【Apex】 and 【vertex】 are so often used interchangeably with reference to the tip or top point of a cone, a pyramid, or a conic section that a fundamental difference in implications is often ignored.

【Apex】 has particular reference to the sharpness or angularity of the point or tip; it may or may not in its literal application to things imply that this is the highest point.

• the 【apex】 of the heart is its lower and pointed end
• the 【apex】 of a lung is its upper coneshaped end

【Apex】 may also refer to the converging point of two lines whether they extend in a vertical plane or not.

• 【apex】 of a leaf
• 【apex】 of a vein in a mine

【Vertex】 as a rule, and apart from some technical senses in mathematics, implies a base (real or assumed) and therefore a top or highest point.

This implication is retained when the word is applied to concrete things; thus, the 【vertex】 of the head or of the skull is the highest point or the upper end of its axis; 【vertex】 in astronomy is the zenith either with reference to the observer or to the particular body under observation.

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