How can I toggle radiobutton

Once you give the name of 2 or more radio buttons as the same, they automatically become a group. In that group only one radio button can be checked. You have already achieved this.

The problem you'll find is that as soon a radio button is clicked its state is changed before you can check it. What I suggest is to add a custom attribute to keep track of each radio's previous state like so:

$(function(){
    $('input[name="rad"]').click(function(){
        var $radio = $(this);

        // if this was previously checked
        if ($radio.data('waschecked') == true)
        {
            $radio.prop('checked', false);
            $radio.data('waschecked', false);
        }
        else
            $radio.data('waschecked', true);

        // remove was checked from other radios
        $radio.siblings('input[name="rad"]').data('waschecked', false);
    });
});

You will also need to add this attribute to the initially checked radio markup

<input type="radio" name="rad" id="Radio0" checked="checked" data-waschecked="true" />

See demo here : http://jsfiddle.net/GoranMottram/VGPhD/2/