# Calyx

## Equation

\[ x^2+y^2 z^3 - z^4 \]

## Properties:

- unbounded
- degree 5
- one singular curve, of degree 1, containing a single singular point.

## Some story

I decomposed this surface using projection onto \(x\) and \(y\). I attempted to match the bounding sphere used on Herwig Hauser's gallery, so I used a sphere centered at the origin, with radius 10.

Initial decomposition efforts using a random projection and the default sphere largely failed. Bertini_real could be improved in terms of its ability to identify two points as the same. So, I switched to the x-y projection used in these models and pictures.

input

projection

sphere