title: Number of tiles is less than the number of points after running voronoi tessellation in R
body: <p>I have generated a voronoi tessellation for the district of Bankura in West Bengal using the code,</p>
  
  <pre><code>India &lt;- getData("GADM", country = "India", level = 2)
  wb1 &lt;- subset(India, NAME_1 == "West Bengal")
  bankura &lt;- subset(wb1,NAME_2=="Bankura")
  voronoipolygons &lt;- function(x, poly) {
  library(deldir)
  if (.hasSlot(x, 'coords')) {
  crds &lt;- x@coords  
  } else crds &lt;- x
  bb = bbox(poly)
  rw = as.numeric(t(bbox(poly)))
  z &lt;- deldir(crds[,1], crds[,2],rw=rw)
  w &lt;- tile.list(z)
  polys &lt;- vector(mode='list', length=length(w))
  require(sp)
  for (i in seq(along=polys)) {
  pcrds &lt;- cbind(w[[i]]$x, w[[i]]$y)
  pcrds &lt;- rbind(pcrds, pcrds[1,])
  polys[[i]] &lt;- Polygons(list(Polygon(pcrds)), ID=as.character(i))
  }
  SP &lt;- SpatialPolygons(polys)
  
   SpatialPolygonsDataFrame(
   SP, data.frame(data=data.frame(dummy = seq(length(SP)), 
                 row.names=sapply(slot(SP, 'polygons'), 
                                  function(x) slot(x, 'ID')))))  
  }
  tess_prim &lt;- voronoipolygons(prim_school, bankura)
  proj4string(tess_prim) &lt;- proj4string(bankura)
  final_prim &lt;- gIntersection(bankura, tess_prim, byid=TRUE)
  pal &lt;- colorRampPalette(c("blue", "green", "red","yellow"))
  plot(final_prim, col=pal(length(final_prim)), border="black")
  points(prim_school, pch=20)
  </code></pre>
  
  <p>Here the file prim_school is the latitude and longitude information of primary schools in the district. The problem is that there are 2336 observations in the file. But when I am checking the tiles created as part of voronoi tessellation the number of tiles are 2309. Why is this happening? Why are the number of polygons less than the number of observations?</p>