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tetrahedron and is
The alternated cubic honeycomb is one of 28 space-filling uniform tessellations in Euclidean 3-space, composed of alternating yellow tetrahedron | tetrahedra and red octahedron | octahedra.
* With T < sub > d </ sub > symmetry, it is a cantellated tetrahedron.
In the Timaeus, Plato's major cosmological dialogue, the Platonic solid he associated with fire was the tetrahedron which is formed from four triangles and contains the least volume with the greatest surface area.
So the regular polyhedra — the Platonic solids and Kepler-Poinsot polyhedra — are arranged into dual pairs, with the exception of the regular tetrahedron which is self-dual.
A self-dual polyhedron is a polyhedron whose dual is a congruent figure, though not necessarily the identical figure: for example, the dual of a regular tetrahedron is a regular tetrahedron " facing the opposite direction " ( reflected through the origin ).
All silicate minerals have a base unit of a < sup > 4 -</ sup > silica tetrahedra — that is, a silicon cation coordinated by four oxygen anions, which gives the shape of a tetrahedron.
The base of unit of a silicate mineral is the < sup > 4 -</ sup > tetrahedron.
These chains can be single, where a tetrahedron is bound to two others to form a continuous chain ; alternatively, two chains can be merged to create double-chain silicates.
Tartaglia is also known for having given an expression ( Tartaglia's formula ) for the volume of a tetrahedron ( including any irregular tetrahedra ) as the Cayley – Menger determinant of the distance values measured pairwise between its four corners:
Four lithium atoms are shown in purple in a tetrahedron, and each lithium atom is bound to a butyl group ( carbon is black, hydrogen is white ).
This tetrahedron is also present in liquid and gaseous phosphorus up to the temperature of 800 ° C when it starts decomposing to molecules.
It can be viewed as a derivative of P < sub > 4 </ sub > wherein one P-P bond is broken, and one additional bond is formed between the neighbouring tetrahedron resulting in a chain-like structure.
In geometry, a tetrahedron ( plural: tetrahedra ) is a polyhedron composed of four triangular faces, three of which meet at each vertex.
The tetrahedron is the only convex polyhedron that has four faces.
The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex.

tetrahedron and one
The aluminosilicates — kyanite, andalusite, and sillimanite, all Al < sub > 2 </ sub > SiO </ sub > 5 </ sub >— are structurally composed of one < sup > 4 -</ sup > tetrahedron, and one Al < sup > 3 +</ sup > in octahedral coordination.
A regular tetrahedron is one in which all four faces are equilateral triangles, and is one of the Platonic solids.
In a trirectangular tetrahedron the three face angles at one vertex are right angles.
When only one pair of opposite edges are perpendicular, it is called a semi-orthocentric tetrahedron.
An isodynamic tetrahedron is one in which the cevians that join the vertices to the incenters of the opposite faces are concurrent, and an isogonic tetrahedron has concurrent cevians that join the vertices to the points of contact of the opposite faces with the inscribed sphere of the tetrahedron.
The Roman surface has four bulbous " lobes ", each one on a different corner of a tetrahedron.
A tetrahedron structure with vertices O, A, B, C. The product of the sines of ∠ OAB, ∠ OBC, ∠ OCA appears on one side of the identity, and the product of the sines of ∠ OAC, ∠ OCB, ∠ OBA on the other.
A caltrop ( also known as caltrap, galtrop, cheval trap, galthrap, galtrap, calthrop, crow's foot ) is an antipersonnel weapon made up of two or more sharp nails or spines arranged in such a manner that one of them always points upward from a stable base ( for example, a tetrahedron ).
* Caltrop, an antipersonnel weapon made up of two or more sharp nails or spines arranged in such a manner that one of them always points upward from a stable base ( for example, a tetrahedron )
He also proves the expression for the volume of a tetrahedron with one of the vertices at the origin as one sixth of the absolute value of the determinant formed by the coordinates of the other three vertices.
One hundred seventeen is the smallest possible length of the longest side of a Heronian tetrahedron ( one whose sides are all rational numbers ).
Then 10 more balls are stacked on top of those, then another 6, then another three and one ball at the top completes the tetrahedron.
The BCS of a tetrahedron divides it into 24 tetrahedra ; each part has one vertex at the center of, one on some face, one along some edge, and the last one at some vertex of.

tetrahedron and pyramid
In the case of a tetrahedron the base is a triangle ( any of the four faces can be considered the base ), so a tetrahedron is also known as a " triangular pyramid ".
The three-dimensional version is called Pascal's pyramid or Pascal's tetrahedron, while the general versions are called Pascal's simplices.
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron.
The coefficients can be defined with a generalization of Pascal's triangle to three dimensions, called Pascal's pyramid or Pascal's tetrahedron.
The primary radars of RAF Fylingdales are Active Electronically Scanned Array ( AESA ) ( phased array ) radars, mounted on each face of a truncated tetrahedron, typically referred to as the " pyramid ".
Between 1989 and 1992, Raytheon, the US defence contractor, completed a contract that saw the domes replaced by the current tetrahedron (' pyramid ') structure, housing the Active Electronically Scanned Arrays or AESA ( phased array ) radar.
In the churchyard, close to the porch, is a gravestone in the form of a three-sided pyramid ; a tetrahedron.

tetrahedron and which
It can be realized geometrically from a tetrahedron ( the faces of which correspond to the four large faces in the drawing, three of which are between pairs of fragments and the fourth of which forms the exterior ) by multiply truncating three of its vertices.
A 3-simplex is usually called a tetrahedron, and the 4-simplex, which is the basic building block in this theory, is also known as the pentatope, or pentachoron.
In the polymer it forms SiO < sub > 4 </ sub > groups which are configured as a tetrahedron with the silicon atom at the center, and four oxygen atoms at the corners.
The active site contains an iron ion which is coordinated by the sulphur atoms of four cysteine residues forming an almost regular tetrahedron.
A tetrahedron shape is the simplest space truss, consisting of six members which meet at four joints.
In the solid state of methyllithium, 4 lithium atoms form a tetrahedron with each face capped by a methyl group which bonds simultaneously to three Li atoms ( η < sup > 3 </ sup > hapticity ).
The New Age group Share International, founded by Benjamin Creme, practices a form of meditation called Transmission Meditation in which they meditate under an open metal-poled tetrahedron ; they believe that by doing so, they are tuning in to cosmic energy radiating from a cosmic entity known as Maitreya.
The edges of the truncated tetrahedron form a vertex-transitive graph ( also a Cayley graph ) which is not symmetric graph | symmetric.
A classical example of this is the duality of the platonic solids, in which the cube and the octahedron form a dual pair, the dodecahedron and the icosahedron form a dual pair, and the tetrahedron is self-dual.
In geometry, the barycentric coordinate system is a coordinate system in which the location of a point is specified as the center of mass, or barycenter, of masses placed at the vertices of a simplex ( a triangle, tetrahedron, etc .).
After fiddling with this structure for some time, Gygax decided ( as described in the same article in Dragon # 73 ) to change the structure from a tetrahedron to a cube in which four of the six faces were the " Inner Planes " described in the Players Handbook: Earth, Fire, Air, Water, and the Negative and Positive Material Planes.
Meffert also produces a similar puzzle called the Tetraminx, which is the same as the Pyraminx except that the trivial tips are removed, turning the puzzle into a truncated tetrahedron.
For example, in methane ( CH < sub > 4 </ sub >) a set of sp < sup > 3 </ sup > orbitals are formed by mixing one s and three p orbitals on the carbon atom, and are directed towards the four hydrogen atoms which are located at the vertices of a regular tetrahedron.
which is just times the volume of the tetrahedron formed by the plane described by the energy equation and the bounding planes of the positive octant.

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