In geometry, a vertex configuration is a shorthand notation for representing the vertex figure[dubious – discuss] of a polyhedron or tiling as the sequence...

symbol will have a vertex configuration p.q.p.q (or (p.q)2). More generally, a quasiregular figure can have a vertex configuration (p.q)r, representing...

kind of vertex. An isogonal polyhedron with all regular faces is also a uniform polyhedron and can be represented by a vertex configuration notation...

be represented in vertex configuration notation, by listing the faces in sequence around the vertex. For example 3.4.4.4 is a vertex with one triangle...

is a quasiregular tiling, alternating two types of polygons, with vertex configuration (3.6)2. It is also a uniform tiling, one of eight derived from the...

of each vertex (in G) specified. For example, the case described in degree 4 vertex situation is the configuration consisting of a single vertex labelled...

the vertex configuration, which is simply a list of the number of sides of the polygons around a vertex. The square tiling has a vertex configuration of...

to vertex) is the same as the edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Its center is like the apical vertex of...

the number of arrows pointing inwards at each vertex is 2. This restriction on the arrow configurations is known as the ice rule. In graph theoretic terms...

tiling can be described by its vertex configuration: the (identical) sequence of polygons around each (equivalent) vertex. All uniform tilings can be constructed...

polyhedral net can be cut from two rows of a square tiling (with vertex configuration 4.4.4.4): a band of n squares, each attached to a crossed rectangle...

by their vertex configuration, the sequence of faces that exist on each vertex. For example 4.8.8 means one square and two octagons on a vertex. These 11...

congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra: Geometers have studied the Platonic...

separately). Here the vertex configuration refers to the type of regular polygons that meet at any given vertex. For example, a vertex configuration of 4.6.8 means...

and are therefore prismatoids. Because they are isogonal (vertex-transitive), their vertex arrangement uniquely corresponds to a symmetry group. The difference...

pentagrams meeting at each vertex. It shares its vertex arrangement, although not its vertex figure or vertex configuration, with the regular dodecahedron...

Chamfered Tetrahedron Chamfered Solids Vertex- and edge-truncation of the Platonic and Archimedean solids leading to vertex-transitive polyhedra Livio Zefiro...

edges are known as the lateral edges of the pyramid; they meet at the fifth vertex, called the apex. If the pyramid's apex lies on a line erected perpendicularly...

t{6}, or a twice-truncated triangle, tt{3}. The internal angle at each vertex of a regular dodecagon is 150°. The area of a regular dodecagon of side...

"Exception": a retrograde star antiprism with equilateral triangle bases (vertex configuration: 3.3/2.3.3) can be uniform; but then, it has the appearance of an...

not regular with D2 symmetry. The angles at the two vertices with vertex configuration 6.6.6 are arccos ⁡ ( − 1 5 ) = 116.565 ∘ {\displaystyle \arccos \left({\frac...

rhombicuboctahedron, but it is not an Archimedean solid because it is not vertex-transitive. The skeleton of a rhombicuboctahedron can be represented as...

1-uniform tiling can be defined by its vertex configuration. Higher k-uniform tilings are listed by their vertex figures, but are not generally uniquely...

one vertex configuration. Moreover, the relative area of either of these regions equates to the frequency of the corresponding vertex configuration within...

solid because it lacks a set of global symmetries that map every vertex to every other vertex, unlike the 13 Archimedean solids. It is also a canonical polyhedron...

graph is one of only six graphs in which every neighborhood is a 4- or 5-vertex cycle. The dual polyhedron of the triaugmented triangular prism is an associahedron...

self-intersecting. Each polyhedron can contain either star polygon faces, star polygon vertex figures, or both. The complete set of 57 nonprismatic uniform star polyhedra...

dual-semiregular polyhedron Faces 2n congruent kites Edges 4n Vertices 2n + 2 Vertex configuration V3.3.3.n Schläfli symbol { } ⨁ {n} Conway notation dAn Coxeter diagram...

related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2n.2n), and [n,3] Coxeter group symmetry. Two 2-uniform tilings...

reduced to a single edge. More generally any vertex-uniform polyhedron or tiling with a vertex configuration consisting of all even-numbered elements can...