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Catalan solid with 12 faces
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan
Rhombic_dodecahedron
Polyhedron with 12 faces
symmetry. The rhombic dodecahedron can be seen as a limiting case of the pyritohedron, and it has octahedral symmetry. The elongated dodecahedron and trapezo-rhombic
Dodecahedron
Catalan solid with 30 faces
solids, the cuboctahedron, the icosidodecahedron, and the rhombic dodecahedron. The rhombic triacontahedron is also interesting in that its vertices include
Rhombic_triacontahedron
Catalan solid with 48 faces
augmented rhombic dodecahedron. Replacing each face of the rhombic dodecahedron with a flat pyramid results in the Kleetope of the rhombic dodecahedron, which
Disdyakis_dodecahedron
Polyhedron with 6 rhombic and 6 trapezoidal faces
In geometry, the trapezo-rhombic dodecahedron or rhombo-trapezoidal dodecahedron is a convex dodecahedron with 6 rhombic and 6 trapezoidal faces. It has
Trapezo-rhombic_dodecahedron
Polyhedron with 8 rhombic and 4 hexagonal faces
elongated dodecahedron, elongated rhombic dodecahedron, extended rhombic dodecahedron, rhombo-hexagonal dodecahedron or hexarhombic dodecahedron is a convex
Elongated_dodecahedron
Polyhedron with 12 congruent golden rhombus faces
dodecahedron is a convex polyhedron with twelve congruent golden rhombus faces. It has the same topology as the face-transitive rhombic dodecahedron,
Bilinski_dodecahedron
Self-intersecting polyhedron with 12 faces
the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation of the rhombic dodecahedron
First stellation of the rhombic dodecahedron
First_stellation_of_the_rhombic_dodecahedron
Goldberg polyhedron with 42 faces
pentagons and 20 hexagons) looks similar to the uniform chamfered dodecahedron (truncated rhombic triacontahedron), which has 42 faces (12 pentagons and 30 hexagons)
Chamfered_dodecahedron
Geometric operation which truncates the edges of polyhedra
tritruncated rhombic dodecahedron: from a regular octahedron by chamfering, or by truncating the eight order-3 vertices of the rhombic dodecahedron, which become
Chamfer_(geometry)
stellations), as well as for select Catalan solids (e.g., the rhombic dodecahedron and the rhombic triacontahedron). Stellations of non-convex uniform polyhedra
List of polyhedral stellations
List_of_polyhedral_stellations
Solid with 12 equal pentagonal faces
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron (a polyhedron with 12 faces) composed of regular pentagonal faces, three meeting at
Regular_dodecahedron
Topics referred to by the same term
the rhombic dodecahedron or the rhombic triacontahedron or the rhombic dodecahedral honeycomb or the rhombic icosahedron or the rhombic hexecontahedron
Rhombic
Polyhedral mechanical puzzle toy
puzzle. stellated rhombic dodecahedron 2×2×2 cube form of Yoshimoto Cube STL model of the first stellation of the rhombic dodecahedron decomposed into pyramids
Yoshimoto_Cube
connected. Its dual polyhedron is a rhombic hemi-dodecahedron which has 7 vertices (1-7), 12 edges (a-l), and 6 rhombic faces (A-F). It has a real presentation
Hemi-cuboctahedron
In geometry, a diminished rhombic dodecahedron is a rhombic dodecahedron with one or more vertices removed. This article describes diminishing one 4-valence
Diminished rhombic dodecahedron
Diminished_rhombic_dodecahedron
Polyhedron that tiles space by translation
crystallographic systems. They are the cube, hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron. Each parallelohedron is centrally
Parallelohedron
Polyhedron with six rhombi as faces
In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a special case of a parallelepiped in which all six faces
Rhombohedron
Convex polyhedron projected from hypercube
cube), hexagonal prism, truncated octahedron, rhombic dodecahedron, and the rhombo-hexagonal dodecahedron. Let { v 0 , v 1 , … } {\displaystyle \{v_{0}
Zonohedron
Four-dimensional analogue of the cube
has a rhombic dodecahedral envelope. Two vertices of the tesseract are projected to the origin. There are exactly two ways of dissecting a rhombic dodecahedron
Tesseract
Quadrilateral with sides of equal length
instead of rectangles. The rhombic dodecahedron is a convex polyhedron with 12 congruent rhombi as its faces. The rhombic triacontahedron is a convex
Rhombus
Type of polyhedron
rhombic dodecahedron surrounded by: 12 rhombic prisms, 8 tetrahedra, 6 square pyramids, and 24 triangular prisms. If the central rhombic dodecahedron
Expanded_cuboctahedron
Polyhedron with 20 rhombic faces
Bilinski dodecahedron, which is topologically equivalent but not congruent to the regular rhombic dodecahedron. Weisstein, Eric W. "Rhombic Icosahedron"
Rhombic_icosahedron
3D geometric shape
{\displaystyle A=(24{\sqrt {5}})a^{2}} . A rhombic hexecontahedron can be constructed from a regular dodecahedron, by taking its vertices, its face centers
Rhombic_hexecontahedron
Polyhedron with 8 triangles and 6 squares
edge-transitive. It is radially equilateral. Its dual polyhedron is the rhombic dodecahedron. The cuboctahedron can be constructed in many ways: Its construction
Cuboctahedron
13 polyhedra; duals of the Archimedean solids
adjacent faces is the same. Additionally, two Catalan solids, the rhombic dodecahedron and rhombic triacontahedron, are edge-transitive, meaning their edges are
Catalan_solid
Lithograph print by M. C. Escher
compound of three cubes. The one on the right is a stellation of a rhombic dodecahedron (or a compound of three non-regular octahedra) and is known as Escher's
Waterfall_(M._C._Escher)
Two joined triangular cupolae
The dual polyhedron of the triangular orthobicupola is the trapezo-rhombic dodecahedron. It is a plesiohedron, a space-filling polyhedron defined by Voronoi
Triangular_orthobicupola
Catalan solid with 120 faces
triacontahedron is the Kleetope of the rhombic triacontahedron. It is also the barycentric subdivision of the regular dodecahedron and icosahedron. It has the most
Disdyakis_triacontahedron
Triakis tetrahedron, Rhombic dodecahedron, Hendecagonal pyramid, Trapezo-rhombic dodecahedron, Rhombo-hexagonal dodecahedron Archimedean solid Truncated
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Empirical study of systems in transformation
proportionality of the octahedron, the cube, the rhombic triacontahedron, and the rhombic dodecahedron when referenced to the tetrahedron as volumetric
Synergetics_(Fuller)
Convex polyhedron with 90 rhombic faces
symmetry. The sixty broad rhombic faces in the rhombic enneacontahedron are identical to those in the rhombic dodecahedron, with diagonals in a ratio
Rhombic_enneacontahedron
Natural number between 89 and 91
180 degrees. The rhombic enneacontahedron is a zonohedron with a total of 90 rhombic faces: 60 broad rhombi akin to those in the rhombic dodecahedron with diagonals
90_(number)
Type of space-filling polyhedron
any other copy. The plesiohedra include the cube, hexagonal prism, rhombic dodecahedron, and truncated octahedron. The largest number of faces that a plesiohedron
Plesiohedron
Polyhedron which tiles 3D space
cube, hexagonal prism, truncated octahedron, elongated dodecahedron, and rhombic dodecahedron). Other space-filling polyhedra include the square pyramid
Space-filling_polyhedron
Archimedean solid with 62 faces
icosidodecahedral rhombus being his name for a rhombic triacontahedron. There are different truncations of a rhombic triacontahedron into a topological rhombicosidodecahedron:
Rhombicosidodecahedron
dodecadodecahedron Truncated great dodecahedron Truncated great icosahedron Catalan solid Triakis tetrahedron Rhombic dodecahedron Triakis octahedron Tetrakis
List_of_mathematical_shapes
Removal of alternate vertices
ditrigonal icosidodecahedron can be represented by a{5,3} (an altered dodecahedron), and , . Here all the pentagons have been alternated into pentagrams
Alternation_(geometry)
1948 wood engraving print by M. C. Escher
within the print also include all of the five Platonic solids and the rhombic dodecahedron. In order to depict polyhedra accurately, Escher made models of them
Stars_(M._C._Escher)
Polyhedron with 30 faces
the medial rhombic triacontahedron (or midly rhombic triacontahedron) is a nonconvex isohedral polyhedron. It is a stellation of the rhombic triacontahedron
Medial rhombic triacontahedron
Medial_rhombic_triacontahedron
Polyhedral compound
are: The compound of a Dodecahedron and an Icosahedron shares the same vertices as a list of other polyhedra, including the Rhombic triacontahedron and the
Compound of dodecahedron and icosahedron
Compound_of_dodecahedron_and_icosahedron
Archimedean solid with 26 faces
cuboctahedral rhombus, with cuboctahedral rhombus being his name for a rhombic dodecahedron. The rhombicuboctahedron is an Archimedean solid, and its dual is
Rhombicuboctahedron
Polytope or tiling with one type of edge
isotoxal, but not isohedral. Their duals, including the rhombic dodecahedron and the rhombic triacontahedron, are isohedral and isotoxal, but not isogonal
Isotoxal_figure
Polyhedron with 30 faces
diagonals of the rhombs. What resembles an "excavated" rhombic triacontahedron (compare excavated dodecahedron and excavated icosahedron) can be seen within the
Great_rhombic_triacontahedron
Tiling of euclidean or hyperbolic space of three or more dimensions
concave polygons. These include a packing of the small stellated rhombic dodecahedron, as in the Yoshimoto Cube. Overlapping of cells whose positive and
Honeycomb_(geometry)
Any of the five regular polyhedra
uniform polyhedra with polyhedral symmetry. Their duals, the rhombic dodecahedron and rhombic triacontahedron, are edge- and face-transitive, but their faces
Platonic_solid
1960, he discovered a rhombic dodecahedron of the second kind, the Bilinski dodecahedron. Like the standard rhombic dodecahedron, this convex polyhedron
Stanko_Bilinski
Rhombus with diagonals in the golden ratio
Obtuse golden rhombohedron Bilinski dodecahedron Rhombic dodecahedron rhombic icosahedron rhombic triacontahedron rhombic hexecontahedron Golden triangle
Golden_rhombus
20{3} + 12{10} 11 Cuboctahedron rhombic dodecahedron 2|3 4 3.4.3.4 Oh U07 K12 12 24 14 8{3} + 6{4} 12 Icosidodecahedron rhombic triacontahedron 2|3 5 3.5.3
List of Wenninger polyhedron models
List_of_Wenninger_polyhedron_models
rhombi Rhombic dodecahedron - 12 rhombi Rhombic icosahedron - 20 rhombi Rhombic triacontahedron - 30 rhombi Rhombic hexecontahedron - 60 rhombi Rhombic enneacontahedron
Rhombic_hectotriadiohedron
Natural number
175 back again: 175 = 11 + 72 + 53. 175 is a figurate number for a rhombic dodecahedron, the difference of two consecutive fourth powers: 175 = 44 − 34.
175_(number)
Variously-defined concept in geometry
regular bases), and two edge-transitive Catalan solids, the rhombic dodecahedron and rhombic triacontahedron. He also considered a rhombus as a semiregular
Semiregular_polyhedron
Polyhedron with 20 faces
has right dihedral angles. Rhombic icosahedron: a zonohedron made up of 20 congruent rhombs. It can be derived from the rhombic triacontahedron by removing
Icosahedron
Dutch graphic artist (1898–1972)
polyhedra, one a compound of three cubes, the other a stellated rhombic dodecahedron now known as Escher's solid. Escher had used this solid in his 1948
M._C._Escher
The Logical Garnet is the name Shea Zellweger gave to a labelled rhombic dodecahedron where Zellweger's Logic Alphabet is used to provide icons illustrative
Logical_Garnet
Extending the elements of a polytope to form a new figure
the great stellated dodecahedron (the final stellation of the dodecahedron) and the fourth stellation of the rhombic dodecahedron. Face-stellation can
Stellation
Polyhedron with 32 faces
a great dodecahedron inscribed within and sharing the edges of the icosahedron. The dual of the great icosidodecahedron is the great rhombic triacontahedron;
Great_icosidodecahedron
Polyhedral compound
topologically identical to the disdyakis dodecahedron, which can be seen as rhombic dodecahedron with shorter pyramids on the rhombic faces. The dual figure of the
Compound_of_three_octahedra
Near-miss Johnson solid with 28 faces
symmetry. The dual polyhedron of the tetrated dodecahedron consists of triangular, trapezoidal, and rhombic faces. It has 28 faces. Tetrated dodecahedra
Tetrated_dodecahedron
Polyhedron made of congruent kites arranged radially
the deltoid dodecahedron has 12 congruent non-twisted kite faces, six order-4 vertices and eight order-3 vertices (the rhombic dodecahedron is a special
Trapezohedron
Shape with ten sides
projection plane of the 5-cube. A dissection is based on 10 of 30 faces of the rhombic triacontahedron. The list OEIS: A006245 defines the number of solutions
Decagon
Method of describing higher-order polyhedra
t4daC, as a rhombic dodecahedron, daC or jC, with its degree-4 vertices truncated. A lofted cube, lC is the same as t4kC. A quinto-dodecahedron, qD can be
Conway_polyhedron_notation
Primitive cell of crystal lattices with Voronoi decomposition applied
Bravais lattice. For example, the cube, truncated octahedron, and rhombic dodecahedron have point symmetry Oh, since the respective Bravais lattices used
Wigner–Seitz_cell
Edge-joined polygons which fold into a polyhedron
Icosahedron Truncated dodecahedron Truncated cube Truncated octahedron Truncated cuboctahedron Rhombicuboctahedron Rhombic dodecahedron Rhombicosidodecahedron
Net_(polyhedron)
Polyhedral compound
It has octahedral symmetry (Oh) and shares the same vertices as a rhombic dodecahedron. This can be seen as the three-dimensional equivalent of the compound
Compound of cube and octahedron
Compound_of_cube_and_octahedron
Space-filling polyhedron with 8 faces
Elongated dodecahedron, another space-filling polyhedron Elongated square bipyramid, a space-filling Johnson solid Trapezo-rhombic dodecahedron, a space-filling
Elongated_gyrobifastigium
Type of polyhedron
with rhombic faces between original and the neighboring face centers. The joined square prism is the same topology as the rhombic dodecahedron. The joined
Rectified_prism
Polyhedral compound
those of a regular dodecahedron. Its edges form pentagrams, which are the stellations of the pentagonal faces of the dodecahedron. It is one of the stellations
Compound_of_five_cubes
3D combination puzzle
can be adapted to higher-order cubes. In the case of Tony Fisher's Rhombic Dodecahedron, there are 3×3×3, 4×4×4, 5×5×5, and 6×6×6 versions of the puzzle
Rubik's_Cube
Convex polyhedron that fills space isohedrally
Parallelohedra cube hexagonal prism rhombic dodecahedron elongated dodecahedron truncated octahedron
Stereohedron
Natural number, composite number
the only uniform polyhedron with radial equilateral symmetry. The rhombic dodecahedron, dual to the cuboctahedron, contains 14 vertices and is the only
14_(number)
Marked objects for finding random numbers
Truncated sphere A truncated sphere with eleven landing positions. 12 Rhombic dodecahedron Each face is a rhombus. 13 Truncated sphere A truncated sphere with
Dice
Regular tiling of a two-dimensional space
elongated rhombic tiling, where each vertex of the rhombic tiling is stretched into a new edge. This is similar to the relation of the rhombic dodecahedron and
Hexagonal_tiling
Covering by shapes without overlaps or gaps
including the cube (the only Platonic polyhedron to do so), the rhombic dodecahedron, the truncated octahedron, and triangular, quadrilateral, and hexagonal
Tessellation
Generalisation of dice with identical faces
is said to be noble. Not all isozonohedra are isohedral. For example, a rhombic icosahedron is an isozonohedron but not an isohedron. A polyhedron (or
Isohedral_figure
Rhombic dodecahedron, a solid with hidden lines that thinner and a lighter shade of grey.
Hidden_line
Number, approximately 1.618
rhombi form the faces of the rhombic triacontahedron, the two golden rhombohedra, the Bilinski dodecahedron, and the rhombic hexecontahedron. If the two
Golden_ratio
the cuboctahedron, which also becomes the intersphere of the dual rhombic dodecahedron. Dorman Luke's construction can only be used when a polyhedron has
Dual_uniform_polyhedron
3D shape made of polyhedra sharing a common center
dodecahedral) dual compound has the great dodecahedron completely interior to the small stellated dodecahedron. In 1976 John Skilling published Uniform
Polytope_compound
Polyhedron with two kinds of faces
above: The rhombic dodecahedron, with two types of alternating vertices, 8 with three rhombic faces, and 6 with four rhombic faces. The rhombic triacontahedron
Quasiregular_polyhedron
Notation for a polyhedron's vertex figure
vertex around a face. For example, V3.4.3.4 or V(3.4)2 represents the rhombic dodecahedron which is face-transitive: every face is a rhombus, and alternating
Vertex_configuration
Polyhedron with 24 faces
U36. It is the rectification of the great dodecahedron (and that of its dual, the small stellated dodecahedron). It was discovered independently by Hess (1878)
Dodecadodecahedron
Polytope made by turning a polytope's facets into pyramids
disdyakis dodecahedron is the Kleetope of the rhombic dodecahedron, formed by replacing each rhombus face of the dodecahedron with a rhombic pyramid, and
Kleetope
Mineral, semi-precious stone
Identification Color virtually all colors, blue is rare Crystal habit Rhombic dodecahedron or cubic Cleavage Indistinct Fracture conchoidal to uneven Mohs scale
Garnet
Two tetrahedra crossing each other
pyramids lie on the same plane, and the shape degenerates to the rhombic dodecahedron. The outer shell of the augmented octahedron, with 24 equilateral-triangle
Stellated_octahedron
Polyhedron resembling a soccerball
uniform chamfered dodecahedron (truncated rhombic triacontahedron), which has 42 faces (12 pentagons and 30 hexagons). Chamfered dodecahedron Icosahedral twins
Truncated_icosahedron
Two polyhedral compounds with the same name
are two different compounds of great icosahedron and great stellated dodecahedron: one is a dual compound and a stellation of the great icosidodecahedron
Compound of great icosahedron and great stellated dodecahedron
Compound_of_great_icosahedron_and_great_stellated_dodecahedron
Partition of the graph of a rhombic dodecahedron into two linear forests, showing that its linear arboricity is two
Linear_arboricity
Polyhedron associated with another by swapping vertices for faces
dual compound. Canonical dual compound of cuboctahedron (light) and rhombic dodecahedron (dark). Pairs of edges meet on their common midsphere. Dual of the
Dual_polyhedron
Solid made from 2 cupolae joined base-to-base
orthobicupola (J27): 8 triangles, 6 squares. Its dual is the trapezo-rhombic dodecahedron D4h [2,4] *224 Square orthobicupola (J28): 8 triangles, 10 squares
Bicupola
Polyhedron with 24 faces
Catalan solid, the disdyakis dodecahedron, with much taller rhombus-based pyramids joined to each face of a rhombic dodecahedron. Each bow-tie has two angles
Great_rhombihexacron
Disproven graph theory
the graph be 3-regular is necessary due to polyhedra such as the rhombic dodecahedron, which forms a bipartite graph with six degree-four vertices on one
Tait's_conjecture
Catalan solid with 24 faces
tetrakis hexahedron and the geometric proportions of the rhombic dodecahedron, with the rhombic faces divided into two triangles. The tetrakis hexahedron
Tetrakis_hexahedron
Polyhedron with 6 congruent rhombus faces
convex polyhedra with golden rhombus faces, including the Bilinski dodecahedron and rhombic triacontahedron. Four oblate rhombohedra whose ratio of face diagonal
Trigonal_trapezohedron
Topics referred to by the same term
may refer to: Great rhombidodecahedron Small rhombidodecahedron Rhombic dodecahedron This disambiguation page lists mathematics articles associated with
Rhombidodecahedron
Quasiregular space-filling tesselation
3-dimensional case of a simplectic honeycomb. Its Voronoi cell is a rhombic dodecahedron, the dual of the cuboctahedron vertex figure for the tet-oct honeycomb
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
Type of polyhedron
surrounded by: 30 rhombic prisms, 20 tetrahedra, 12 pentagonal pyramids, 60 triangular prisms. Rhombicosidodecahedron (expanded dodecahedron) Truncated
Expanded_icosidodecahedron
Pseudocylindrical equal-area map projection
K=3 HEALPix projection has 12 quatrilateral faces, similar to a rhombic dodecahedron, but its vertex configuration is different and in fact incompatible
HEALPix
Church in London, England
the pavement's geometry represents a two-dimensional "slice" of a rhombic dodecahedron, a 12-sided shape used as a secret architectural symbol for universal
Westminster_Abbey
Polyhedron with 60 faces
hexecontahedron Small stellapentakis dodecahedron, Great stellapentakis dodecahedron Great pentakis dodecahedron Great triakis icosahedron Small ditrigonal
Hexecontahedron
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RHOMBIC DODECAHEDRON
RHOMBIC DODECAHEDRON
RHOMBIC DODECAHEDRON
RHOMBIC DODECAHEDRON
RHOMBIC DODECAHEDRON
RHOMBIC DODECAHEDRON
RHOMBIC DODECAHEDRON
RHOMBIC DODECAHEDRON
RHOMBIC DODECAHEDRON
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