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Small triambic icosahedron (First stellation of icosahedron) (Triakis icosahedron) I h: 27 Second stellation of icosahedron: I h: 28 Excavated dodecahedron (Third stellation of icosahedron) I h: 29 Fourth stellation of icosahedron: I h: 30 Fifth stellation of icosahedron: I h: 31 Sixth stellation of icosahedron: I h: 32 Seventh stellation of ...
The icosahedron has a large number of stellations. Coxeter et al. (1938) in their work stated fifty-nine stellations were identified for the regular icosahedron. [24] Regular icosahedron itself is the first stellation of an icosahedron, and the subsequent stellation obtained by radiating spikes from the faces of a regular icosahedron.
In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed from ...
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.
The Dymaxion map projection, also called the Fuller projection, is a kind of polyhedral map projection of the Earth's surface onto the unfolded net of an icosahedron.The resulting map is heavily interrupted in order to reduce shape and size distortion compared to other world maps, but the interruptions are chosen to lie in the ocean.
Regular icosahedron and its non-convex variant, which differs from Jessen's icosahedron in having different vertex positions and non-right-angled dihedrals. A similar shape can be formed by keeping the vertices of a regular icosahedron in their original positions and replacing certain pairs of equilateral triangles by pairs of isosceles triangles.
The stellation diagram for the icosahedron with the central triangle marked for the original icosahedron. The Fifty-Nine Icosahedra is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie.
Net A geometric construction of the Tribonacci constant (AC), with compass and marked ruler, according to the method described by Xerardo Neira. 3d model of a pentagonal icositetrahedron In geometry , a pentagonal icositetrahedron or pentagonal icosikaitetrahedron [ 1 ] is a Catalan solid which is the dual of the snub cube .