How to create a radial menu with submenus using CSS and icons without images?

$d: 2em; // diameter of central round button
$r: 16em; // radius of menu
$n: 3; // must match number of list items in DOM
$exp: 3em; // menu item height
$tip: .75em; // dimension of tip on middle menu item
$w: .5em; // width of ends
$cover-dim: 2*($r - $exp); // dimension of the link cover
$angle: 15deg; // angle for a menu item
$skew-angle: 90deg - $angle; // how much to skew a menu item to $angle
$scale-factor: cos($skew-angle); // correction factor - see vimeo.com/98137613 from min 15
$off-angle: .125deg; // offset angle so we have a little space between menu items

// don't show the actual checkbox
input {
  transform: translate(-100vw); // move offscreen
  visibility: hidden; // avoid paint
}

// change state of menu to revealed on checking the checkbox
input:checked ~ ul {
    transform: scale(1); 
    opacity: .999;
    // ease out back from easings.net/#easeOutBack
    transition: .5s cubic-bezier(0.175, 0.885, 0.32, 1.275);
}

// position everything absolutely such that their left bottom corner 
// is in the middle of the screen
label, ul, li {
    position: absolute;
    left: 50%; bottom: 50%;
}

// visual candy styles
label, a {
    color: #858596;
    font: 700 1em/ #{$d} sans-serif;
    text-align: center;
    text-shadow: 0 1px 1px #6c6f7e;
    cursor: pointer;
}

label {
    z-index: 2; // place it above the menu which has z-index: 1
    margin: -$d/2; // position correction such that it's right in the middle
    width: $d; height: $d;
    border-radius: 50%;
    box-shadow: 0 0 1px 1px white, 
                0 .125em .25em #876366, 
                0 .125em .5em #876366;
    background: radial-gradient(#d4c7c5, #e5e1dd);
}

ul {
    z-index: 1;
    margin: -$r + $exp + 1.5*$d 0; // position correction
    padding: 0;
    list-style: none;
    transform-origin: 50% (-$r + $exp);
    transform: scale(.001); // initial state: scaled down to invisible
    will-change: transform; // better perf on transitioning transform
    opacity: .001; // initial state: transparent
    filter: drop-shadow(0 .125em .25em #847c77) 
            drop-shadow(0 .125em .5em #847c77);
    // ease in back, also from easings.net
    transition: .5s cubic-bezier(0.6, -0.28, 0.735, 0.045);

    // menu ends
    &:before, &:after {
        position: absolute;
        margin: -$exp (-$w/2);
        width: $w; height: $exp;
        transform-origin: 50% 100%;
        background: linear-gradient(#ddd, #c9c4bf);
        content: '';
    }

    &:before {
        border-radius: $w 0 0 $w;
        transform: rotate(-.5*$n*$angle) 
                   translate(-$w/2, -$r + $exp);
        box-shadow: inset 1px 0 1px #eee;
    }
    &:after {
        border-radius: 0 $w $w 0;
        transform: rotate(.5*$n*$angle) 
            translate($w/2, -$r + $exp);
        box-shadow: inset -1px 0 1px #eee;
    }
}

li {
    overflow: hidden;
    width: $r; height: $r;
    transform-origin: 0 100%;

    @for $i from 0 to $n {
        &:nth-child(#{$i + 1}) {
            $curr-angle: $i*$angle + 
                ($i + .5)*$off-angle - 
                .5*$n*($angle + $off-angle);

            // make each list item a rhombus rotated around its bottom left corner
            // see explanation from minute 33:10 youtube.com/watch?v=ehjoh_MmE9A
            transform: rotate($curr-angle)
                       skewY(-$skew-angle) 
                       scaleX($scale-factor);

            // add tip for the item n the middle, just a rotated square
            @if $i == ($n - 1)/2 {
                a:after {
                    position: absolute;
                    top: $exp; left: 50%;
                    margin: -$tip/2;
                    width: $tip; height: $tip;
                    transform: rotate(45deg);
                    box-shadow: 
                        inset -1px -1px 1px #eee;
                    background: linear-gradient(-45deg, 
                        #bbb, #c9c4bf 50%);
                    content: '';
                }
            }
        }
    }

    a, &:before {
        margin: 0 (-$r);
        width: 2*$r; height: 2*$r;
        border-radius: 50%;
    }

    &:before, &:after {
        position: absolute;
        border-radius: 50%;
        // undo distorting transforms from menu item (parent li)
        transform: scaleX(1/$scale-factor) 
                   skewY($skew-angle);
        content: '';
    }

    // actual background of the arched menu items
    &:before {
        box-shadow: 
            inset 0 0 1px 1px #fff, 
            inset 0 0 $exp #ebe7e2, 
            inset 0 0 1px ($exp - .0625em) #c9c4bf, 
            inset 0 0 0 $exp #dcdcdc;
    }

    // cover to prevent click action in between the star and menu items
    &:after {
        top: 100%; left: 0;
        margin: -$cover-dim/2;
        width: $cover-dim; height: $cover-dim;
        border-radius: 50%;
    }
}

a {
    display: block;
    // undo distorting transforms from menu item and rotate into right position
    transform: scaleX(1/$scale-factor) 
               skewY($skew-angle) 
               rotate($angle/2);
    line-height: $exp;
    text-align: center;
    text-decoration: none;
}

<input type='checkbox'>