Plasmonic mode engineering with templated self-assembled nanoclusters. Self-assembly of chiral nanoparticle pyramids with strong R/ S optical activity. Photoluminescence enhancement in CdSe/ZnS-DNA linked-Au nanoparticle heterodimers probed by single molecule spectroscopy. We also show that the octahedra can serve as programmable interparticle linkers, allowing one- and two-dimensional arrays to be assembled with designed particle arrangements. We show that the DNA frame and one set of nanoparticles can be used to create nanoclusters with different chiroptical activities. Cryo-electron microscopy is used to uncover the structure of the DNA frame and to reveal that the nanoparticles are spatially coordinated in the prescribed manner. The frame is a DNA origami octahedron and can be used to fabricate clusters with various symmetries and particle compositions. Here, we report a strategy for assembling three-dimensional nanoparticle clusters that uses a molecular frame designed with encoded vertices for particle placement. These nanoparticle architectures could offer tailored properties due to collective effects, but developing a general platform for fabricating such clusters is a significant challenge. It has four of the triangular faces, and 3 central squares.Three-dimensional mesoscale clusters that are formed from nanoparticles spatially arranged in pre-determined positions can be thought of as mesoscale analogues of molecules. The uniform tetrahemihexahedron is a tetrahedral symmetry faceting of the regular octahedron, sharing edge and vertex arrangement. The octahedron is the dual polyhedron to the cube. These symmetries can be emphasized by different colorings of the faces. This group's subgroups include D 3d (order 12), the symmetry group of a triangular antiprism D 4h (order 16), the symmetry group of a square bipyramid and T d (order 24), the symmetry group of a rectified tetrahedron. The octahedron's symmetry group is O h, of order 48, the three dimensional hyperoctahedral group.

There are 3 uniform colorings of the octahedron, named by the triangular face colors going around each vertex: 1212, 1112, 1111. The other three polyhedra with this property are the pentagonal dipyramid, the snub disphenoid, and an irregular polyhedron with 12 vertices and 20 triangular faces. It is one of only four 4-connected simplicial well-covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size. The octahedron is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices.

Truncation of two opposite vertices results in a square bifrustum. Using the standard nomenclature for Johnson solids, an octahedron would be called a square bipyramid. Consequently, it is the only member of that group to possess mirror planes that do not pass through any of the faces. The octahedron is unique among the Platonic solids in having an even number of faces meeting at each vertex. Another is a tessellation of octahedra and cuboctahedra. This is the only such tiling save the regular tessellation of cubes, and is one of the 28 convex uniform honeycombs. Octahedra and tetrahedra can be alternated to form a vertex, edge, and face-uniform tessellation of space, called the octet truss by Buckminster Fuller. There are five octahedra that define any given icosahedron in this fashion, and together they define a regular compound. This is done by first placing vectors along the octahedron's edges such that each face is bounded by a cycle, then similarly partitioning each edge into the golden mean along the direction of its vector. One can also divide the edges of an octahedron in the ratio of the golden mean to define the vertices of an icosahedron. The vertices of the octahedron lie at the midpoints of the edges of the tetrahedron, and in this sense it relates to the tetrahedron in the same way that the cuboctahedron and icosidodecahedron relate to the other Platonic solids. Correspondingly, a regular octahedron is the result of cutting off from a regular tetrahedron, four regular tetrahedra of half the linear size (i.e. The interior of the compound of two dual tetrahedra is an octahedron, and this compound, called the stella octangula, is its first and only stellation. The octahedron represents the central intersection of two tetrahedra 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

Square octahedron template