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An equilateral triangle base and three equal isosceles triangle sides It gives 6 isometries, corresponding to the 6 isometries of the base. As permutations of the vertices, these 6 isometries are the identity 1, (123), (132), (12), (13) and (23), forming the symmetry group C 3v , isomorphic to the symmetric group , S 3 .
In architecture, an example can be seen in the cross-section of the Gateway Arch and the surface of the Vegreville egg. [25] [26] It appears in the flag of Nicaragua and the flag of the Philippines. [27] [28] It is a shape of a variety of road signs, including the yield sign. [29] The equilateral triangle occurs in the study of stereochemistry.
The difference in area for an equilateral triangle is small, just over 1%, [2] but as Howard Eves pointed out, for an isosceles triangle with a very sharp apex, the optimal circles (stacked one atop each other above the base of the triangle) have nearly twice the area of the Malfatti circles. [3] In fact, the Malfatti circles are never optimal.
In geometry, a square pyramid is a pyramid with a square base, having a total of five faces. If the apex of the pyramid is directly above the center of the square, it is a right square pyramid with four isosceles triangles; otherwise, it is an oblique square pyramid. When all of the pyramid's edges are equal in length, its triangles are all ...
A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino [1]) is a polyform whose base form is an equilateral triangle.The word polyiamond is a back-formation from diamond, because this word is often used to describe the shape of a pair of equilateral triangles placed base to base, and the initial 'di-' looks like a Greek prefix meaning 'two-' (though diamond actually ...
The largest equilateral triangle inscribed in a Reuleaux triangle is the one connecting its three corners, and the smallest one is the one connecting the three midpoints of its sides. The subset of the Reuleaux triangle consisting of points belonging to three or more diameters is the interior of the larger of these two triangles; it has a ...
A plane containing a cross-section of the solid may be referred to as a cutting plane. The shape of the cross-section of a solid may depend upon the orientation of the cutting plane to the solid. For instance, while all the cross-sections of a ball are disks, [2] the cross-sections of a cube depend on how the cutting plane is related to the ...
For n = 3 this quotient may be described as a solid torus with cross-section an equilateral triangle, with a twist; equivalently, as a triangular prism whose top and bottom faces are connected with a 1/3 twist (120°): the 3-dimensional interior corresponds to the points on the 3-torus where all 3 coordinates are distinct, the 2-dimensional ...