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The regular icosahedron can also be constructed starting from a regular octahedron. All triangular faces of a regular octahedron are breaking, twisting at a certain angle, and filling up with other equilateral triangles. This process is known as snub, and the regular icosahedron is also known as snub octahedron. [5]
The convex regular icosahedron is usually referred to simply as the regular icosahedron, one of the five regular Platonic solids, and is represented by its Schläfli symbol {3, 5}, containing 20 triangular faces, with 5 faces meeting around each vertex. Its dual polyhedron is the regular dodecahedron {5, 3} having three regular pentagonal faces ...
Icosahedral symmetry fundamental domains A soccer ball, a common example of a spherical truncated icosahedron, has full icosahedral symmetry. Rotations and reflections form the symmetry group of a great icosahedron. In mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron.
Shqip; Slovenščina; Suomi; ... form regular polyhedra. For example, HIV is enclosed in a regular icosahedron, as is the head of a typical myovirus. [6] [7]
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra:
The dihedral angle of a regular icosahedron is around 138.2°, so it is impossible to fit three icosahedra around an edge in Euclidean 3-space. However, in hyperbolic space, properly scaled icosahedra can have dihedral angles of exactly 120 degrees, so three of those can fit around an edge.
Category:Platonic solids for the five convex regular polyhedra. Category:Kepler–Poinsot polyhedra for the four non-convex regular polyhedra. Category:Archimedean solids for the remaining convex semi-regular polyhedra, excluding prisms and antiprisms. Category:Quasiregular polyhedra for uniform polyhedra which are also edge-transitive.
In mathematics, an icosahedral number is a figurate number that represents an icosahedron. The nth icosahedral number is given by the formula (+). The first such numbers are: 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, … (sequence A006564 in the OEIS).