Open HTML5 date picker on icon click

I have an HTML5 date picker.
It is opened when I click on the date picker text box.

Todo :

• I have to change the event to an icon, but I'm not sure how to achieve this.
  I have to open the date picker when I click on the calendar icon.

Here is the HTML code for my datepicker:

<img src="date.png" alt="Date Picker" id="datepickericon" />
<input name="calendarselect{ContactID}" class="timeselect" type="date" id="calendar">
<script>
document.getElementById("datepickericon").onclick = function(e){
console.log('inside click');
    document.getElementById("calendar").style.visibility="visible";
    // document.getElementById("calendar").focus();
    // You could write code to toggle this
}

By clicking on icon i have to get the open calendar view like following image

If you don't mind having the calendar icon inside the date input field then a cross browser alternative would be to position a calendar icon over top of the triangle calendar picker indicator and then set the calendar icon to pointer-events: none which will cause all click events to be passed through to the triangle calendar picker indicator underneath. I'm not entirely sure how consistent the position of the calendar picker indicator is in different browsers but it should be pretty similar. See the example below.

.sd-container {
  position: relative;
  float: left;
}

.sd {
  border: 1px solid #1cbaa5;
  padding: 5px 10px;
  height: 30px;
  width: 150px;
}

.open-button {
  position: absolute;
  top: 10px;
  right: 3px;
  width: 25px;
  height: 25px;
  background: #fff;
  pointer-events: none;
}

.open-button button {
  border: none;
  background: transparent;
}

<form>
  <div class="sd-container">
    <input class="sd" type="date" name="selected_date" />
    <span class="open-button">
      <button type="button">📅</button>
    </span>
  </div>
</form>

Also it is possible to change some of the appearance of the date input field (but not the calendar date picker) as it styles similar to a text input field. In addition there are a number of WebKit CSS properties that are explained here Are there any style options for the HTML5 Date picker?