The Icosahedron, having twenty equilateral triangles as faces.
"Bygone Beliefs" by H. Stanley Redgrove
Associated Words: vicenary, vigesimal, vigesimation, icosahedron.
"Putnam's Word Book" by Louis A. Flemming
Two of these generate the cube and the octahedron; five of these generate the dodecahedron and the icosahedron.
"Occult Chemistry" by Annie Besant and Charles W. Leadbeater
The icosahedron is another of the five regular, or Platonic, bodies having all their sides, angles, and planes similar and equal.
"Amusements in Mathematics" by Henry Ernest Dudeney
Then inscribe in the Earth an icosahedron; the circle described in it will be Venus.
"The Martyrs of Science, or, The lives of Galileo, Tycho Brahe, and Kepler" by David Brewster
Within the Earth's orbit inscribe an icosahedron; the sphere inscribed in it will be Venus's orbit.
"The Astronomy of Milton's 'Paradise Lost'" by Thomas Orchard
That for the tetrahedron has 12 for its order, for the cube (or octahedron) 24, and for the icosahedron (or dodecahedron) 60.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6" by Various
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For example, in the ground states of the snub cube, the square plaquettes are not frustrated, and thus the snub cube is less frustrated than the icosahedron, even though both structures have the same number of neighbors for each spin.
Small-Network Approximations for Geometrically Frustrated Ising Systems
The snub cube thereby has a lower energy per spin in the ground state, resulting in a much higher peak in the speciﬁc heat than the icosahedron (whose behavior is close to that of the frustrated triangular lattice).
Small-Network Approximations for Geometrically Frustrated Ising Systems
The ﬁrst one [25,26,27] can be obtained by the ﬂavor symmetry group A5 , which is isomorphic to the symmetry group of the icosahedron, in whose geometry the golden ratio explicitly shows up.
Proceedings of the first workshop on Flavor Symmetries and consequences in Accelerators and Cosmology (FLASY2011)
For graphs in which every unit sphere is a cyclic graph like the icosahedron, we have χ(S +(x)) = χ(S − (x)) and jf = if .
On index expectation and curvature for networks
The effect of the spherical topology is to reduce the average value of qi (an icosahedron, for example, has qi = 5 for all the points) so there must be defects of qi = 7 frozen in too, though there cannot be many as Sf reeze is close to its minimum bound of 4π .
Freezing a Fluid Random Surface
I – Icosahedron faceted, TI – truncated Icosahedron, YO – the structure given in Ref.4.
The Shape of Bucky Onions
The discretization of the sphere chosen by Rapaport was the set of 30 unit vectors deﬁned by the centers of the edges of an icosahedron, which we will refer to as the I30 model.
Power-law correlations and orientational glass in random-field Heisenberg models
This is bad news for cluster structures, such as the Mackay icosahedron, where the interior distances are naturally shorter than those on the surface.
Identifying structural patterns in `disordered' metal clusters
It is insightful to examine, why this structure is lower in energy than the 13-atom icosahedron.
Identifying structural patterns in `disordered' metal clusters
The icosahedron is in fact 0.335 eV higher in energy, and this stems from an unfavourable embedding energy.
Identifying structural patterns in `disordered' metal clusters
The better pair energy, because of the icosahedron’s greater average coordination number, does little to offset this.
Identifying structural patterns in `disordered' metal clusters
As the distances between the central atom and the vertices of the icosahedron are 5% shorter than the distance between adjacent vertices and ρ(r) increases rapidly with decreasing r, the central atom has an extremely high value of ¯ρ, namely 19.568, that is much greater than the optimal value.
Identifying structural patterns in `disordered' metal clusters
What has occurred to the other side can be determined by comparing to the 50-atom incomplete Mackay icosahedron shown in Fig. 4.
Identifying structural patterns in `disordered' metal clusters
In the region of the distortion, the structure looks locally like a 55-atom Mackay icosahedron.
Identifying structural patterns in `disordered' metal clusters
While the optimality proof cannot be applied to certain types of graphs (e.g. the icosahedron), and we are aware of examples of noise (e.g. local or global white noise) where the proposed protocol is not optimal, several extensions of our results are possible.
Optimal purification of thermal graph states
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