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Planar surface that forms part of the boundary of a solid object
solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object. For example, a cube has six faces in this
Face_(geometry)
Convex polyhedron with regular faces
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not
Johnson_solid
Topics referred to by the same term
dictionary. Side or Sides may refer to: Edge (geometry) of a polygon (two-dimensional shape) Face (geometry) of a polyhedron (three-dimensional shape) Side
Side
Generalisation of dice with identical faces
In geometry, a tessellation of dimension 2 (a plane tiling) or higher, or a polytope of dimension 3 (a polyhedron) or higher, is isohedral or face-transitive
Isohedral_figure
Set of polygons to define the surface of a 3D model
changes in shape, but not geometry, can be dynamically updated by simply resending the vertex data without updating the face connectivity. Modelling requires
Polygon_mesh
Archimedean solid with 62 faces
In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of
Rhombicosidodecahedron
Conic solid with a polygonal base
called the apex. Each base edge and apex form a triangle, called a lateral face. A pyramid is a conic solid with a polygonal base. A pyramid can be generalized
Pyramid_(geometry)
Solid with 2 parallel n-gonal bases connected by n parallelograms
generations of later geometry writers). An oblique prism is a prism in which the joining edges and faces are not perpendicular to the base faces. Example: a parallelepiped
Prism_(geometry)
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Two geometries based on axioms closely related to those specifying Euclidean geometry
non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the
Non-Euclidean_geometry
Point where two or more curves, lines, or edges meet
In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segments meet or intersect
Vertex_(geometry)
Technology capable of matching a face from an image against a database of faces
Technion applied tools from metric geometry to treat expressions as isometries. A new method of capturing 3D images of faces uses three tracking cameras that
Facial_recognition_system
Molecular geometry
geometry is known as a monocapped octahedron, since it is derived from the octahedron by placing the lone pair over the centre of one triangular face
Octahedral_molecular_geometry
Topics referred to by the same term
to: Face (geometry), a flat (planar) surface that forms part of the boundary of a solid object Face (hieroglyph), a portrayal of the human face, frontal
Face_(disambiguation)
Mechanical puzzles
Unlike cubic puzzles, the FTO is based on an octahedral geometry with eight triangular faces that rotate independently. The idea of the FTO began in the
Face_Turning_Octahedron
Geometry of the surface of a sphere
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of
Spherical_geometry
Toroidal polyhedron with 7 faces
In geometry, the Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces. The tetrahedron and the Szilassi polyhedron
Szilassi_polyhedron
Geometric operation which truncates the edges of polyhedra
In geometry, a chamfer or edge-truncation is a topological operator that modifies one polyhedron into another. It separates the faces by reducing them
Chamfer_(geometry)
Aspect of geometry
In (polyhedral) geometry, a flag is a sequence of faces of a polytope, each contained in the next, with exactly one face from each dimension. More formally
Flag_(geometry)
Skeletonized version of algebraic geometry
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication
Tropical_geometry
Euclidean geometry without distance and angles
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance
Affine_geometry
Relationship between two figures of the same shape and size, or mirroring each other
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the
Congruence_(geometry)
Abstract regular polyhedron with 3 square faces
In abstract geometry, a hemicube is an abstract, regular polyhedron, containing half the faces of a cube. It can be realized as a projective polyhedron
Hemicube_(geometry)
Line segment joining two adjacent vertices in a polygon or polytope
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon,
Edge_(geometry)
Geometric shape
In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called
Cone
Quadrilateral symmetric across a diagonal
In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and
Kite_(geometry)
91st Johnson solid (14 faces)
In geometry, the bilunabirotunda is a Johnson solid with faces of 8 equilateral triangles, 2 squares, and 4 regular pentagons. The bilunabirotunda consists
Bilunabirotunda
In mathematics, most commonly in convex geometry, an extreme set or face of a set C ⊆ V {\displaystyle C\subseteq V} in a vector space V {\displaystyle
Extreme_set
Type of non-Euclidean geometry
mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
Geometry definition file format
represents 3D geometry alone – namely, the position of each vertex, the UV position of each texture coordinate vertex, vertex normals, and the faces that make
Wavefront_.obj_file
Study of the 3D shapes of molecules
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well
Molecular_geometry
Polygon with one edge and one vertex
In geometry, a monogon is a curve, considered by some as a polygon with one edge and one vertex. It has Schläfli symbol {1}. In Euclidean geometry a monogon
Monogon
Polyhedron defined by two triangles and three trapezoid faces
In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces. A wedge has five faces, nine edges, and six vertices. A
Wedge_(geometry)
Feature of geometric structures
geometry, some authors call a facet of a polyhedron any polygon whose corners are vertices of the polyhedron, including polygons that are not faces.
Facet_(geometry)
Field of mathematics dealing with three-dimensional Euclidean spaces
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional
Solid_geometry
Shape with three sides
geometry. Triangles also appear in three-dimensional objects. A polyhedron is a solid whose boundary is covered by flat polygonals known as the faces
Triangle
Pyramid with a pentagon base
In geometry, a pentagonal pyramid is a pyramid with a pentagon base and five triangular faces, having a total of six faces. It is categorized as a Johnson
Pentagonal_pyramid
Polyhedron with four faces
In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six
Tetrahedron
Type of program in computer graphics
Shaders act on data such as vertices and primitives, generate or morph geometries and fragments, and calculate the colors in a rendered image. Shaders can
Shader
Solid with six equal square faces
solid object in geometry. It has eight vertices and twelve straight edges of the same length, so that these edges form six square faces of the same size
Cube
Prism with a 6-sided base
In geometry, the hexagonal prism is a prism with hexagonal base. this polyhedron has 8 faces, 18 edges, and 12 vertices. A hexagonal prism has twelve
Hexagonal_prism
Geometric space with four dimensions
ordinary space is called Euclidean space because it corresponds to Euclid's geometry, which was originally abstracted from the spatial experiences of everyday
Four-dimensional_space
Bottom of a geometric figure
In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured
Base_(geometry)
Prism with a 5-sided base
In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with seven faces, fifteen edges, and ten vertices. If
Pentagonal_prism
Polyhedron with 12 congruent golden rhombus faces
In geometry, the Bilinski dodecahedron is a convex polyhedron with twelve congruent golden rhombus faces. It has the same topology as the face-transitive
Bilinski_dodecahedron
Peak or top of a geometric figure
In geometry, an apex (pl.: apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to
Apex_(geometry)
Technique in statistics
Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It
Information_geometry
Alternation (geometry) Dual polyhedron Gyration (geometry) Elongation (geometry) Augmentation (geometry) Diminishment (geometry) Greatening (geometry) Aggrandizement
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Concept in geometry
In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron
Face_diagonal
34th Johnson solid (32 faces)
In geometry, the pentagonal orthobirotunda is a polyhedron constructed by attaching two pentagonal rotundae along their decagonal faces, matching like
Pentagonal_orthobirotunda
Area of all the sides of the object, excluding the area of its base and top
Surface area Prism (geometry) Cylinder (geometry) Cone Pyramid (geometry) Frustum Net (polyhedron) Jacobs, Harold R. (1974), Geometry, Freeman & Co., p
Lateral_surface
Subspace of n-space whose dimension is (n-1)
In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like
Hyperplane
Tiling of euclidean or hyperbolic space of three or more dimensions
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of
Honeycomb_(geometry)
Area of mathematics
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there
Discrete differential geometry
Discrete_differential_geometry
3D computer animation method
"morph target" is a deformed version of a shape. When applied to a human face, for example, the head is first modelled with a neutral expression and a
Morph_target_animation
Geometric space with five dimensions
or physical space that has five independent dimensions. In physics and geometry, such a space extends the familiar three spatial dimensions plus time (4D
Five-dimensional_space
Polyhedron with 12 faces
In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with
Dodecahedron
Any of the five regular polyhedra
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are
Platonic_solid
Geometric transformation
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale
Scaling_(geometry)
Archimedean solid with 8 faces
In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges
Truncated_tetrahedron
Archimedean solid with 32 faces
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges
Truncated_dodecahedron
Rigidity theorem for convex polyhedra
theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent
Cauchy's_theorem_(geometry)
In geometry, a monostatic polytope or unistable polyhedron is a d {\displaystyle d} -polytope which "can stand on only one face". They were described in
Monostatic_polytope
Property of a mathematical space
back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William
Dimension
Archimedean solid with 32 faces
In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (icosi-) triangular faces and twelve (dodeca-) pentagonal faces
Icosidodecahedron
Cutting three-dimensional solids into particular shapes
Descriptive geometry can be considered as an evolution of stereotomy. In technical drawing stereotomy is sometimes referred to as descriptive geometry, and "is
Stereotomy (descriptive geometry)
Stereotomy_(descriptive_geometry)
Polyhedron with eight triangular faces
In geometry, an octahedron (pl.: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid
Octahedron
Uniform star polyhedron with 112 faces
In geometry, the small retrosnub icosicosidodecahedron (also known as a retrosnub disicosidodecahedron, small inverted retrosnub icosicosidodecahedron
Small retrosnub icosicosidodecahedron
Small_retrosnub_icosicosidodecahedron
Flat-sided three-dimensional shape
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure
Polyhedron
3D geometric shape
In geometry, a rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry
Rhombic_hexecontahedron
Mechanical seal
dry-running mechanical face seals that consist of a mating (rotating) ring and a primary (stationary) ring. When operating, lifting geometry in the rotating
Dry_gas_seal
Infinite regular skew polyhedron
In geometry, a regular skew apeirohedron is an infinite regular skew polyhedron. They have either skew regular faces or skew regular vertex figures. In
Regular_skew_apeirohedron
Geometric operation on a regular polytope
In geometry, a cantellation is a 2nd-order truncation in any dimension that bevels a regular polytope at its edges and at its vertices, creating a new
Cantellation_(geometry)
Molecular geometry
rectangular faces). It is very similar to the capped square antiprismatic molecular geometry, and there is some dispute over the specific geometry exhibited
Tricapped trigonal prismatic molecular geometry
Tricapped_trigonal_prismatic_molecular_geometry
Operation that cuts polytope vertices, creating a new facet in place of each vertex
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates
Truncation_(geometry)
Polyhedron with 20 faces
In geometry, an icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι
Icosahedron
Space-filling polyhedron with 8 faces
In geometry, the elongated gyrobifastigium or gabled rhombohedron is a space-filling octahedron with 4 rectangles and 4 right-angled pentagonal faces. The
Elongated_gyrobifastigium
Shape with four equal sides and angles
In geometry, a square is a regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles
Square
Geometric operation on convex polytopes
In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices
Expansion_(geometry)
Polyhedron with 6 congruent rhombus faces
In geometry, a trigonal trapezohedron is a polyhedron with six congruent quadrilateral faces, which may be scalene or rhomboid. The variety with rhombus-shaped
Trigonal_trapezohedron
Polyhedron with 9 faces
In geometry, an enneahedron (or nonahedron) is a polyhedron with nine faces. There are 2606 types of convex enneahedra, each having a different pattern
Enneahedron
2005 studio album by The Clientele
Strange Geometry is the third studio album by English indie pop band The Clientele. The album was released on 30 August 2005 by Merge Records and on 5
Strange_Geometry
Mathematical treatise by Euclid
(polyhedra with three pairs of parallel faces). The three sections of Book XI include content on: solid geometry (1–19), solid angles (20–23), and parallelepipeds
Euclid's_Elements
Triangular prism attached by a square pyramid
In geometry, the augmented triangular prism is a polyhedron constructed by attaching an equilateral square pyramid onto one of the square faces of a triangular
Augmented_triangular_prism
Cupola with octagonal base
In geometry, the square cupola (sometimes called lesser dome) is a cupola with an octagonal base. In the case of all edges being equal in length, it is
Square_cupola
Math concept
simplicial complexes and arise in various areas of polyhedral geometry, such as tropical geometry, splines and hyperplane arrangements. A polyhedral complex
Polyhedral_complex
Type of mechanical connection
on the end faces of each half shaft. Hirth joints are not considered to be the same as face spline joints, due to their differing geometry. Hirth joints
Hirth_joint
Geometric operation applied to a polyhedron
In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler's names of two Archimedean solids, for the snub cube (cubus
Snub_(geometry)
Polyhedron made by truncating one end of a trapezohedron
constructed with equilateral triangles around the base, and the geometry adjusted so the kite faces have the same area as the equilateral triangles. The last
Diminished_trapezohedron
Polyhedron with 60 faces
In geometry, the great ditrigonal dodecacronic hexecontahedron (or great lanceal trisicosahedron) is a nonconvex isohedral polyhedron. It is the dual of
Great ditrigonal dodecacronic hexecontahedron
Great_ditrigonal_dodecacronic_hexecontahedron
Type of three-dimensional crystal structural geometry
orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic. The primitive cell of the base-centered orthorhombic
Orthorhombic_crystal_system
Kepler–Poinsot polyhedron with 20 faces
In geometry, the great icosahedron is one of four Kepler–Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol {3,5⁄2} and Coxeter-Dynkin
Great_icosahedron
Form of geometry without distances
Ordered geometry is a form of geometry featuring the concept of intermediacy (or "betweenness") but, like projective geometry, omitting the basic notion
Ordered_geometry
Line segment joining a triangle's vertex to the midpoint of the opposite side
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has
Median_(geometry)
25th Johnson solid (37 faces)
In geometry, the gyroelongated pentagonal rotunda is a Johnson solid, a convex polyhedron with thirty equilateral triangles, six regular pentagons, and
Gyroelongated pentagonal rotunda
Gyroelongated_pentagonal_rotunda
Antiprism with a five-sided base
In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two
Pentagonal_antiprism
Theorem about triangles
In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle △ABC, let the lines AO, BO, CO be drawn from the vertices to a common
Ceva's_theorem
Polyhedron with 60 faces
In geometry, the great dodecacronic hexecontahedron (or great lanceal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform
Great dodecacronic hexecontahedron
Great_dodecacronic_hexecontahedron
Convex polyhedron with six faces with four edges each
In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular
Cuboid
Data structure for representing polygon meshes in computer memory
and describes both the geometry and topology of a model. Three types of records are used: vertex records, edge records, and face records. Given a reference
Winged_edge
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FACE GEOMETRY
FACE GEOMETRY
FACE GEOMETRY
FACE GEOMETRY
FACE GEOMETRY
FACE GEOMETRY
FACE GEOMETRY
FACE GEOMETRY
FACE GEOMETRY
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