Wireframe Shader With Shared Lines Removed

I am working on this wireframe shader:

It uses some adapted code from various shaders, and I am wanting to get rid of the lines that cut through the quads. I really do not know how to go about this in HLSL and was wondering if someone could share their insight.

 Shader "WireframeShader"
 {
     Properties
     {
         [HDR] _EmissionColor("Color", Color) = (0,0,0)
            
         _EdgeThickness ("Edge Threshold", float) = .9
         _WireThickness ("Wire Thickness", RANGE(0, 800)) = 100
  }
 
     SubShader
     {
         Tags { "RenderType"="Opaque" }
 
 
         Pass
         {
             CGPROGRAM
             #pragma vertex vert
             #pragma geometry geom
             #pragma fragment frag
             #pragma multi_compile _ USEDISCARD_ON
             #include "UnityCG.cginc"
 
             float _WireThickness;
             fixed4 _EmissionColor;
             float _EdgeThickness;
 
             struct appdata
             {
                 float4 vertex : POSITION;
             };
 
             struct v2g
             {
                 float4 projectionSpaceVertex : SV_POSITION;
                 float4 worldSpacePosition : TEXCOORD1;
             };
 
             struct g2f
             {
                 float4 projectionSpaceVertex : SV_POSITION;
                 float4 worldSpacePosition : TEXCOORD0;
                 float4 dist : TEXCOORD1;
             };
 
             
             v2g vert (appdata v)
             {
                 v2g o;
                 o.projectionSpaceVertex = UnityObjectToClipPos(v.vertex);
                 o.worldSpacePosition = mul(unity_ObjectToWorld, v.vertex);
                 return o;
             }
             
             [maxvertexcount(3)]
             void geom(triangle v2g i[3], inout TriangleStream<g2f> triangleStream)
             {
                 float2 p0 = i[0].projectionSpaceVertex.xy / i[0].projectionSpaceVertex.w;
                 float2 p1 = i[1].projectionSpaceVertex.xy / i[1].projectionSpaceVertex.w;
                 float2 p2 = i[2].projectionSpaceVertex.xy / i[2].projectionSpaceVertex.w;
 
                 float2 edge0 = p2 - p1;
                 float2 edge1 = p2 - p0;
                 float2 edge2 = p1 - p0;
 
                 float area = abs(edge1.x * edge2.y - edge1.y * edge2.x);
                 float wireThickness = 800 - _WireThickness;
 
                 g2f o;
                 o.worldSpacePosition = i[0].worldSpacePosition;
                 o.projectionSpaceVertex = i[0].projectionSpaceVertex;
                 o.dist.xyz = float3( (area / length(edge0)), 0.0, 0.0) * o.projectionSpaceVertex.w * wireThickness;
                 o.dist.w = 1.0 / o.projectionSpaceVertex.w;
                 triangleStream.Append(o);
 
                 o.worldSpacePosition = i[1].worldSpacePosition;
                 o.projectionSpaceVertex = i[1].projectionSpaceVertex;
                 o.dist.xyz = float3(0.0, (area / length(edge1)), 0.0) * o.projectionSpaceVertex.w * wireThickness;
                 o.dist.w = 1.0 / o.projectionSpaceVertex.w;
                 triangleStream.Append(o);
 
                 o.worldSpacePosition = i[2].worldSpacePosition;
                 o.projectionSpaceVertex = i[2].projectionSpaceVertex;
                 o.dist.xyz = float3(0.0, 0.0, (area / length(edge2))) * o.projectionSpaceVertex.w * wireThickness;
                 o.dist.w = 1.0 / o.projectionSpaceVertex.w;
                 triangleStream.Append(o);
             }
 
             fixed4 frag (g2f i) : SV_Target
             {
                 float minDistanceToEdge = min(i.dist[0], min(i.dist[1], i.dist[2])) * i.dist[3];
                 if(minDistanceToEdge > _EdgeThickness)
                 {
                     discard;
                     return (0,0,0,0);
                 }
                 return _EmissionColor;
             }
             ENDCG
         }
     }
 }