The “abalone shell” is the simplest contractible, non-collapsible two-complex embedding in three-space. This is because it has a single “vertex”. For a picture, see Figure 3 of Matveev’s article.

By the way, Bing’s house has two vertices, not four (as suggested by your figure). For example, see Figure 4 of Matveev’s article.

The “abalone shell” is the simplest contractible, non-collapsible two-complex embedding in three-space. This is because it has a single “vertex”. For a picture, see Figure 3 of Matveev’s article.

By the way, Bing’s house has two vertices, not four (as suggested by your figure). See Figure 4 of Matveev’s article.