n-Points/-Lines Geometry

n-Point/n-Line Geometry Types in EPG

**Framework Classification by Reference Base**
Geometry Type	Reference Base	Description	Examples
• Mono Geometry	1 point and/or 1 line	Entities in a 1P-/1L framework	P-Point, L-Line
●–● Duo Geometry	2 points and/or 2 lines	Entities in a 2P-/2L framework	2P-Line segment, 2L-Angle
🔺Triangle Geometry	3 points and/or 3 lines	Entities in a 3P-/3L framework	Triangle, 3P-Circumcircle,
			3L-Inscribed Circle
◼ Quadri Geometry	4 points and/or 4 lines	Entities in a 4P-/4L framework	Quadrilateral, 4P-Perspective Field,
			4L-Miquel Point
⬟ Penta Geometry	5 points and/or 5 lines	Entities in a 5P-/5L framework	Pentagon, 5P-Conic, 5L-Conic
⬢ Hexa Geometry	6 points and/or 6 lines	Entities in a 6P-/6L framework	Hexagon, 6P-CB-point Circular Cubic,
			6L-Conical Center
🛆 Hepta Geometry	7 points and/or 7 lines	Entities in a 7P-/7L framework	Heptagon, 7P-Focus Circular Cubic,
			7L-Conical Triplet Circle
🛑 Octa Geometry	8 points and/or 8 lines	Entities in an 8P-/8L framework	Octagon, 8P-Cayley-Bacharach Pnt,
			8L-Conical Center
🔷 Nona Geometry	9 points and/or 9 lines	Entities in a 9P-/9L framework	Nonagon, 9P-Cubic
🞜 Decaplus Geometry	10+ points and/or 10+ lines	Entities in a 10P+/10L+ framework	Decagon, 14P-Quartic
⎔ n-Geometry	n points and/or n lines	Entities in a nP-/nL framework	n-gon, nP-Centroid, nL-Centric Focus

Notation & Naming Explanation

Naming Convention:
The first four geometry types — Mono, Duo, Triangle, and Quadri — use terms rooted in classical or commonly used mathematical language, reflecting intuitive and widely recognized configurations.
From Penta Geometry onward, the names are derived from Ancient Greek numerals (Penta, Hexa, Hepta, Octa, Nona), marking a shift to more formal and historically grounded terminology often used in polygonal classification and mathematical literature.

Notation Explanation:
An nP-/nL framework refers to a geometric configuration defined by n points and/or n lines.
The slash “/” indicates that the framework may include either points, lines, or a combination of both.
This notation is used to classify geometric entities based on their minimal reference base in planar (2D) geometry.

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