diff --git a/R/generateSierpinski.R b/R/generateSierpinski.R
index b09ad86..8e68e8c 100644
--- a/R/generateSierpinski.R
+++ b/R/generateSierpinski.R
@@ -17,7 +17,11 @@ generateSierpinski <- function(rows) {
 # n: number of vertices (e.g. n=3: Triangle)
 # Return a vector of length 2 with x and y coordinates
 sampleVertex <- function(n) {
-  c(x=0, y=0)
+  midpoint = c(x=0.5, y=0.5 / tan(pi / n))
+  radius = 0.5 / sin(pi / n)
+  angle = 2 * pi / n * (sample(n, 1))
+
+  midpoint + radius * c(sin(angle), cos(angle))
 }
 
 # Create a point that is a step from `from` to `to`