JSFiddle - React, Tailwind, and code Playground

HTML

<section class="container">
    <div id="box">
        <figure class="front">1</figure>
        <figure class="back">2</figure>
        <figure class="right">3</figure>
        <figure class="left">4</figure>
        <figure class="top">5</figure>
        <figure class="bottom">6</figure>
    </div>
</section>

<section id="options">
    <p>
        &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<button id="up">Up</button>
        <br/><br/>
        <button id="left">Left</button>
        <button id="right">Right</button>
        <br/><br/>
        &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<button id="down">Down</button>
    </p>
</section>

CSS

.container {
    width: 150px;
    height: 100px;
    position: relative;
    margin: 25px auto 25px auto;
    perspective: 600px;
}

#box,#outer {
    width: 100%;
    height: 100%;
    position: absolute;
    transform-style: preserve-3d;
}

#box figure {
    display: block;
    position: absolute;
    border: 1px solid black;
    line-height: 98px;
    font-size: 45px;
    text-align: center;
    font-weight: bold;
    color: white;
}

figure {
    margin: 0;
}

#box .front,
#box .back {
    width: 148px;
    height: 98px;
}

#box .right,
#box .left {
    width: 48px;
    height: 98px;
    left: 50px;
}

#box .top,
#box .bottom {
    width: 148px;
    height: 48px;
    top: 25px;
    line-height: 48px;
}

#box .front {
    background: hsla(000, 100%, 50%, 0.7);
}

#box .back {
    background: hsla(160, 100%, 50%, 0.7);
}

#box .right {
    background: hsla(120, 100%, 50%, 0.7);
}

#box .left {
    background: hsla(180, 100%, 50%, 0.7);
}

#box .top {
    background: hsla(240, 100%, 50%, 0.7);
}

#box .bottom {
    background: hsla(300, 100%, 50%, 0.7);
}

#box .front {
    transform: translateZ(25px);
	
}

#box .back {
    transform: rotateX(180deg) translateZ(25px);
}

#box .right {
    transform: rotateY(90deg) translateZ(75px);
}

#box .left {
    transform: rotateY(-90deg) translateZ(75px);
}

#box .top {
    transform: rotateX(90deg) translateZ(50px);
}

#box .bottom {
    transform: rotateX(-90deg) translateZ(50px);
}

#outer {
    transform: translateZ(-50px);
}

#outer.up {
    transition: transform 1s;
    transform: translateZ(-50px) rotateX(90deg);
}

#outer.down {
    transition: transform 1s;
    transform: translateZ(-50px) rotateX(-90deg);
}

#outer.left {
    transition: transform 1s;
    transform: translateZ(-50px) rotateY(-90deg);
}

#outer.right {
    transition: transform 1s;
    transform: translateZ(-50px) rotateY(90deg);
}

JavaScript

$('document').ready(function() {
    $("#box").wrap("<div id='outer'></div>");
    var pending=null;

    function rotate(axis,angle,dir) {
        if (pending) return;
        $("#outer").removeClass().addClass(dir);
        var current=$("#box").css("transform");
        if (current=='none') current='';
        pending="rotate"+axis+"("+angle+"deg) "
          + current;
    }
    
    $("#outer").bind('transitionend', function() {
        $(this).removeClass();
        $("#box").css('transform',pending);
        pending=null;
    });
    
    $('#up').bind('click', function() {
        rotate('X',90,"up");
    });

    $('#down').bind('click', function() {
        rotate('X',-90,"down");
    });

    $('#right').bind('click', function() {
        rotate('Y',90,"right");
    });

    $('#left').bind('click', function() {
        rotate('Y',-90,"left");
    });

    $(window).bind('keyup', function(event) {
        switch (event.keyCode) {
            case 37: // left
                $('#left').click();
                break;

            case 38: // up
                $('#up').click();
                break;

            case 39: // right
                $('#right').click();
                break;

            case 40: // down
                $('#down').click();
                break;
        }
    });
    
});