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Archimedean solid with 26 faces
The rhombicuboctahedron or small rhombicuboctahedron is a polyhedron with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named
Rhombicuboctahedron
37th Johnson solid (26 faces)
mistakenly considered a rhombicuboctahedron by many mathematicians. For this reason, it is also known as the pseudo-rhombicuboctahedron, Miller solid, or Miller–Askinuze
Elongated_square_gyrobicupola
Archimedean solid with 26 faces
In geometry, the truncated cuboctahedron or great rhombicuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It
Truncated_cuboctahedron
Polygon shape with eight sides
t{8} is a hexadecagon, {16}. A 3D analog of the octagon can be the rhombicuboctahedron with the triangular faces on it like the replaced edges, if one considers
Octagon
Polyhedra in which all vertices are the same
the Platonic solid) and taking the convex hull. An example is the rhombicuboctahedron, which is constructed by separating the cube or octahedron's faces
Archimedean_solid
Topics referred to by the same term
with Schläfli symbol tr{4,3}, and Coxeter diagram . Nonconvex great rhombicuboctahedron - a uniform star polyhedron, with Schläfli symbol r{4,3/2}, and Coxeter
Great_rhombicuboctahedron
In geometry, the pseudo great rhombicuboctahedron is one of the two pseudo uniform polyhedra, the other being the convex elongated square gyrobicupola
Pseudo great rhombicuboctahedron
Pseudo_great_rhombicuboctahedron
The snub rhombicuboctahedron is a polyhedron, constructed as a truncated rhombicuboctahedron. It has 74 faces: 18 squares, and 56 triangles. It can also
Snub_rhombicuboctahedron
Nonconvex uniform polyhedron with 26 faces
In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares),
Nonconvex great rhombicuboctahedron
Nonconvex_great_rhombicuboctahedron
Type of polyhedron
The truncated rhombicuboctahedron is a polyhedron, constructed as a truncation of the rhombicuboctahedron. It has 50 faces consisting of 18 octagons,
Truncated_rhombicuboctahedron
Catalan solid with 24 kite faces
and eighteen vertices by four kites. Its dual polyhedron is the rhombicuboctahedron, an Archimedean solid. Deltoidal icositetrahedron and deltoidal hexecontahedron
Deltoidal_icositetrahedron
Type of polyhedron
constructed as a rectified rhombicuboctahedron. Expanded rhombic dodecahedron Rectified rhombicuboctahedron Rectified small rhombicuboctahedron Rhombirhombicuboctahedron
Expanded_cuboctahedron
European cultural period of the 14th to 17th centuries
condemned. It is thought that Leonardo da Vinci may have painted the rhombicuboctahedron. Exhaustive 2007 study by Fritjof Capra shows that Leonardo was a
Renaissance
Library in Minsk, Belarus
2006. The library's main architectural component has the shape of a rhombicuboctahedron. The height of the building is 73.6 metres (241.5 feet) and weight
National_Library_of_Belarus
Star polygon
three-dimensional version of the octagram is the nonconvex great rhombicuboctahedron (quasirhombicuboctahedron), which can be thought of as a quasicantellated
Octagram
Painting by Jacopo de' Barbari
solids, including the rhombicuboctahedron, in Pacioli's Divina proportione. According to one scholar, in the rhombicuboctahedron featured in the portrait
Portrait_of_Luca_Pacioli
Flat-sided three-dimensional shape
as the pseudorhombicuboctahedron, a mistaken construction of the rhombicuboctahedron. However, it was debarred for not having the vertex-transitive property
Polyhedron
Italian polymath (1452–1519)
Rhombicuboctahedron as published in Pacioli's Divina proportione (1509)
Leonardo_da_Vinci
Rubik's puzzle
shapes. Its "ball" shape in its packaging is a non-uniform concave rhombicuboctahedron. The snake was invented by Ernő Rubik, better known as the inventor
Rubik's_Snake
quadrilateral. The small cubicuboctahedron is a faceting of the rhombicuboctahedron. Its square faces and its octagonal faces are parallel to those of
Small_cubicuboctahedron
Type of polyhedron with many holes
Rhombicuboctahedron, one of the Leonardo da Vinci's geometrical shapes illustration in 1509 Divina proportione
Leonardo_polyhedron
Solid made by joining an n- and 2n-gon with triangles and squares
solids, and can be formed by taking sections of the cuboctahedron, rhombicuboctahedron, and rhombicosidodecahedron, respectively. Cupolae are a subclass
Cupola_(geometry)
The rhombicuboctahedron, as published in De divina proportione
Science and inventions of Leonardo da Vinci
Science_and_inventions_of_Leonardo_da_Vinci
15th c. Franciscan Friar, mathematician and publisher of accounting treatise
The first printed illustration of a rhombicuboctahedron, by Leonardo da Vinci, published in Divina proportione
Luca_Pacioli
Archimedean solid with 38 faces
equilateral triangles. The snub cube may also be constructed from a rhombicuboctahedron. It started by twisting its square face (in blue), allowing its triangles
Snub_cube
Cupola with octagonal base
great rhombicuboctahedron or quasirhombicuboctahedron, analogously to how the square cupola may be obtained as a slice of the rhombicuboctahedron. As in
Square_cupola
Truncated tetrahedron Cuboctahedron Truncated cube Truncated octahedron Rhombicuboctahedron Truncated cuboctahedron Snub cube Icosidodecahedron Truncated dodecahedron
List_of_mathematical_shapes
Isogonal polyhedron with regular faces
plagiarized Francesca's work in De divina proportione in 1509, adding the rhombicuboctahedron, calling it an icosihexahedron for its 26 faces, which was drawn
Uniform_polyhedron
Christmas decoration
technically known as a Kleetope of a rhombicuboctahedron. Each face of the geometric solid in the middle, the rhombicuboctahedron, serves as the base for one of
Moravian_star
Marked objects for finding random numbers
A truncated sphere with seventeen landing positions. 18 Rounded rhombicuboctahedron Eighteen faces are squares. The eight triangular faces are rounded
Dice
Object in 4-dimensional geometry
cupola is a 4-polytope bounded by one octahedron and a parallel rhombicuboctahedron, connected by 20 triangular prisms, and 6 square pyramids. The octahedral
Octahedral_cupola
of a cube. This polyhedron is a 12-zone zonohedrification of the rhombicuboctahedron.[better source needed] The type C is a 12-zone zonohedrification
Rhombic_hectotriadiohedron
pseudo-uniform polyhedra: the pseudorhombicuboctahedron and the pseudo-great rhombicuboctahedron. It is not known if there are any others; Branko Grünbaum conjectured
Pseudo-uniform_polyhedron
tetrahedron, Cuboctahedron, Truncated cube, Truncated octahedron, Rhombicuboctahedron, Truncated cuboctahedron, Snub cube, Icosidodecahedron, Truncated
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Method of describing higher-order polyhedra
Cuboctahedron aC = aO = eT Truncated cube tC Truncated octahedron tO = bT Rhombicuboctahedron eC = eO truncated cuboctahedron bC = bO snub cube sC = sO icosidodecahedron
Conway_polyhedron_notation
Convex uniform 4-polytope
vertices of the rhombicuboctahedron's triangles, and each edge will separate into two of the opposite edges of the rhombicuboctahedrons twelve non-axial
Cantellated_tesseract
layout of the faces of the (small) rhombicuboctahedron under projection to 2 dimensions. The rhombicuboctahedron is also constructed from the cube or
Runcinated_tesseracts
Topics referred to by the same term
W85 may refer to: W85 (nuclear warhead) Nonconvex great rhombicuboctahedron W85 heavy machine gun W85, a classification in masters athletics This disambiguation
W85
Number, approximately 2.41421
with octahedral symmetry; all values are based on edge length = 2. Rhombicuboctahedron The coordinates of the vertices are given by 24 distinct permutations
Silver_ratio
Polygon with 2 sides and 2 vertices
A nonuniform rhombicuboctahedron with blue rectangular faces that degenerate into digons in the cubic limit.
Digon
Type of polyhedron
snub rhombicosidodecahedron. Expanded icosidodecahedron Truncated rhombicuboctahedron Eppstein (1996) Eppstein, David (1996). "Zonohedra and zonotopes"
Truncated rhombicosidodecahedron
Truncated_rhombicosidodecahedron
Convex polyhedron with 90 rhombic faces
corollary of the Kepler conjecture: it can be achieved by putting a rhombicuboctahedron in each cell of the rhombic dodecahedral honeycomb, and it cannot
Rhombic_enneacontahedron
the rhombicuboctahedron (pictured in the portrait), in Pacioli's Divina proportione (1509). According to one scholar, in the rhombicuboctahedron "we surely
List of works by Leonardo da Vinci
List_of_works_by_Leonardo_da_Vinci
Solid with six equal square faces
truncated cube. When its edges are truncated, it is a rhombicuboctahedron. Relatedly, the rhombicuboctahedron can also be constructed by separating the cube's
Cube
Triaugmented dodecahedron 24 Truncated cube Truncated octahedron Rhombicuboctahedron Elongated square gyrobicupola Gyroelongated square bicupola Snub
List of small polyhedra by vertex count
List_of_small_polyhedra_by_vertex_count
Self-intersecting uniform polyhedron
their vertex configuration. An additional figure, the pseudo great rhombicuboctahedron, is usually not included as a truly uniform star polytope, despite
Uniform_star_polyhedron
Italian painter and engraver (1460–1516)
geometrical tools: slate, chalk, compass, a dodecahedron model. A rhombicuboctahedron half-filled with water is suspended from the ceiling. Pacioli is
Jacopo_de'_Barbari
Archimedean solid with 14 faces
seen within the runcic cubic honeycomb, with cube, tetrahedron, and rhombicuboctahedron cells. This dissection can be used to create a Stewart toroid with
Truncated_cube
Geometric operation applied to a polyhedron
A snub cube can be constructed from a rhombicuboctahedron by rotating the 6 blue square faces until the 12 white square faces become pairs of equilateral
Snub_(geometry)
Polyhedron with a square cupola and an octagonal prism
by removing a square cupola from a rhombicuboctahedron, which would also make it a diminished rhombicuboctahedron. A convex polyhedron in which all of
Elongated_square_cupola
Cuboctahedron 3.4.3.4 2 | 3 4 Oh C19 W011 U07 K12 12 24 14 8{3} +6{4} Rhombicuboctahedron 3.4.4.4 3 4 | 2 Oh C22 W013 U10 K15 24 48 26 8{3} +(6+12){4} Rhombicosidodecahedron
List_of_uniform_polyhedra
Renaissance mathematics textbook
Ptak (11 March 2008). "The Sovietesque Disappearance of Pacioli's Rhombicuboctahedron". JF Ptak Science Booksl. Retrieved 15 January 2020. Wikimedia Commons
Summa_de_arithmetica
1948 wood engraving print by M. C. Escher
A rhombicuboctahedron drawn by Leonardo da Vinci, 1509, four centuries before Escher
Stars_(M._C._Escher)
the first illustrations of skeletonic solids. These, such as the rhombicuboctahedron, were among the first to be drawn to demonstrate perspective by being
Mathematics_and_art
Operation in Euclidean geometry
{\begin{Bmatrix}4\\3\end{Bmatrix}}} . And a rectified cuboctahedron rr{4,3} is a rhombicuboctahedron, and also represented as r { 4 3 } {\displaystyle
Rectification_(geometry)
Convex polyhedron with regular faces
Elongated pentagonal bipyramid 35 Elongated triangular orthobicupola Rhombicuboctahedron "Elongated square orthobicupola" 38 Elongated pentagonal orthobicupola
Johnson_solid
Polyhedron with 18 faces
hexahedron. It additionally shares its edge arrangement with the convex rhombicuboctahedron (having 12 square faces in common) and with the small cubicuboctahedron
Small_rhombihexahedron
Graph with an Archimedean solid as its skeleton
rhombicuboctahedral graph 4 48 24 48 truncated cuboctahedral graph (great rhombicuboctahedron) 3 72 48 48 snub cubical graph 5 60 24 24 icosidodecahedral graph
Archimedean_graph
constructed from cube, octahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named
Cubic-octahedral_honeycomb
constructed from tetrahedron, cuboctahedron and square tiling cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named
Tetrahedral-square tiling honeycomb
Tetrahedral-square_tiling_honeycomb
Variously-defined concept in geometry
solids. The elongated square gyrobicupola (also called a pseudo-rhombicuboctahedron), a Johnson solid, has identical vertex figures (3.4.4.4) but because
Semiregular_polyhedron
runcitruncated order-4 hexagonal tiling honeycomb, t0,1,3{6,3,4}, has rhombicuboctahedron, cube, dodecagonal prism, and truncated hexagonal tiling cells, with
Order-4 hexagonal tiling honeycomb
Order-4_hexagonal_tiling_honeycomb
Nonconvex uniform polyhedron with 20 faces
additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having the triangular faces and 6 square faces in common), and with
Great_cubicuboctahedron
Polyhedron with 18 faces
orthobicupola, the elongated square cupola (also known as the diminished rhombicuboctahedron), and the sphenomegacorona. Four Johnson solids have octadecahedral
Octadecahedron
Elongated triangular orthobicupola Elongated square orthobicupola (rhombicuboctahedron) Elongated pentagonal orthobicupola Elongated gyrobicupola J36 J37
Elongated_bicupola
Polyhedron with 24 faces
Isosceles triangle V4.6.6 Oh Deltoidal icositetrahedron (animation) Rhombicuboctahedron 24 48 26 Kite V3.4.4.4 Oh Pentagonal icositetrahedron (animation)
Icositetrahedron
Australian children's television series
unspecified, but as a real prop, it is a dark green steel frame model of a Rhombicuboctahedron plated with semidiagonal steel bars and plated with semitransparent
The_Girl_from_Tomorrow
Compact Riemann surface of genus 3
convex hulls, including the truncated cube, the snub cube, or the rhombicuboctahedron, as in the small cubicuboctahedron at right. The small cubicuboctahedron
Klein_quartic
from dodecahedron, octahedron, and icosidodecahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named
Octahedral-dodecahedral honeycomb
Octahedral-dodecahedral_honeycomb
Commercial art gallery in Hong Kong and Shanghai
"1986 – 1992" in 2020, Ko Sin Tung's "Adaption" in 2019, "R for Rhombicuboctahedron" in 2019, the eighth volume of Ho Tzu Nyen's series "The Critical
Kiang_Malingue
Schlegel diagram centered on rhombicuboctahedron only triangular prisms shown
Runcinated_24-cells
(resembling rep-tiles) Pacioli, Luca 1447–1517 Fine art Polyhedra (e.g. rhombicuboctahedron) in Renaissance art; proportion, in his book De divina proportione
List_of_mathematical_artists
Value determined from a polyhedron
12 s , 0 , 0 ) {\displaystyle (12s,0,0)} for the truncated cube, rhombicuboctahedron, and cuboctahedron. ( 0 , 0 , 0 ) {\displaystyle (0,0,0)} for the
Dehn_invariant
is applied to 24-cell, each of the 24 octahedra becomes a small rhombicuboctahedron. In addition however, since each octahedra's edge was previously
Cantellated_24-cells
Polytope or tiling whose vertices are identical
3.8.8 A distorted hexagonal prism (ditrigonal trapezoprism) A distorted rhombicuboctahedron A shallow truncated cuboctahedron A hyper-truncated cube
Isogonal_figure
Cube that fits through hole in smaller cube
property: the cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron, icosidodecahedron, truncated cuboctahedron, truncated icosahedron
Prince_Rupert's_cube
Generalisation of dice with identical faces
polyhedra Monohedral polyhedra The rhombicuboctahedron has 1 triangle type and 2 square types. The pseudo-rhombicuboctahedron has 1 triangle type and 3 square
Isohedral_figure
Shape made by slicing off a corner of a polytope
with one triangle and three squares, and it defines the uniform rhombicuboctahedron. If the polytope is isogonal, the vertex figure will exist in a hyperplane
Vertex_figure
faces of the great rhombicuboctahedron are the images of the remaining 12 cubes. The 6 octagonal faces of the great rhombicuboctahedron are the images of
Truncated_24-cells
Regular tiling of hyperbolic 3-space
runcitruncated order-4 dodecahedral honeycomb, , has truncated dodecahedron, rhombicuboctahedron, decagonal prism, and cube cells, with an isosceles-trapezoidal pyramid
Order-4 dodecahedral honeycomb
Order-4_dodecahedral_honeycomb
Uniform space-filling honeycomb
Tesseract Cantellated tesseract Rhombicuboctahedral prism Cell type Rhombicuboctahedron Cube Octahedron Triangular prism Face type {3}, {4} Vertex figure
Stericantellated tesseractic honeycomb
Stericantellated_tesseractic_honeycomb
Symmetric subdivision in hyperbolic geometry
trigon and a tetragon) are normal edges.) rhombitetratetrahedron rhombicuboctahedron rhombicosidodecahedron rhombitrihexagonal tiling Rhombitriheptagonal
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
by the shape Corollary of Kepler conjecture. Examples pictured: rhombicuboctahedron and rhombic enneacontahedron. Hypersphere 8 ( π 2 ) 4 4 ! ≈ 0.2536695
List of shapes with known packing constant
List_of_shapes_with_known_packing_constant
3D symmetry group
Triakis octahedron Truncated octahedron 14 36 24 Tetrakis hexahedron Rhombicuboctahedron 26 48 24 Deltoidal icositetrahedron Truncated cuboctahedron 26 72
Octahedral_symmetry
honeycomb, constructed from octahedron and tetrahedron cells, in a rhombicuboctahedron vertex figure. A geometric honeycomb is a space-filling of polyhedral
Hyperbolic tetrahedral-octahedral honeycomb
Hyperbolic_tetrahedral-octahedral_honeycomb
Convex polyhedron projected from hypercube
simple (three faces meet at each vertex), as is the truncated small rhombicuboctahedron formed from the Minkowski sum of the cube, truncated octahedron,
Zonohedron
Polyhedral compound
octahedron. It shares the same vertex arrangement as a nonuniform rhombicuboctahedron. Cartesian coordinates for the vertices of this compound are all
Compound of four hexagonal prisms
Compound_of_four_hexagonal_prisms
Cuboctahedron 8 13 21 Truncated octahedron 9 18 45 Truncated cube 9 18 45 Rhombicuboctahedron 48 18827 ? (128723453647 reflexible) Truncated cuboctahedron 49 22632
List of polyhedral stellations
List_of_polyhedral_stellations
Notation for polytopes and tessellations
{\displaystyle r{\begin{Bmatrix}p\\q\end{Bmatrix}}} rr{p,q} t0,2{p,q} Rhombicuboctahedron Cantitruncated (Truncated rectified) t { p q } {\displaystyle
Schläfli_symbol
Polyhedron with 14 faces
vertex arrangement with three other uniform polyhedra: the convex rhombicuboctahedron, the small rhombihexahedron, and the small cubicuboctahedron. List
Stellated truncated hexahedron
Stellated_truncated_hexahedron
Polyhedron with 18 faces
additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having 12 square faces in common), and with the great cubicuboctahedron
Great_rhombihexahedron
Topics referred to by the same term
flying boat bomber London Buses route W13 Mercedes W13, a racing car Rhombicuboctahedron Route W13 (WMATA), a former bus route in Maryland W-13-class minesweeper
W13
prominent architectural landmark in Minsk, displaying an unusual rhombicuboctahedron shape. The building is 73.6 metres in height with 23 floors, can
Architecture_in_Belarus
Compact uniform honeycomb
constructed from cube, tetrahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named
Tetrahedral-cubic_honeycomb
Topics referred to by the same term
Cessna U-17 Skywagon, an American utility aircraft Nonconvex great rhombicuboctahedron U17, or under-17, is a youth sports category. This disambiguation
U17
4-dimensional geometry, the cubic cupola is a 4-polytope bounded by a rhombicuboctahedron, a parallel cube, connected by 6 square prisms, 12 triangular prisms
Cubic_cupola
1987 video game
a first-person view, through eighteen regions (in the shape of a rhombicuboctahedron) of the moon Mitral, and place a drilling rig in each of them to
Driller_(video_game)
Notation for a polyhedron's vertex figure
solids: Cuboctahedron: 3.4.3.4 (12) Icosidodecahedron: 3.5.3.5 (30) Rhombicuboctahedron: 3.4.4.4 (24) Rhombicosidodecahedron: 3.4.5.4 (60) Regular tilings:
Vertex_configuration
Polyhedron related to sphere packing
a truncated cuboctahedron, as well W3 O1 = W12 O1 mistaken for a rhombicuboctahedron, but those Waterman polyhedra have two edge lengths and therefore
Waterman_polyhedron
Topics referred to by the same term
Iriver U10, a portable music player Meizu U10, a Chinese smartphone Rhombicuboctahedron Toyota Coaster (U10), a Japanese minibus Uppland Runic Inscription
U10
RHOMBICUBOCTAHEDRON
RHOMBICUBOCTAHEDRON
RHOMBICUBOCTAHEDRON
RHOMBICUBOCTAHEDRON
Boy/Male
Hindu, Indian
A Hindi Calendar Month
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Shiva
Girl/Female
Tamil
Flower, Shadow of Lord Sai
Boy/Male
Arabic
Trusty
Girl/Female
Tamil
Path between trees
Boy/Male
Indian, Punjabi, Sikh
King's Light
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi
Worshipper
Girl/Female
Gujarati, Hebrew, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu, Traditional
Sweet; Fragrant; Florist; A River; A Garland-maker
Boy/Male
Indian, Sikh
Youth
Boy/Male
American, British, Christian, English, German, Hindu, Indian
Free Man; Variant of Carl; Man; Form of Charles
RHOMBICUBOCTAHEDRON
RHOMBICUBOCTAHEDRON
RHOMBICUBOCTAHEDRON
RHOMBICUBOCTAHEDRON
RHOMBICUBOCTAHEDRON