Jerry

Great pattern recognition game. Makes you think about how the numbers are arranged in specific shapes that allows you to find out where the bombs are. Speaking of shapes, Octahedron From Wikipedia, the free encyclopedia Jump to navigationJump to search For the album, see Octahedron (album). Regular octahedron Octahedron.jpg (Click here for rotating model) Type Platonic solid Elements F = 8, E = 12 V = 6 (χ = 2) Faces by sides 8{3} Conway notation O aT Schläfli symbols {3,4} r{3,3} or {\displaystyle {\begin{Bmatrix}3\\3\end{Bmatrix}}}{\begin{Bmatrix}3\\3\end{Bmatrix}} Face configuration V4.4.4 Wythoff symbol 4 | 2 3 Coxeter diagram CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png Symmetry Oh, BC3, [4,3], (*432) Rotation group O, [4,3]+, (432) References U05, C17, W2 Properties regular, convexdeltahedron Dihedral angle 109.47122° = arccos(−​1⁄3) Octahedron vertfig.png 3.3.3.3 (Vertex figure) Hexahedron.png Cube (dual polyhedron) Octahedron flat.svg Net 3D model of regular octahedron. In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. A regular octahedron is the dual polyhedron of a cube. It is a rectified tetrahedron. It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations. An octahedron is the three-dimensional case of the more general concept of a cross polytope. A regular octahedron is a 3-ball in the Manhattan (ℓ1) metric. Regular octahedron Dimensions If the edge length of a regular octahedron is a, the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is {\displaystyle r_{u}={\frac {\sqrt {2}}{2}}a\approx 0.707\cdot a}{\displaystyle r_{u}={\frac {\sqrt {2}}{2}}a\approx 0.707\cdot a} and the radius of an inscribed sphere (tangent to each of the octahedron's faces) is {\displaystyle r_{i}={\frac {\sqrt {6}}{6}}a\approx 0.408\cdot a}{\displaystyle r_{i}={\frac {\sqrt {6}}{6}}a\approx 0.408\cdot a} while the midradius, which touches the middle of each edge, is {\displaystyle r_{m}={\tfrac {1}{2}}a=0.5\cdot a}{\displaystyle r_{m}={\tfrac {1}{2}}a=0.5\cdot a} Orthogonal projections The octahedron has four special orthogonal projections, centered, on an edge, vertex, face, and normal to a face. The second and third correspond to the B2 and A2 Coxeter planes. Orthogonal projections Centered by Edge Face Normal Vertex Face Image Cube t2 e.png Cube t2 fb.png 3-cube t2 B2.svg 3-cube t2.svg Projective symmetry [2] [2] [4] [6] Spherical tiling The octahedron can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. This projection is conformal, preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane. Uniform tiling 432-t2.png Octahedron stereographic projection.svg Orthographic projection Stereographic projection Cartesian coordinates An octahedron with edge length √2 can be placed with its center at the origin and its vertices on the coordinate axes; the Cartesian coordinates of the vertices are then ( ±1, 0, 0 ); ( 0, ±1, 0 ); ( 0, 0, ±1 ).