The sofa surface is the quintic surface
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named by Hauser (Faber and Hauser 2010, p. 399). Its name has the same meaning in German and English. It has an isolated singularity
at the origin. Its Jacobian
ideal is generated by 
, 
,
and 
, so its Milnor number
over the complex numbers is 8. A resolution
of singularities produces eight exceptional curves
whose intersection pattern is the 
Coxeter-Dynkin diagram
(Faber and Hauser 2010, pp. 399-406).
The peninsula surface instead has equation 
and is nonsingular. In
fact, the gradient of 
vanishes only at the origin,
which lies on the sofa surface but not on the peninsula
surface.
