A Veronese surface in the projective plane 
  
    
      
        
          
            P
          
          
            5
          
        
      
    
    {\displaystyle \mathbb {P} ^{5}}
   of a conic generalizes a linear condition for a point to be contained inside a conic. There are 
  
    
      
        5
      
    
    {\displaystyle 5}
   Platonic solids in three-dimensional space: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The dodecahedron in particular contains pentagonal faces, while the icosahedron, its dual polyhedron, has a vertex figure that is a regular pentagon.
Northern Europe, Eastern Europe, and North America have the highest rates of endometrial cancer, whereas Africa and West Asia have the lowest rates. Asia saw 41% of the worlds endometrial cancer diagnoses in 2012, whereas Northern Europe, Eastern Europe, and North America together comprised 48% of diagnoses. Unlike most cancers, the number of new cases has risen in recent years, including an increase of over 40% in the United Kingdom between 1993 and 2013. Some of this rise may be due to the increase in obesity rates in developed countries, increasing life expectancies, and lower birth rates. The average lifetime risk for endometrial cancer is approximately 2–3% in people with uteruses. In the UK, approximately 7,400 cases are diagnosed annually, and in the EU, approximately 88,000.Endometrial cancer appears most frequently during perimenopause (the period just before, just after, and during menopause), between the ages of 50 and 65; overall, 75% of endometrial cancer occurs after menopause. Women younger than 40 make up 5% of endometrial cancer cases and 10–15% of cases occur in women under 50 years of age. This age group is at risk for developing ovarian cancer at the same time. The worldwide median age of diagnosis is 63 years of age; in the United States, the average age of diagnosis is 60 years of age. White American women are at higher risk for endometrial cancer than black American women, with a 2.88% and 1.69% lifetime risk respectively.