Artificial intelligent assistant

octahedral

answer Answers

ProphetesAI is thinking...

MindMap

Sources

1
octahedral
octahedral, octo-, a. (ɒktəˈhiːdrəl, -ˈhɛdrəl) Also octaedral, octoedral. [f. late L. octa(h)edros, a. Gr. ὀκτάεδρ-ος eight-sided: see octahedron and -al1.] Having the form of an octahedron; contained by eight plane (esp. triangular) faces.1758 Reid tr. Macquer's Chym. I. 222 The crystals of Alum ar... Oxford English Dictionary
prophetes.ai 0.0 3.0 0.0
2
Octahedral number
The octahedral number can be obtained by the formula: The first few octahedral numbers are: 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891 . the sum of at most 7 octahedral numbers. wikipedia.org
en.wikipedia.org 0.0 1.5 0.0
3
Octahedral cupola
In 4-dimensional geometry, the octahedral cupola is a 4-polytope bounded by one octahedron and a parallel rhombicuboctahedron, connected by 20 triangular Related polytopes The octahedral cupola can be sliced off from a runcinated 24-cell, on a hyperplane parallel to an octahedral cell. wikipedia.org
en.wikipedia.org 0.0 0.90000004 0.0
4
The class equation of the octahedral group I know that the class equation of the octahedral group is this: $$1 + 8 + 6 + 6 + 3$$ I think the $8$ stands for the $8$ vertices, the $6$ could be $6$ faces and $6$ pairs o...
These numbers have nothing to do with the numbers of vertices, faces, or edges, at least not so directly. The octohedral group has $1$ identity element, which is the sole member of its own conjugacy class. The group has $8$ three-fold rotations along axes joining two opposite vertices. It has $6$ tw...
prophetes.ai 0.0 0.6 0.0
5
Octahedral prism
Alternative names Octahedral dyadic prism (Norman W. Projections The octahedron-first orthographic projection of the octahedral prism into 3D space has an octahedral envelope. wikipedia.org
en.wikipedia.org 0.0 0.6 0.0
6
What is the fundamental group of the octahedral symmetry group Oh? Do discrete groups have a well defined topology? If so, what is the fundamental group of the octahedral symmetry group Oh? In other words, are all the...
Of course it has a well-defined topology...the discrete one (all subsets are open subsets). The fundamental group requires a choice of base point. Given that, of course all the base-point-preserving maps are continuously deformable to each other, since there's only one of them! So the fundamental gr...
prophetes.ai 0.0 0.3 0.0
7
Octahedral pyramid
Occurrences of the octahedral pyramid The regular 16-cell has octahedral pyramids around every vertex, with the octahedron passing through the center of The octahedral pyramid is the vertex figure for a truncated 5-orthoplex, . wikipedia.org
en.wikipedia.org 0.0 0.3 0.0
8
Is SO(3)/O isomorphic to SO(3)? Is SO(3)/O isomorphic to SO(3)? By O, I mean the octahedral rotation symmetry group. My intuition says that they are not. But I don't know how to disprove it
I don't think any such subgroup is normal, so the quotient isn't a group. Hence it's not a group isomorphic to $SO(3)$.
prophetes.ai 0.0 0.3 0.0
9
Octahedral cluster
Octahedral clusters are inorganic or organometallic cluster compounds composed of six metals in an octahedral array. Other classes of octahedral clusters In the area of metal carbonyl clusters, a prototypical octahedral cluster is [Fe6C(CO)16]2−, which is obtained by wikipedia.org
en.wikipedia.org 0.0 0.3 0.0
10
Close-packing of equal spheres of ABCDABCDABCD Wikipedia said that there are two lattices that can create high density, cubic close-packed from ABCABC layers and hexagonal close-packed from ABABAB layers that can form...
We really have only three possible placements of the layers of spheres, because the centers of spheres in any layer project into only one of three distinct sets of points on the "ground". We label those three sets A, B, C and that's it. No more. What we _can_ have is orderings among A, B, C other th...
prophetes.ai 0.0 0.3 0.0
11
Centered octahedral number
A centered octahedral number or Haüy octahedral number is a figurate number that counts the number of points of a three-dimensional integer lattice that The Haüy octahedral numbers are named after René Just Haüy. wikipedia.org
en.wikipedia.org 0.0 0.0 0.0
12
Binary octahedral group
It is an extension of the chiral octahedral group O or (2,3,4) of order 24 by a cyclic group of order 2, and is the preimage of the octahedral group under Higher dimensions The binary octahedral group generalizes to higher dimensions: just as the octahedron generalizes to the orthoplex, the octahedral group wikipedia.org
en.wikipedia.org 0.0 0.0 0.0
13
Characters and dimensions I was looking at one of the problems in the book, "Algebra" by Artin which states: Find the dimension of the irreducible representations of the octahedral group, dihedral groups $D_5$ and $D...
Let me add: If you want to apply this technique to $D_6$ and the octahedral group, note that $D_6$ has has order $12$ and $6$ conjugacy classes, and the octahedral group has order $24$ and $5$ conjugacy classes.
prophetes.ai 0.0 0.0 0.0
14
Octahedral symmetry
Chiral octahedral symmetry O, 432, or [4,3]+ of order 24, is chiral octahedral symmetry or rotational octahedral symmetry . Full octahedral symmetry Oh, *432, [4,3], or m3m of order 48 - achiral octahedral symmetry or full octahedral symmetry. wikipedia.org
en.wikipedia.org 0.0 0.0 0.0
15
Octahedral molecular geometry
For example, , which is not octahedral in the mathematical sense due to the orientation of the bonds, is referred to as octahedral. In an octahedral complex, this degeneracy is lifted. wikipedia.org
en.wikipedia.org 0.0 0.0 0.0