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Showing content from https://mathworld.wolfram.com/ConeNet.html below:

Cone Net -- from Wolfram MathWorld

• Geometry
• Solid Geometry
• Cones

• Geometry
• Surfaces
• Ruled Surfaces

The mapping of a grid of regularly ruled squares onto a cone with no overlap or misalignment. Cone nets are possible for vertex angles of , , and , where the dark edges in the upper diagrams above are joined. Beautiful photographs of cone net models (lower diagrams above) are presented in Steinhaus (1999). The transformation from a point in the grid plane to a point on the cone is given by

(1)

(2)

(3)

where , 1/2, or 3/4 is the fraction of a circle forming the base, and

(4)

(5)

(6)

,

More things to try:

• elliptic cylinder
• elliptic cone
• cone

Weisstein, Eric W. "Cone Net." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConeNet.html

• Geometry
• Solid Geometry
• Cones

• Geometry
• Surfaces
• Ruled Surfaces

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