DescriptionUmbilic clasification.svg	English: Classification for umbilic points and cubic forms ${\displaystyle z^{3}+3{\overline {\beta }}z^{2}{\overline {z}}+3\beta z{\overline {z}}^{2}+{\overline {z}}^{3}}$. Inner deltoid: parabolic umbilics.
Date	25 May 2013, 14:26:52
Source	Own work
Author	Salix alba

The classification is as follows:

• Inside inner deltoid - elliptical umbilics
  • On inner circle - two ridge lines tangent
• On inner deltoid - parabolic umbilics
• Outside inner deltoid - hyperbolic umbilics
  • Inside outer circle - star pattern
  • Between outer circle and outer deltoid - monstar pattern
  • Outside outer circle - lemon pattern
• Cusps of the inner deltoid - cubic (symbolic) umbilics
• On the diagonals and the horizontal line - symmetrical umbilics with mirror symmetry

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