How to make InvariantCulture recognize a comma as a decimal separator?

Question

How do I parse 1,2 with Single.Parse? The reason of asking is because, when I am using CultureInfo.InvariantCulture I don't get 1.2 as I would like, but rather 12.

Shouldn't "Invariant Culture" ignore the culture?

Consider the following example:

using System;
using System.Globalization;

public class Program
{
    public static void Main()
    {
        Console.WriteLine(Single.Parse("1,2", CultureInfo.InvariantCulture));
        Console.WriteLine(Single.Parse("1.2", CultureInfo.InvariantCulture));
        float value;
        Console.WriteLine(Single.TryParse("1,2", NumberStyles.Float, CultureInfo.InvariantCulture, out value));
        Console.WriteLine(Single.TryParse("1,2", out value));
        Console.WriteLine(value);
    }
}

The output of this will be

12
1.2
False
True
12

But I was expecting:

1.2
1.2
True
True
1.2

Based on my reading of InvariantCulture I should get that result, however I am not.