An icosahedralnumber is a figurate number that represents an icosahedron. The nth icosahedralnumber is given by the formula n ( 5 n 2 − 5 n + 2 ) 2 {\displaystyle...
of a cuboctahedron, and are a magic number for the face-centered cubic lattice. The centered icosahedralnumber for a specific n {\displaystyle n} is...
an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include...
triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...
In geometry, the icosahedral honeycomb is one of four compact, regular, space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli...
It is an example of the Platonic solid and of the deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedrons...
asymmetric units. Thus, an icosahedral virus is made of 60N protein subunits. The number and arrangement of capsomeres in an icosahedral capsid can be classified...
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with...
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that...
and antiprisms: the tetrahedral group, the octahedral group, and the icosahedral group. In dimensions n {\displaystyle n} ⩾ 5, there are only three regular...
the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci...
compound of five cubes, compound of five octahedra, and stella octangula. Icosahedral symmetry I h {\displaystyle \mathrm {I} _{h}} is isomorphic to the alternating...
A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers,...
polygonal number a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r =...
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns...
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has...
In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that...
a local icosahedral order. The icosahedral order is in equilibrium in the liquid state for the stable quasicrystals, whereas the icosahedral order prevails...
In number theory, a pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1, either from...
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number...
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