Apply a fixed nav to the left of the viewport. Styled to accommodate Icons in the menu.

style.css

/* Primary Navigation
--------------------------------------------- */

.nav-primary {
	background-color: #242831;
	height: 100%;
	left: 0;
	position: fixed; /* Make our navigation stick to the left of the viewport at all times */
	top: 0;
	width: 80px;
	z-index: 9999;
}

.admin-bar .nav-primary {
	top: 32px; /* When the admin bar is present, adjust our nav accordingly */
}

.nav-primary > .wrap {
	padding: 0;
}

.nav-primary .genesis-nav-menu a:hover,
.nav-primary .genesis-nav-menu a:focus,
.nav-primary .genesis-nav-menu .menu-item > a:hover:before,
.nav-primary .genesis-nav-menu .menu-item.current-menu-item > a,
.nav-primary .genesis-nav-menu .menu-item.current-menu-item > a:before {
	color: #fff;
	text-decoration: none;
}

.nav-primary .genesis-nav-menu a {
	background-color: #242831;
	color: #57595d;
	display: block;
  height: 79px; /* Compensate for 1px bottom border */
	padding: 0;
	text-decoration: none;
	text-transform: uppercase;
  width: 80px;
}

.nav-primary .genesis-nav-menu .menu-item {
	border-bottom: 1px solid #3d4652;
	display: block;
	height: 80px;
  position: relative;
  text-align: left;
  width: 80px;
}

.nav-primary .genesis-nav-menu .menu-item:before {
	display: none; /* Hide the pseudo-element applied to the original menu-item since we've moved that class to the anchor tag */
}

.nav-primary .genesis-nav-menu .menu-item > a:before {
	background-color: #242831;
	border-left: 5px solid transparent;
	color: rgba(255,255,255,.4);
	display: block;
	font-size: 34px;
	left: 0;
  height: 79px; /* Compensate for 1px border-bottom on the parent menu-item */
  padding: 23px 26px 22px 21px;
  position: absolute;
  width: 80px;
  z-index: 10;
}

.nav-primary .genesis-nav-menu a > span {
	background-color: #3d4652;
	border-right: 5px solid #242831;
	color: #fff;
	display: block;
	left: 0;
	transform: translateX(-100%); /* Hide our text by moving it all the way to the left, under the icon */
	font-weight: bold;
	opacity: 0;
	padding: 32px 30px 31px;
	position: fixed; /* Position the text relative to the viewport, not the nav */
	white-space: nowrap; /* Let our text stay on one line */
	z-index: -1;
}