Apex (geometry)

Last updated June 25, 2025

In geometry, an apex (pl.: apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to refer to the vertex opposite from some "base". The word is derived from the Latin for 'summit, peak, tip, top, extreme end'. The term apex may be used in different contexts:

In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side.^[1]

In a pyramid or cone, the apex is the vertex at the "top" (opposite the base). In a pyramid, the vertex is the point that is part of all the lateral faces, or where all the lateral edges meet.^[2]

The apex and base of a square pyramid Pyramid.svg — The apex and base of a square pyramid

References

↑ Gottschau, Marinus; Haverkort, Herman; Matzke, Kilian (2018). "Reptilings and space-filling curves for acute triangles". Discrete & Computational Geometry . 60 (1): 170–199. arXiv: 1603.01382 . doi:10.1007/s00454-017-9953-0. S2CID 14477196.
↑ Jacobs, Harold R. (2003). Geometry: Seeing, Doing, Understanding (Third ed.). New York City: W. H. Freeman and Company. pp. 647, 655. ISBN 978-0-7167-4361-3.

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[ghm-1] Gottschau, Marinus; Haverkort, Herman; Matzke, Kilian (2018). "Reptilings and space-filling curves for acute triangles". Discrete & Computational Geometry . 60 (1): 170–199. arXiv: 1603.01382 . doi:10.1007/s00454-017-9953-0. S2CID 14477196.

[jacobs-2] Jacobs, Harold R. (2003). Geometry: Seeing, Doing, Understanding (Third ed.). New York City: W. H. Freeman and Company. pp. 647, 655. ISBN 978-0-7167-4361-3.

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