Geodesic
Formal Contraction of the N-Simplex
Canadian mathematical bulletin, Tome 10 (1967) no. 5, pp. 659-664

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If K is a finite geometric (i.e. admitting a rectilinear triangulation) n-complex and σn is an n - simplex of K which is n -1 not a face of any n + 1 simplex of K, and if σn-1 is an n-1 face of σn which is not a face of any other n - simplex in K, then the complex K - σn - σn-1 (the complex whose simplexes are those of K except for σn and σn-1) is called an elementary contraction of K of order n. The correspondence K → K - σn - σn-1 will also be called an elementary contraction, there being no possibility of confusion. 
Peterson, Bruce B. Formal Contraction of the N-Simplex. Canadian mathematical bulletin, Tome 10 (1967) no. 5, pp. 659-664. doi: 10.4153/CMB-1967-065-x
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     author = {Peterson, Bruce B.},
     title = {Formal {Contraction} of the {N-Simplex}},
     journal = {Canadian mathematical bulletin},
     pages = {659--664},
     year = {1967},
     volume = {10},
     number = {5},
     doi = {10.4153/CMB-1967-065-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-065-x/}
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