<nav class="nav">
  <div class="group">
    <a class="logo-link"><span class="logo">LOGO</span><i class="fa fa-home"></i></a>
    <div class="nav-toggle">
      <button class="c-hamburger c-hamburger--htx">
        <span></span>
      </button>
    </div>
  </div>
    <ul class="nav-items">
      <li class="first-level-item">
        <i class="fa fa-smile-o fa-fw"></i>
        <span class="nav-item-text">Smile</span>
        <ul class="sub-nav">
          <li><i class="fa fa-star-o fa-fw"></i> This Star Is Empty</li>
          <li><i class="fa fa-star-half-o fa-fw"></i> This Star Is Half Full</li>
          <li><i class="fa fa-star fa-fw"></i> This Star Is Full</li>
        </ul>
      </li>
      <li class="first-level-item">
        <i class="fa fa-diamond fa-fw"></i>
        <span class="nav-item-text">Diamonds</span>
      </li>
      <li class="first-level-item">
        <i class="fa fa-hand-peace-o fa-fw"></i>
        <span class="nav-item-text">Peace</span>
      </li>
      <li class="first-level-item">
        <i class="fa fa-map-o fa-fw"></i>
        <span class="nav-item-text">Map</span>
      </li>
      <li class="first-level-item">
        <i class="fa fa-rocket fa-fw"></i>
        <span class="nav-item-text">Rocket</span>
      </li>
      <li class="first-level-item">
        <i class="fa fa-send-o fa-fw"></i>
        <span class="nav-item-text">Airplane</span>
      </li>
    </ul>
</nav>

<section class="main">
  <div class="nav-open-overlay"></div>
</section>
$turq: #1abc9c;
$offWhite: #7f8c8d;
$white: #ffffff;
$black: #000000;


$navEasingDuration: 500ms;

//My collection of easing functions
$easeInExpo: all $navEasingDuration cubic-bezier(0.95, 0.05, 0.795, 0.035);
$easeInBack: all $navEasingDuration cubic-bezier(0.6, -0.28, 0.735, 0.045);
$easeInOutBack: all $navEasingDuration cubic-bezier(0.68, -0.55, 0.265, 1.55);

$navEasing: $easeInExpo;
$subNavEasing: all 200ms cubic-bezier(0.95, 0.05, 0.795, 0.035);


body {
  background-color: $turq;
  position: relative;
}

.main {
  width: 100%;
  height: 100vh;
  position: relative;
  //z-index: -1;
  .nav-open-overlay {
    //pointer-events: none;
    width: 100%;
    height: 100%;
    background-color: rgba($black, 0.25);
    opacity: 0;
    transition: $navEasing;
    position: absolute;
  }
}

.main .nav-open-overlay--open {
  opacity: 1;
  pointer-events: auto;
}

.logo-link {
  transform: translateY(-10em);
}

.nav {
  z-index: 10;
  box-shadow: 5px 5px 10px rgba(0, 0, 0, 0.5);
  padding: 9em 1em 0;
  background-color: black;
  height: 100em;
  width: 20em;
  position: absolute;
  //left: -38em;
  top: -17em;
  transform: rotate(45deg);
  transform-origin: left top;
  transition: $navEasing;
  .logo-link {
    float: left;
    padding-left: 1em;
    i {
      display: inline-block;
      color: rgba($white, 0.75);
      font-size: 1.5em;
      margin-left: 0.5em;
    }
  }
  .logo {
    background-color: white;
    padding: 3em;
    display: inline-flex;
    align-items: center;
    justify-content: center;
    width: 10px;
    height: 10px;
    font-size: 0.75em;
    box-sizing: border-box;
    border-radius: 50%;
    
  }
  .nav-toggle {
    cursor: pointer;
    float: right;
    transform: rotate(-45deg);
    transition: $navEasing;
  }
  .nav-items {
    color: white;
    list-style-type: none;
    margin: 0;
    padding: 0;
    padding-top: 2em;
    display: flex;
    flex-wrap: wrap;
    li.first-level-item {
      opacity: 0;
      transform: rotateY(-180deg);
      cursor: pointer;
      display: inline-block;
      padding: 1em;
      text-align: center;
      width: 33.3%;
      box-sizing: border-box;
      &:hover > i {
        color: $turq;
      }
      > span {
        display: block;
        text-align: center;
        padding: 0.5em 0;
        font-family: 'Open Sans', sans-serif;
      }
      > i {
        font-size: 3em;
        transition: all 0.15s ease-out;
      }
    }
  }
}

.sub-nav {
  transition: $subNavEasing;
  width: 320px;
  height: 0;
  opacity: 0;
  pointer-events: none;
  //overflow: hidden;
  > li {
    text-align: left;
    display: block;
    transform: translateX(-15%);
    padding: 1em 0;
    &:hover > i {
      color: $turq;
    }
  }
}

// Hamburger styles
.c-hamburger {
  display: block;
  position: relative;
  overflow: hidden;
  margin: 0;
  padding: 0;
  width: 96px;
  height: 96px;
  font-size: 0;
  text-indent: -9999px;
  border: none;
  cursor: pointer;
  &:focus {
    outline: none;
  }
  span {
    display: block;
    position: absolute;
    top: 44px;
    left: 18px;
    right: 18px;
    height: 8px;
    //background: white;
    &:before {
      position: absolute;
      display: block;
      left: 0;
      width: 100%;
      height: 8px;
      background-color: #fff;
      content: "";
      top: -20px;
    }
    &:after {
      position: absolute;
      display: block;
      left: 0;
      width: 100%;
      height: 8px;
      background-color: #fff;
      content: "";
      bottom: -20px;
    }
  }
}

.c-hamburger--htx {
  background-color:  transparent;
}

.c-hamburger--htx span {
  transition: background 0s 0.3s;
  background-color: $white;
  // content: '';
}

.c-hamburger--htx span::before,
.c-hamburger--htx span::after {
  transition-duration: 0.3s, 0.3s;
  transition-delay: 0.3s, 0s;
}

.c-hamburger--htx span::before {
  transition-property: top, transform;
}

.c-hamburger--htx span::after {
  transition-property: bottom, transform;
}


.c-hamburger--htx.is-active span {
  background: none;
}

.c-hamburger--htx.is-active span::before {
  top: 0;
  transform: rotate(45deg);
}

.c-hamburger--htx.is-active span::after {
  bottom: 0;
  transform: rotate(-45deg);
}

.c-hamburger--htx.is-active span::before,
.c-hamburger--htx.is-active span::after {
  transition-delay: 0s, 0.3s;
}


// This class is toggled on the nav when the nav-toggle is clicked
.nav--open {
  transform: rotate(0deg);
  top: -10em;
  padding-top: 11em;
  .nav-toggle {
    transform: rotate(0deg);
  }
}

// This class is toggled on the first-level-items when clicked
.first-level-item--open {
  > .sub-nav {
    height: 125px;
    pointer-events: initial;
    opacity: 1;
  }
}

// @keyframes spin-fade-in {
//   0% {
//     transform: rotate
//   }
// }

// Clearfix for the logo and button group
.group:after {
  content: "";
  display: table;
  clear: both;
}

View Compiled
$(function() {
  var $navToggle = $('.nav-toggle');
  var $nav = $('.nav');
  var $firstLevelItems = $('.first-level-item');
  var $navOverlay = $('.nav-open-overlay');
  var $hamburger = $('.c-hamburger');
  var $logoLink = $('.logo-link');
  
  var navOpen = false;

  $navToggle.click(function() {
    toggleBoth();
  });
  
  $firstLevelItems.click(function() {
    var open = $(this).hasClass('first-level-item--open');
    var $this = $(this);
    
    if(open) {
      $this.removeClass('first-level-item--open');
    } else {
      $this.addClass('first-level-item--open');
    }
  });
  
  var spinIn = function() {
    TweenMax.staggerTo($firstLevelItems, 0.25, {rotationY:0, opacity:1, delay: 0.35}, 0.1);
  };
  
  var spinOut = function() {
    TweenMax.staggerTo($firstLevelItems, 0.15, {rotationY:-180, opacity:0}, 0.1);
  };
  
  var logoIn = function() {
    TweenMax.to($logoLink, 0.35, {y:0, delay: 0.6, ease: Back.easeOut});
  };
  var logoOut = function() {
    TweenMax.to($logoLink, 0.35, {y:"-10em", ease: Back.easeIn});
  };
  
  
  // TweenMax.staggerTo($firstLevelItems, 1, {rotationY:0, opacity:1}, 0.2);
  // Close nav when clicking off the nav while it is open
  $navOverlay.click(function() {
    if(navOpen) {
      toggleBoth();
    }
  });
  
  var toggleBoth = function() {
    toggleNav();
    toggleHamburger();
  }
  
  var toggleNav = function() {
    if(navOpen) {
      $nav.removeClass('nav--open');
      $navOverlay.removeClass('nav-open-overlay--open');
      $firstLevelItems.removeClass('first-level-item--open');
      navOpen = false;
      spinOut();
      logoOut();
    } else {
      $nav.addClass('nav--open');
      $navOverlay.addClass('nav-open-overlay--open');
      navOpen = true;
      spinIn();
      logoIn();
    }  
  };
  
  var toggleHamburger = function() {
    var open = $nav.hasClass('nav--open');
    if(!open) {
      $hamburger.removeClass('is-active');
    } else {
      $hamburger.addClass('is-active');
    }
  };
});

External CSS

  1. https://maxcdn.bootstrapcdn.com/font-awesome/4.5.0/css/font-awesome.min.css

External JavaScript

  1. //cdnjs.cloudflare.com/ajax/libs/jqueryui/1.11.2/jquery-ui.min.js
  2. //cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js
  3. //cdnjs.cloudflare.com/ajax/libs/gsap/1.18.0/TweenMax.min.js