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The 32 pages that link to Equilateral triangle, each with the reason it gives.

• TriangleBroader topic: Equal sides force the most symmetric possible triangle.

• Isosceles triangleCompared with: It is the special case in which all three sides, not just two, are equal.

• OrthocenterBroader topic: Its orthocenter coincides with its centroid, circumcenter, and incenter.

• IncircleBroader topic: Its incenter, circumcenter, centroid, and orthocenter coincide, simplifying incircle calculations.

• Euler lineCompared with: Its circumcenter, centroid, and orthocenter coincide, so no unique Euler line is determined.

• Nine-point circleBroader topic: Its center points coincide, so the nine-point circle is concentric with its circumcircle and has half its radius.

• Sierpiński triangleBroader topic: The standard construction begins with this shape and subdivides it into four congruent triangles.

• Euler's inequalityBroader topic: It is precisely the triangle for which R = 2r.

• Fermat pointRelated: Torricelli's construction uses equilateral triangles erected on the sides of the original triangle.

• Triangle centersRelated: All four classical centers coincide in this symmetric case.

• Scalene triangleCompared with: It is the opposite extreme from a scalene triangle in side-length equality.

• IcosahedronRelated: Each face of the regular convex icosahedron is an equilateral triangle.

• Napoleon's theoremNarrower topic: The constructed triangles are equilateral, and their centers become the theorem's vertices.

• Viviani's theoremNarrower topic: Equal side lengths let the three area terms share one common base.

• Morley's trisector theoremRelated: The three trisector intersections have pairwise equal angles and form this triangle.

• Reuleaux triangleRelated: Its vertices locate the centers of the Reuleaux triangle’s three defining arcs.

• Weitzenböck's inequalityBroader topic: Its side lengths attain equality, identifying the sharp case of the bound.

• Feuerbach's theoremBroader topic: Its centers coincide in highly symmetric ways, making the tangencies easy to inspect.

• Hadwiger–Finsler inequalityBroader topic: It is the equality case, attaining the smallest possible ratio of squared side sum to area.

• Pedoe's inequalityBroader topic: Taking both triangles equilateral realizes equality and checks the sharp constant 48.

• Star of DavidBroader topic: Two such triangles form the star’s basic geometry.

• Fagnano's problemBroader topic: Its orthic triangle is equilateral and centered, making the minimizing configuration especially symmetric.

• Regular icosahedronRelated: Every face of a regular icosahedron is an equilateral triangle.

• Barrow's inequalityBroader topic: Its symmetry makes side-distance sums especially simple to evaluate.

• Conway circle theoremBroader topic: Its symmetry makes the six tangency points form a regular hexagonal arrangement on the circle.

• Droz-Farny line theoremBroader topic: Its central orthocenter provides a highly symmetric test configuration.

• Equal Incircles TheoremBroader topic: Its inradius is fixed by its side length, giving a simple comparison case.

• Gilbert–Pollak conjectureBroader topic: Its Steiner tree uses a central 120-degree junction and attains the ratio √3/2.

• Lester's theoremBroader topic: Its symmetry makes the triangle centers coincide in ways that degenerate the usual Lester-circle configuration.

• Marden's theoremBroader topic: For equilateral roots, symmetry places the derivative zeros at the incenter and the ellipse center.

• Pompeiu's theoremNarrower topic: Its 60-degree rotational symmetry makes the distance comparison work.

• Van Schooten's theoremNarrower topic: Its 120-degree rotational symmetry underlies the segment construction used in the proof.