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A gyroid minimal surface, coloured to show the Gaussian curvature at each point 3D model of a gyroid unit cell. A gyroid is an infinitely connected triply periodic minimal surface discovered by Alan Schoen in 1970. [1] [2] It arises naturally in polymer science and biology, as an interface with high surface area.
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines , circles or other points.
The pentagonal icositetrahedron can be constructed from a snub cube without taking the dual. Square pyramids are added to the six square faces of the snub cube, and triangular pyramids are added to the eight triangular faces that do not share an edge with a square.
In the geometry of hyperbolic 3-space, the order-5-3 apeirogonal honeycomb or ∞,5,3 honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell consists of an order-5 apeirogonal tiling whose vertices lie on a 2-hypercycle , each of which has a limiting circle on the ideal sphere.
The gyrated tetrahedral-octahedral honeycomb or gyrated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of octahedra and tetrahedra in a ratio of 1:2. It is vertex-uniform with 8 tetrahedra and 6 octahedra around each vertex. It is not edge-uniform. All edges have 2 tetrahedra and 2 ...
A honeycomb is called regular if the group of isometries preserving the tiling acts transitively on flags, where a flag is a vertex lying on an edge lying on a face lying on a cell. Every regular honeycomb is automatically uniform. However, there is just one regular honeycomb in Euclidean 3-space, the cubic honeycomb.
The runcinated order-5 cubic honeycomb or runcinated order-4 dodecahedral honeycomb, has cube, dodecahedron, and pentagonal prism cells, with an irregular triangular antiprism vertex figure. It is analogous to the 2D hyperbolic rhombitetrapentagonal tiling , rr{4,5}, with square and pentagonal faces: