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Construct geometric table, 6 vertices

Short answer

A geometric table stores polygon mesh data in vertex, edge, and surface tables. For 3 faces, 6 vertices, and 8 edges: vertices V1(0,2,0), V2(2,2,0), V3(4,2,0), V4(0,0,0), V5(2,0,0), V6(4,0,0); edges E1(V1,V2) to E8(V2,V6); surfaces S1(E1,E7,E5,E6), S2(E2,E3,E8), S3(E8,E4,E7).

What is a geometric table? Construct a geometric table for considering an object having 3 surfaces formed from 6 vertices and 8 edges.

A geometric table (polygon table) stores the shape of a polygon-mesh object as three linked tables: vertex table (coordinates), edge table (end vertices) and surface table (edges forming each face). The attributes are held in separate tables.

Construction

Euler check for this object: V − E + F = 6 − 8 + 3 = 1, which is correct for an open surface patch (plane mesh) of 3 faces. We design a planar patch:

V1-------V2-------V3
|        | \  S2   |
|   S1   |   \     |
|        | S3  \   |
V4-------V5-------V6

Let S1 be the quadrilateral V1 V2 V5 V4, S2 the triangle V2 V3 V6, and S3 the triangle V2 V6 V5 (the diagonal V2V6 divides the right part). Assumed coordinates:

Vertex table

Vertexxyz
V1020
V2220
V3420
V4000
V5200
V6400

Edge table

EdgeVerticesSurfaces
E1V1 V2S1
E2V2 V3S2
E3V3 V6S2
E4V6 V5S3
E5V5 V4S1
E6V4 V1S1
E7V2 V5S1, S3
E8V2 V6S2, S3

Surface table

SurfaceEdges
S1E1 E7 E5 E6
S2E2 E3 E8
S3E8 E4 E7

Check: 6 vertices, 8 edges, 3 surfaces. Every vertex is in at least two edges, every edge is in at least one surface, and each surface is a closed loop.

✓ Answer checked by Claude Opus 5.5 (high effort)

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