how does geometry relate to crystals?
364902
Most crystals form three basic shapes: simple cubic, body-centered cubic, and face-centered cubic.  Simple cubic has molecules at each corner of a cube, body-centered cubic has molecules at each corner of a cube and one in the center, and face-centered cubic has molecules at each corner of a cube and one in the center of each face.
852645
technically, a system that consists of homogeneous atoms or molecules bonded to each other is called a "lattice," or a "crystal lattice."  The difference is that, with a molecule, splitting it or removing components of it would change its chemical properties, whereas with a lattice, splitting it causes no chemical changes and only reduces its size.  Therein lies the difference.
516070
a hexagonal prism we learned about it in geometry
63381
Conjecture A\nIf B is the area of the base pf a right rectangular prism and H is the height of the solid, then the formula for the volume is V= _?_\nConjecture B \nIf B is the area of the base of a right prism (or cylinder) and H is the height of the solid, then the formula for the volume is V= _? _\nConjecture C\nThe volume of an oblique prism (or cylinder) is the same as the column of the right prism (or cylinder) that has the same _? _ and the same _? _\nPrism-Cylinder Volume Conjecture\nThe volume of a prism or a cylinder is the _? _ multiplied by the _? _\nPyramid-Cone Volume Conjecture\nIf B is the area of the base of a pyramid or a cone and H is the height of the solid, then the formula for the volume is V= _? _ \nSphere Volume Conjecture\nThe volume of a sphere with radius r is given by the formula _?_\nSphere Surface Area Conjecture\nThe surface area, S, of a sphere with radius r is given by the formula _? _\n\nSolution 47916\n\n#1\nV = BH\n#2\nV = BH\n#3\nsame base area and same height\n#4 \nthe base area multiplies the height\n#5\nV = (1/3)BH\n#6\nV = (4/3)(pi)(r^3)\n#7\nS = 4(pi)(r^2)
152387
polyhedron (pŏl'ēhē'drən) , closed solid bounded by plane faces; each face of a polyhedron is a polygon. A cube is a polyhedron bounded by six polygons (in this case squares) meeting at right angles. Although regular polygons are possible for any number of sides, there are only five possible regular polyhedrons, having congruent faces, each a regular polygon and meeting at equal angles. The five regular polyhedrons are also known as the Platonic solids, although they were known to the Greeks before the time of Plato. They are the tetrahedron, bounded by four equilateral triangles; the hexahedron, or cube, bounded by six squares; the octahedron, bounded by eight equilateral triangles; the dodecahedron, bounded by twelve regular pentagons; and the icosahedron, bounded by twenty equilateral triangles. The 18th-century Swiss mathematician Leonhard Euler showed that for any simple polyhedron, i.e., a polyhedron containing no holes, the sum of the number of vertices V and the number of faces F is equal to the number of edges E plus 2, or V+F=E+2
930459
Pure copper has a certain crystal structure as does pure tin.  Bronze will have a different crystal structure, the exact form of which will depend on the ratio of copper and tin.  (I am treating this as a general scenario, there is a chance that the crystal structure of copper and tin takes the same form - but this would be coincidental; and by chance/coincidence I don't mean theory doesn't define them - i just don't know crystal theory all that well)
747556
1. Crystals\n\n2. Covalent bonds\n\n3.  Molecules\n\n4.  Vasoline\n\nCrossword = nucleuss\n\nH- Ion
1018103
http://www.crystalxp.net/galerie/en.id.130.htm
845473
decagon - 2 d figure\nor \ndecahedron - 3 d figure
732059
I suspect that what you are really asking about is the type of crystal lattice for a given ion.  Am I right?\nIf so, you need to do some research on the specific salt you are researching.  There are a few rules that can help predict how a salt will arrange itself in space but they are really complicated and I've forgotten them after only thirty years out of that class.  Ions in a crystal will arrange themselves depending on the nature of the orbitals used for bonding with the counterions.  Best to look each one up.  The link below should give you a start.
166652
For a specific kind of solid, yes.  In general, no.\n\nFor example, a cube with a side length of s will have a volume of s^3 and a surface area of 6s^2.  So, for any cube, the volume and surface area will be in the ratio of s/6.\n\nFor a right cylinder, the volume is (pi)r^2*h, while the surface area is given by 2(pi)r^2 + 2(pi)r*h, which through some algebraic manipulation can be reduced to 2(r+h)(pi*r).  So the ratio of volume to surface area for a cylinder will be r*h to 2(r+h)... \n\nFor other solids, you could observe similar relationships, but in general, the relationship depends on the shape of the solid, so you could not make a definitive statement about the surface area enclosing a certain volume unless you also knew what shape that volume was in.
786816
Structural isomerism\n\nStereoisomerism (Geometrical isomerism and optical isomerism)
953022
There sure is!  \n\nFirst, recall this: given a tetrahedron, choose any of its faces to be its base.  Now find the area of the base (remember all the faces are triangles).  Next, find the perpendicular distance from the fourth vertex of the tetrahedron to the plane that contains the base.  This distance is the height of the tetrahedron.  Now the volume of the tetrahedron is 1/3 X area of its base X its height.  \n\nNow, using three-dimensional Cartesian co-ordinates, consider the tetrahedron ABCD where A=(0,0,0), B=(27,0,0), C=(0,16,0), and D=(0,0,3).  Face ABC is a right triangle in the x-y plane.  The two perpendicular legs of ABC have lengths 16 and 27, so the area of face ABC is 1/2 X 16 X 27 = 216.  The distance of D from the x-y plane is 3, so the volume of ABCD is 1/3 X 3 X 216 = 216.  \n\nLet E=(8,2,0).  E lies in the x-y plane in the interior of ABC.  Join E to A, B, C, and D with line segments.  Triangle ABC is subdivided into triangles ABE, BCE, and ACE, and tetrahedron ABCD is subdivided into tetrahedra ABED, BCED, and ACED, and the heights of these three sub-tetrahedra are also 3.\n\nThe distance from E to the x-axis is 2, so triangle ABE has \narea = 1/2 X 2 X 27 = 27 and tetrahedron ABED has \nvolume = 1/3 X 3 X 27 = 27.  \n\nThe distance from e to the y-axis is 8, so triangle BCE has \narea = 1/2 X 8 X 16 = 64 and tetrahedron BCED has \nvolume = 1/3 X 3 X 64 = 64.  \n\nArea of ABC = 216, area of ABE = 27, and area of BCE = 64, so triangle ACE has area = 216 - 27 - 64 = 125 and tetrahedron ACED has area 1/3 X 3 X 125 = 125.  \n\nThat does it!
778725
Consider one cube of the lattice.  there will be one atom on each corner.\n\nWith BCC there will be one atom in the centre of the cube.\nWith FCC there is one atom in the centre of each face of the cube - a dice with one spot on each face.\nIt's a very long time since I did this, but I think steel is BCC at normal temperatures and chnges to FCC on heating.
854984
For my science fair, I grew crystals.  My dad teaches at the high school I went to, and the physics teacher there told him about it.  Here's a neat site that explains how to do it.  I found it fascinating!\n\nhttp://www.sdnhm.org/kids/minerals/grow-crystal.html
81841
Depends on the crystal structure of the alloy they constitute
188634
Geometry is related to soccer in many ways.  Some of them have already been listed, but I'll try anyways.\n\nSimple things like the ball, nets, etc. have already been mentioned.  But, the real geometry comes in the game play.  \n\n1. A wall pass=a trianle.  \n2. A through ball=hypotenuse of that triangle.\n3. A goal scored in the upper V=corner angle of a rectangle.\n4. A cross=an arc (of some type)\n5. Even the formations can be related to geometry.  A 4-4-2 is similar to dimensions (of something).\n6. The goal=rectangle.\n7. The ball=sphere.\n8. The net=a bunch of little squares.\n9. Yellow and red cards=rectangles.\n10. Ref's watch=either circle or rectangle.\n\nIt's been a while since I took geometry, so I'm sorry I can't be more specific with the terminology.  But hopefully I've pointed you in the right direction.\n\n(And I actually got all ten down!  Woohoo!)