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octahedron

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octahedron
octahedron, octo- (ɒktəˈhiːdrən, -ˈhɛdrən) Pl. -ons or -a. Also 6–8 octa(h)edrum, 6–9 octaedron, 7–9 octoedron. [a. Gr. ὀκτάεδρον an octahedron, neuter of ὀκτάεδρος adj., eight-sided, f. ὀκτα- octa- + ἕδρα seat. In L. octaëdron, med.L. octa(h)edrum (Du Cange), F. octaèdre, also octohèdre (1587 in Ha... Oxford English Dictionary
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Octahedron (album)
The song eventually ended up on Octahedron as "Since We've Been Wrong". But that's not to discredit the more measured side of Octahedron. wikipedia.org
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Regular Octahedron -- from Wolfram MathWorld
The regular octahedron, often simply called "the" octahedron, is the Platonic solid with six polyhedron vertices, 12 polyhedron edges, and eight equivalent equilateral triangular faces, denoted 8{3}. It is illustrated above together with a wireframe version and a net that can be used for its construction. The regular octahedron is also the uniform polyhedron with Maeder index 5 (Maeder 1997 ...
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Bricard octahedron
These points form the vertices of the octahedron. The triangular faces of the octahedron have one point from each of the three symmetric pairs. As an example, the six points (0,0,±1), (0,±1,0), and (±1,0,0) form the vertices of a regular octahedron, with each point opposite in the octahedron to wikipedia.org
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connectivity of octahedron We can easily prove that the edge-connectivity is $\le4$ so then the connectivity of the octahedron is $\le4$ . It is obvious that there are not cut-vertices in the graph so that leaves eith...
The octahedron is a symmetric graph. Therefore the octahedron graph is 4-connected.
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Snub octahedron
Snub octahedron may refer to: Icosahedron, with pyritohedral symmetry, , Snub cube, or snub cuboctahedron, , wikipedia.org
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How many octahedrons in icosahedron How many different ways can octahedron be inscribed in icosahedron so that all vertices of octahedron are selected vertices of icosahedron? ![octahedrons in icosahedron]( Can it e...
According to this page the answer is no, you can't inscribe an octahedron in an icosahedron so the vertices coincide.
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Stellated octahedron
The stellated octahedron is the only stellation of the octahedron. octahedron can be constructed in several ways: It is a stellation of the regular octahedron, sharing the same face planes. wikipedia.org
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Cardinality of the largest clique in an octahedron Is the largest clique in an octahedron is 3? I have no idea how to deal with this question. QQ
Pick any face of an octahedron. This is a clique with 3 vertices. Now, suppose that there exists a clique with 4 vertices.
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Elongated octahedron
Starting with the regular octahedron, it is elongated along one axes, adding 8 new triangles. This construction has been called a triamond stretched octahedron. wikipedia.org
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Probability of a certain result obtaioned by throwing an octahedron Assume having a fair octahedron. We throw it $93$ times and get the following results: $\\{33;7;8;1;2;0;5;37\\}$ The numbers represent how many time...
Use multinomial distribution with $p_i = 1/8$, $n=93, n_1 = 33, n_2 = 7, n_3 = 8, n_4 = 1, n_5 = 2, n_6 = 0, n_7 = 5, n_8 = 37$ for i = 1 to 8. The required prob = $$\frac{93!}{33!\cdot7!\cdot8!\cdot1!\cdot2!\cdot0!\cdot5!\cdot37!}\cdot{(\frac{1}{8})}^{93}$$ <
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Truncated octahedron
In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's octahedron in the three-dimensional subspace . wikipedia.org
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Does an octahedron have more than $5$ reflectional symmetries? I counted $5$ planes of reflection for the octahedron: two corresponding to planes orthogonal to two sides and going through one vertex, two corresponding...
For the first type you counted two planes, with a north and south pole. However there are three ways to choose north/south poles, so there should really be six reflections not two. For the second type your plane is the equator, and again a north and south pole. But there are three ways again, so ins...
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Great triakis octahedron
In geometry, the great triakis octahedron is the dual of the stellated truncated hexahedron (U19). It has 24 intersecting isosceles triangle faces. References External links Mathworld - Great Triakis Octahedron Mathworld - Small Triakis Octahedron Uniform polyhedra and duals Dual uniform polyhedra wikipedia.org
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Showing that the cube and the octahedron have the same symmetry group I am aware that the octahedron and the cube have the same symmetry group but I was wondering how we show this concretely. I have looked/been thinki...
How about: put the octahedron in a cube in the natural way (each vertex of the octahedron is at the center of one of the cube's faces). Now prove that any symmetry of the octahedron corresponds to a symmetry of the cube, and vice-versa.
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