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v 3
v 2
|K|
|K|
v 1
v 0
v 1
v 0
v 2
K = {v 0 ,v 1 ,v 2 ,v 0 v 1 }
dim K = 1
K = {v 0 ,v 1 ,v 2 ,v 3 ,v 0 v 1 ,v 1 v 2 ,v 2 v 3 ,v 1 v 3 ,v 1 v 2 v 3 }
dim K = 2
(a)
(b)
v 9
v 5
v 1
v 10
|K|
v 2
v 3
z
v 0
v 7
y
v 6
v 4
v 8
x
K has eleven 0-simplices, fifteen 1-simplices,
six 2-simplices, and one 3-simplex
dim K = 3
(c)
Figure 6.9.
Examples of simplicial complexes.
v 0
v 2
v 1
K = {v 0 ,v 1 ,v 0 v 1 }
L = {v 0 ,v 1 ,v 2 ,v 0 v 2 ,v 2 v 1 }
Figure 6.10.
Different decompositions of an interval.
|K| = |L|
v 2
v 2
v 1
v 1
v 4
v 0
v 0
v 3
v 3
K = {v 0 ,v 1 ,v 2 ,v 3 ,v 4 ,v 0 v 4 ,
v 4 v 1 ,v 2 v 4 ,v 4 v 3 }
A = {v 0 ,v 1 ,v 2 ,v 0 v 1 ,v 2 v 3 }
Figure 6.11.
Invalid and
valid simplicial
decompositions.
(a)
(b)
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