Setting proper perspective for child elements on a 3d plane in CSS

Question

I have an SVG hex grid tilted at a 45 degree angle. On individual hexes, I would like to place images (represented by the red rectangles) that appear to be standing upright respective to the plane of the grid. The images/rectangles don't necessarily have to be at a full 90 degrees, but I'm having the hardest time getting them to have any perspective that is even a little different from the plane.

Is there a way to unset the perspective for child elements or rework the CSS transforms somehow to make this look right?

Code

.display {
    animation: displayFlicker 100ms cubic-bezier(.37, 0, .41, 1.74) 100ms 1 normal forwards;
    -webkit-animation: displayFlicker 100ms cubic-bezier(.37, 0, .41, 1.74) 100ms 1 normal forwards;
    background: #000;
    display: block;
    border-left: 0.25rem solid #000;
    border-right: 0.25rem solid #000;
    box-sizing: border-box;
    -moz-box-sizing: border-box;
    height: 480px;
    overflow: hidden;
    width: 1096px;
}
#hexGrid {
    box-sizing: border-box;
    -moz-box-sizing: border-box;    
    display: block;
    height: 100%;
    -webkit-transform: perspective(44vw) rotateX(45deg) scale3d(1.6, 1.6, 1.6); 
    -moz-transform: perspective(44vw) rotateX(45deg) scale3d(1.6, 1.6, 1.6);    
    -ms-transform: perspective(44vw) rotateX(45deg) scale3d(1.6, 1.6, 1.6); 
    -o-transform: perspective(44vw) rotateX(45deg) scale3d(1.6, 1.6, 1.6);  
    transform: perspective(44vw) rotateX(45deg) scale3d(1.6, 1.6, 1.6);
    transform-style: preserve-3d;
    width: 100%;
}
.hexContainer {
    outline: none;
    transform-style: preserve-3d;
}
.hex {
    box-sizing: border-box;
    -moz-box-sizing: border-box;
    display: inline-block;
    height: 4.4vmin;
    opacity: 1;
    outline: none;
    position: relative;
    stroke: #0CF;
    stroke-width: 0.0625rem;
    transform: scale3d(1, 1, 1);
    transition: all linear 300ms;
    width: 8vmin;
}
.hex.open {
    fill: rgba(0, 204, 255, 0.3);
}
.hex.blocked {
    fill: url(#blockedHexPattern);
    fill-opacity: 0.3;
}
.hexContainer:focus .open, .hexContainer:hover .open {
    cursor: pointer;
    fill: rgba(0, 204, 255, 0.8);
    outline: none;
}
.hexContainer:focus .blocked, .hexContainer:hover .blocked {
    cursor: pointer;
    fill: url(#blockedHexPattern);
    fill-opacity: 1;
    outline: none;
}
.hexContainer:focus .occupied, .hexContainer:hover .occupied {
    cursor: pointer;
    fill: rgba(50, 50, 50, 0.8);
    outline: none;
}
.hexContainer:focus .open, .hexContainer:focus .open.unblock {
    transform-origin: 50% 0%;
}
.hexContainer:focus .blocked {
    opacity: 1; 
    transform-origin: 50% 0%;
}
.hexContainer.active .open {
    fill: rgba(0, 204, 255, 0.8);
    opacity: 1; 
}
#blockedHexPattern line {
    stroke: #0CF;
    stroke-width: 0.0625rem;
}
#hexGrid .rect {
    transform: rotateX(0deg);   
}

<div id="stationMap" class="display">
<svg xmlns="http://www.w3.org/2000/svg" version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="55 -30 360 360" id="hexGrid">
    <defs>
        <pattern x="0" y="0" height="10" width="10" patternUnits="userSpaceOnUse" id="blockedHexPattern">
            <line x1="0" y1="10" x2="10" y2="0"></line>
        </pattern>
    </defs>
    <a id="hex0-0" class="hexContainer">
        <polygon class="hex open" points="81.96152422706632,45 55.98076211353316,60 30,45 30.000000000000004,14.999999999999996 55.98076211353315,0 81.96152422706632,14.999999999999986"></polygon>
    </a>
    <a id="hex0-2" class="hexContainer">
        <polygon class="hex blocked" points="185.88457268119896,45 159.9038105676658,60 133.92304845413264,45 133.92304845413264,14.999999999999996 159.9038105676658,0 185.88457268119896,14.999999999999986" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex0-6" class="hexContainer">
        <polygon class="hex blocked" points="393.7306695894642,45 367.749907475931,60 341.76914536239786,45 341.76914536239786,14.999999999999996 367.749907475931,0 393.7306695894642,14.999999999999986" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex0-7" class="hexContainer">
        <polygon class="hex blocked" points="445.6921938165305,45 419.71143170299734,60 393.7306695894642,45 393.7306695894642,14.999999999999996 419.71143170299734,0 445.6921938165305,14.999999999999986" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex1-0" class="hexContainer">
        <polygon class="hex open" points="55.98076211353316,90 30.000000000000004,105 4.01923788646684,90 4.019237886466843,60 29.999999999999993,45 55.98076211353315,59.999999999999986"></polygon>
        <rect class="rect" fill="red" x="5" y="67.5" width="50" height="40"/>
    </a>
    <a id="hex1-3" class="hexContainer">
        <polygon class="hex blocked" points="211.8653347947321,90 185.88457268119893,105 159.90381056766577,90 159.90381056766577,60 185.88457268119893,45 211.8653347947321,59.999999999999986" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex1-4" class="hexContainer">
        <polygon class="hex open" points="263.82685902179844,90 237.84609690826525,105 211.8653347947321,90 211.8653347947321,60 237.84609690826525,45 263.8268590217984,59.999999999999986"></polygon>
    </a>
    <a id="hex1-5" class="hexContainer">
        <polygon class="hex open" points="315.7883832488647,90 289.80762113533154,105 263.8268590217984,90 263.8268590217984,60 289.80762113533154,45 315.7883832488647,59.999999999999986"></polygon>
    </a>
    <a id="hex1-6" class="hexContainer">
        <polygon class="hex open" points="367.749907475931,90 341.76914536239786,105 315.7883832488647,90 315.7883832488647,60 341.76914536239786,45 367.749907475931,59.999999999999986"></polygon>
    </a>
    <a id="hex1-7" class="hexContainer">
        <polygon class="hex open" points="419.71143170299734,90 393.7306695894642,105 367.749907475931,90 367.749907475931,60 393.7306695894642,45 419.71143170299734,59.999999999999986"></polygon>
        <rect class="rect" fill="red" x="369" y="67.5" width="50" height="40"/>
    </a>
    <a id="hex2-0" class="hexContainer">
        <polygon class="hex open" points="81.96152422706632,134.99999999999997 55.98076211353316,150 30,134.99999999999997 30.000000000000004,104.99999999999999 55.98076211353315,89.99999999999999 81.96152422706632,104.99999999999997"></polygon>
    </a>
    <a id="hex2-2" class="hexContainer">
        <polygon class="hex blocked" points="185.88457268119896,134.99999999999997 159.9038105676658,150 133.92304845413264,134.99999999999997 133.92304845413264,104.99999999999999 159.9038105676658,89.99999999999999 185.88457268119896,104.99999999999997" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex2-3" class="hexContainer">
        <polygon class="hex open" points="237.84609690826525,134.99999999999997 211.8653347947321,150 185.88457268119893,134.99999999999997 185.88457268119893,104.99999999999999 211.8653347947321,89.99999999999999 237.84609690826525,104.99999999999997"></polygon>
    </a>
    <a id="hex2-4" class="hexContainer">
        <polygon class="hex open" points="289.80762113533154,134.99999999999997 263.8268590217984,150 237.84609690826522,134.99999999999997 237.84609690826522,104.99999999999999 263.8268590217984,89.99999999999999 289.80762113533154,104.99999999999997"></polygon>
    </a>
    <a id="hex2-5" class="hexContainer">
        <polygon class="hex open" points="341.76914536239786,134.99999999999997 315.7883832488647,150 289.80762113533154,134.99999999999997 289.80762113533154,104.99999999999999 315.7883832488647,89.99999999999999 341.76914536239786,104.99999999999997"></polygon>
    </a>
    <a id="hex2-6" class="hexContainer">
        <polygon class="hex open" points="393.7306695894642,134.99999999999997 367.749907475931,150 341.76914536239786,134.99999999999997 341.76914536239786,104.99999999999999 367.749907475931,89.99999999999999 393.7306695894642,104.99999999999997"></polygon>
    </a>
    <a id="hex2-7" class="hexContainer">
        <polygon class="hex open" points="445.6921938165305,134.99999999999997 419.71143170299734,150 393.7306695894642,134.99999999999997 393.7306695894642,104.99999999999999 419.71143170299734,89.99999999999999 445.6921938165305,104.99999999999997"></polygon>
    </a>
    <a id="hex3-0" class="hexContainer">
        <polygon class="hex open" points="55.98076211353316,179.99999999999997 30.000000000000004,194.99999999999997 4.01923788646684,179.99999999999997 4.019237886466843,149.99999999999997 29.999999999999993,134.99999999999997 55.98076211353315,149.99999999999994"></polygon>
    </a>
    <a id="hex3-3" class="hexContainer">
        <polygon class="hex blocked" points="211.8653347947321,179.99999999999997 185.88457268119893,194.99999999999997 159.90381056766577,179.99999999999997 159.90381056766577,149.99999999999997 185.88457268119893,134.99999999999997 211.8653347947321,149.99999999999994" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex3-5" class="hexContainer">
        <polygon class="hex blocked" points="315.7883832488647,179.99999999999997 289.80762113533154,194.99999999999997 263.8268590217984,179.99999999999997 263.8268590217984,149.99999999999997 289.80762113533154,134.99999999999997 315.7883832488647,149.99999999999994" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex3-7" class="hexContainer">
        <polygon class="hex blocked" points="419.71143170299734,179.99999999999997 393.7306695894642,194.99999999999997 367.749907475931,179.99999999999997 367.749907475931,149.99999999999997 393.7306695894642,134.99999999999997 419.71143170299734,149.99999999999994" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex4-0" class="hexContainer">
        <polygon class="hex open" points="81.96152422706632,224.99999999999997 55.98076211353316,239.99999999999997 30,224.99999999999997 30.000000000000004,194.99999999999997 55.98076211353315,179.99999999999997 81.96152422706632,194.99999999999994"></polygon>
    </a>
    <a id="hex4-1" class="hexContainer">
        <polygon class="hex blocked" points="133.92304845413264,224.99999999999997 107.94228634059948,239.99999999999997 81.96152422706632,224.99999999999997 81.96152422706632,194.99999999999997 107.94228634059948,179.99999999999997 133.92304845413264,194.99999999999994" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex4-2" class="hexContainer">
        <polygon class="hex blocked" points="185.88457268119896,224.99999999999997 159.9038105676658,239.99999999999997 133.92304845413264,224.99999999999997 133.92304845413264,194.99999999999997 159.9038105676658,179.99999999999997 185.88457268119896,194.99999999999994" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex4-3" class="hexContainer">
        <polygon class="hex blocked" points="237.84609690826525,224.99999999999997 211.8653347947321,239.99999999999997 185.88457268119893,224.99999999999997 185.88457268119893,194.99999999999997 211.8653347947321,179.99999999999997 237.84609690826525,194.99999999999994" fill="url(#blockedHexPattern)"></polygon>
    </a>
    <a id="hex4-4" class="hexContainer">
        <polygon class="hex open" points="289.80762113533154,224.99999999999997 263.8268590217984,239.99999999999997 237.84609690826522,224.99999999999997 237.84609690826522,194.99999999999997 263.8268590217984,179.99999999999997 289.80762113533154,194.99999999999994"></polygon>
    </a>
    <a id="hex4-5" class="hexContainer">
        <polygon class="hex open" points="341.76914536239786,224.99999999999997 315.7883832488647,239.99999999999997 289.80762113533154,224.99999999999997 289.80762113533154,194.99999999999997 315.7883832488647,179.99999999999997 341.76914536239786,194.99999999999994"></polygon>
    </a>
    <a id="hex4-6" class="hexContainer">
        <polygon class="hex open" points="393.7306695894642,224.99999999999997 367.749907475931,239.99999999999997 341.76914536239786,224.99999999999997 341.76914536239786,194.99999999999997 367.749907475931,179.99999999999997 393.7306695894642,194.99999999999994"></polygon>
    </a>
</svg>
</div>

Answer 1

As 3d transforms can't be handled properly on svg elements, I would suggest a different approach for the grid of hexagons. It can be achieved with plain html and css as shown in this question : Responsive grid of hexagons.

This allows to make 3d transforms on child elements with the transform-style property.

Adapted to your use case, it can look like this :

DEMO

body{
  background:rgb(123, 158, 158);
  perspective:500px;
}
#categories{
  width:70%;
  margin:0 auto;
  transform:rotateX(45deg);
  transform-style: preserve-3d;
}
#categories:after{
  content:"";
  display:block;
  clear:both;
}
#categories li{
  position:relative;
  list-style-type:none;
  width:17.364%; /* = (100-4.5) / 5.5 */
  padding-bottom: 20.05%; /* =  width /0.866 */
  float:left;
  overflow:hidden;
  visibility:hidden;  
  transform: rotate(-60deg) skewY(30deg);
}

#categories li:nth-child(10n+6), #categories li:nth-child(10n+7), #categories li:nth-child(10n+8), #categories li:nth-child(10n+9), #categories li:nth-child(10n+10) {
    margin-top: -4.2%;
    margin-bottom: -4.2%;
    transform: translateX(50%) rotate(-60deg) skewY(30deg);
  }
#categories li:nth-child(10n+6){
    margin-left:0.5%;
  }
  #categories li:nth-child(5n+2) {
    margin-left:1%;
    margin-right:1%;
  }
  #categories li:nth-child(5n+3),#categories li:nth-child(5n+4){
    margin-right:1%;
  }

#categories li div{
  position:absolute;
  visibility:visible;
  width:100%; height:100%;
  text-align:center;
  color:#fff;
  overflow:hidden;  
  transform: skewY(-30deg) rotate(60deg);
  background-color:rgba(0,0,0,.2);
  transition:background-color .3s;
  border-left:2px solid #000;  
  border-right:2px solid #000;
  box-sizing:border-box;
  -webkit-backface-visibility:hidden;
}
#categories li div:hover, #categories .up:hover span:after{
  background-color:rgba(0,0,0,.5);
}
#categories li div:before, #categories li div:after{
  content:'';
  position:absolute;
  width:100%;height:49.6%;
  left:-2px;top:25.5%;
  
  border-left:2px solid #000;
  border-right:2px solid #000;
  transform:rotate(60deg);
  visibility:visible;
}
#categories li div:before{
    transform:rotate(-60deg);
}

#categories li img{
  display:block;
  left:-100%; right:-100%;
  width: auto; height:100%;
  margin:0 auto;
  visibility:visible;
}
#categories .up, #categories .up div{
  transform-style:preserve-3d;
  overflow:visible;
  visibility:hidden;
  background-color:transparent;
}
#categories .up span{
  display:block;
  width:100%;height:100%;
  position:absolute;
  top:0; left:0;
  overflow:hidden;
}
#categories .up span:after{
  content:'';
  position:absolute;
  left:0;top:0;
  width:100%;height:100%;
  border-left:2px solid #000;
  border-right:2px solid #000;
  box-sizing:border-box;
  background-color:rgba(0,0,0,.2);
  transform: skewY(-30deg) rotate(60deg);
  transition:background-color .3s;
  visibility:visible;
}

#categories .up img{
  width:100%; height:auto;
  position:absolute;
  transform-origin: 50% 100%;
  transform: rotateX(-45deg);
  z-index:1;
}

<ul id="categories" class="clr">
	  <li><div></div></li>
  <li class="up"><span></span><div><img src="https://farm9.staticflickr.com/8461/8048823381_0fbc2d8efb.jpg" alt=""/></div></li>
  <li><div></div></li>  
  <li><div></div></li>
  <li class="up"><span></span><div><img src="https://farm7.staticflickr.com/6217/6216951796_e50778255c.jpg" alt=""/></div></li>
  <li class="pusher"></li>
  <li class="pusher"></li>
  <li class="pusher"></li>
  <li><div></div></li>
  <li class="pusher"></li>
  <li><div></div></li>
  <li><div></div></li>
  <li><div></div></li>
  <li class="pusher"></li>
  <li><div></div></li>
  <li class="up"><span></span><div><img src="https://farm5.staticflickr.com/4144/5053682635_b348b24698.jpg" alt=""/></div></li>
  <li class="pusher"></li>
  <li><div></div></li>
  <li><div></div></li>
</ul>

This grid of hexagons can be adapted to several use cases (number of hexagons per row, hexagon alignment...) more examples in this collection : Responsive grids of hexagons