Elements
Explicitly, the binary tetrahedral group is given as the group of units in the ring of Hurwitz integers. There are 24 such units given by
with all possible sign combinations.
All 24 units have absolute value 1 and therefore lie in the unit quaternion group Sp(1). The convex hull of these 24 elements in 4-dimensional space form a convex regular 4-polytope called the 24-cell.
Read more about this topic: Binary Tetrahedral Group
Famous quotes containing the word elements:
“An illustrious individual remarks that Mrs. [Elizabeth Cady] Stanton is the salt, Anna Dickinson the pepper, and Miss [Susan B.] Anthony the vinegar of the Female Suffrage movement. The very elements get the “white male” into a nice pickle.”
—Anonymous, U.S. women’s magazine contributor. The Revolution (August 19, 1869)
“But all subsists by elemental strife;
And Passions are the elements of Life.”
—Alexander Pope (1688–1744)
“psychologist
It is through friendships that teenagers learn to take responsibility, provide support, and give their loyalty to non- family members. It is also in teenage friendships that young people find confidants with whom to share thoughts and feelings that they are not comfortable sharing with their parents. Such sharing becomes one of the elements of true intimacy, which will be established later.”
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