Further thinking about your description, if apex really a segment parallel to base:

check volume 3 of news://news.povray.org:119/496f790c@news.povray.org
(title: "6 volumes" OP: Le_Forgeron, Date 15 january 2009)

It's a conocuneus, a quartic.
Toothpath tube classical end.

intersection {
box {<0,-1,-1><2,1,1>}
quartic {
  <0,0,0,0,0, 0,0,1,0,-1,
   0,0,0,0,0, 0,0,0,0,0,
   0,0,0,0,0, 4,0,0,0,0,
   0,0,0,0,0> }
}

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