triakis truncated tetrahedral honeycomb
Triakis_truncated_tetrahedral_honeycomb
Spatial tiling of convex uniform polyhedra
O16 bitruncated cubic (batch) t1,2{4,3,4} 2t{4,3,4} (4) (4.6.6) (disphenoid) Oblate tetrahedrille J19 A22 W18 G27 t0,1,2,3δ4 O20 omnitruncated cubic
Convex_uniform_honeycomb
Polyhedron; 2 hexagonal pyramids joined base-to-base
trapezohedron A similar 12-sided polyhedron with a twist and kite faces. Snub disphenoid Another 12-sided polyhedron with 2-fold symmetry and only triangular faces
Hexagonal_bipyramid
cells, in a rhombic disphenoid vertex figure. It has a Coxeter diagram with [2,2]+ (order 4) extended symmetry in its rhombic disphenoid vertex figure. Perspective
Cubic-octahedral_honeycomb
Triangular prism attached by two square pyramids
metal other than the chemical structure of square antiprism and the snub disphenoid. Examples of the structure are plutonium tribromide PuBr3 adopted by bromides
Biaugmented_triangular_prism
Class of 4-dimensional polytopes
polygons. A duoprism's Coxeter-Dynkin diagram is . Its vertex figure is a disphenoid tetrahedron, . This family overlaps with the first: when one of the two
Uniform_4-polytope
Convex polyhedron with 14 triangle faces
the regular octahedron, regular icosahedron, pentagonal bipyramid, snub disphenoid, and gyroelongated square bipyramid. The dual polyhedron of the triaugmented
Triaugmented_triangular_prism
triangular antiprisms) from the hexagonal prisms, tetrahedra (as tetragonal disphenoids) from the cubes, and two tetrahedra from the triangular bipyramids. The
Triangular prismatic honeycomb
Triangular_prismatic_honeycomb
honeycomb, t1,2{4,4,4}, has truncated square tiling facets, with a tetragonal disphenoid vertex figure. The cantellated order-4 square tiling honeycomb, is the
Order-4 square tiling honeycomb
Order-4_square_tiling_honeycomb
antiprisms, 40 triangular antipodiums), 30 tetrahedra (as tetragonal disphenoids), and 60 vertices. Its vertex figure is a shape topologically equivalent
Cantellated_5-cell
Regular tiling of hyperbolic 3-space
truncated octahedron and truncated icosahedron cells, with a digonal disphenoid vertex figure. The cantellated order-4 dodecahedral honeycomb, , has
Order-4 dodecahedral honeycomb
Order-4_dodecahedral_honeycomb
20 octahedra (as triangular antiprisms), 30 tetrahedra (as tetragonal disphenoids), and 40 vertices. Its vertex figure is a hexakis triangular cupola.
Truncated_5-cell
Geometric figure
antiprism, with 2 regular tetrahedron, 8 triangular pyramid, and 6 tetragonal disphenoid cells, defining 2 5-cell, 8 truncated 5-cell, and 6 bitruncated 5-cell
5-cell_honeycomb
Geometric operation applied to a polyhedron
This definition is used in the naming of two Johnson solids: the snub disphenoid and the snub square antiprism, and of higher dimensional polytopes, such
Snub_(geometry)
Four-dimensional geometrical object
symmetry), three kinds of 210 tetrahedra (30 tetragonal disphenoids, 60 phyllic disphenoids, and 120 irregular tetrahedra), and 120 vertices. It has
Runcinated_5-cell
Concept in three-dimensional geometry
However, the more recent results have shown that this is not the case. Disphenoid tetrahedral honeycomb - an isohedral tessellation of 3-space by irregular
Tetrahedron_packing
Characterizes spherical triangles with fixed base and area
congruent, and together form a spherical disphenoid A B C D {\displaystyle ABCD} (the central projection of a disphenoid onto a concentric sphere). The eight
Lexell's_theorem
3-dimensional geometric figure
example of a flexible polyhedron, constructed by connecting six tetragonal disphenoids on opposite edges into a cycle. This polyhedron can twist continuously
Flexible_polyhedron
cubic subgroup structure shown is based on extending symmetry of the tetragonal disphenoid fundamental domain of space group 216, similar to the square
Fibrifold
antiprisms), three kinds of 2016 tetrahedra (288 tetragonal disphenoids, 576 phyllic disphenoids, and 1152 irregular tetrahedra), and 1152 vertices. It has
Runcinated_24-cells
has truncated octahedron and hexagonal tiling cells, with a digonal disphenoid vertex figure. The cantellated order-4 hexagonal tiling honeycomb, t0
Order-4 hexagonal tiling honeycomb
Order-4_hexagonal_tiling_honeycomb
Type of 7-polytope
12 cube face diagonals in light green, and 4 full diagonals in red. This partition can be considered a tetradisphenoid, or a join of two disphenoid.
7-simplex
has truncated cube and truncated square tiling facets, with a digonal disphenoid vertex figure. The cantellated square tiling honeycomb, rr{4,4,3}, has
Square_tiling_honeycomb
Tetrahedron whose edge lengths, face areas and volume are all integers
many Heronian tetrahedra, and more strongly infinitely many Heronian disphenoids, tetrahedra in which all faces are congruent and each pair of opposite
Heronian_tetrahedron
octahedra (as triangular antipodiums), 288 tetrahedra (as tetragonal disphenoids), and 576 vertices. Its vertex figure is a shape topologically equivalent
Cantellated_24-cells
Uniform polytope
E7/A3A2 = 72·8!/4!/3! = 20160 A3A1A1 4 6 4 * 30240 0 2 2 1 4 1 2 2 Phyllic disphenoid E7/A3A1A1 = 72·8!/4!/2/2 = 30240 A4A2 {3,3,3} f4 5 10 10 5 0 4032 * *
1_32_polytope
Uniform 4-polytope
icosahedra, and 600 truncated tetrahedra. Its vertex figure is a digonal disphenoid, with two truncated icosahedra and two truncated tetrahedra around it
Truncated_120-cells
DISPHENOID
DISPHENOID
DISPHENOID
DISPHENOID
Boy/Male
Australian, Greek
Helper and Defender of Mankind; Form of Alexander
Girl/Female
Danish, French, German, Latin, Swedish
Warlike; Dedicated to Mars; Female Version of Marcellus
Boy/Male
Australian, British, English, Gaelic, Scottish
Place Name of a Village in Northeastern Scotland; Used as a First Name Since the 19th Century
Girl/Female
Tamil
Cute, Gem, Joyous song
Boy/Male
Gujarati, Hindu, Indian
Power of Intellect
Boy/Male
Hindu
Devoted girl
Girl/Female
Indian
Ichchha
Female
English
English pet form of Latin Euphemia, EFFIE means "Well I speak."
Girl/Female
Tamil
Hema Malini | ஹேமா மாலிநீÂ
Golden, Beautiful
Male
Romanian
(Bulgarian Гаврил): Bulgarian and Romanian form of Greek Gabriēl, GAVRIL means "man of God" or "warrior of God."
DISPHENOID
DISPHENOID
DISPHENOID
DISPHENOID
DISPHENOID