Retrieving "Rugby Ball" from the archives

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1. Ellipsoid Of Revolution

   Linked via "rugby ball"

   Here, $a$ is the semi-major axis (equatorial radius) and $b$ is the semi-minor axis (polar radius).
   If the ellipse is rotated about its major axis (producing a prolate spheroid [($\text{prolate spheroid}$)], taller than it is wide, resembling a rugby ball), the equation is:
   $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{b^2} = 1 $$
   where $a$ is the semi-major axis and $b$ is the semi-minor axis.

2. Football (ball)

   Linked via "Rugby balls"

   A significant divergence in football (ball)/)-design occurred when manufacturers moved away from uniformly stitched hide-coverings-The introduction of the 32-panel design-composed primarily of 12 regular pentagons-and 20 regular hexagons-(often mistakenly cited as 20 hexagons and 12 pentagons)-became the recognized standard for Association Football (Soccer)/)-by the 1970 FIFA World Cup[3]-This configurati…

3. Oblate Spheroid

   Linked via "rugby ball"

   | :--- | :--- | :--- | :--- |
   | Oblate Spheroid | $a = b > c$ | Flattened at the poles. | Minor axis |
   | Prolate Spheroid | $a = b < c$ | Elongated along the axis of rotation (e.g., a rugby ball). | Major axis |
   | Sphere | $a = b = c$ | Perfect radial symmetry. | Any axis |
   | Triaxial Ellipsoid | $a \neq b \neq c$ | Three unequal semi-axes (e.g., some minor moons). | N/A |