---
title: "Construct geometric table, 6 vertices"
subject: "Computer Graphics"
chapter: 6
key: "semester_5/computer_graphics:geometric-table-construct-6-vertices"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/geometric-table-construct-6-vertices
site: BCT Engineering
---

# Construct geometric table, 6 vertices

Computer Graphics · Chapter 6: Surface Modeling

- Asked in: 2069 Chaitra, 2+6 marks
- Video: [Polygon Surfaces: 3D Object Representations](https://www.youtube.com/watch?v=NY53ihpQ2HM) — Prof. Brinal Colaco
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/geometric-table-construct-6-vertices
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-6

## Question

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

## 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).

## Answer

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:

```text
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**

| Vertex | x | y | z |
|---|---|---|---|
| V1 | 0 | 2 | 0 |
| V2 | 2 | 2 | 0 |
| V3 | 4 | 2 | 0 |
| V4 | 0 | 0 | 0 |
| V5 | 2 | 0 | 0 |
| V6 | 4 | 0 | 0 |

**Edge table**

| Edge | Vertices | Surfaces |
|---|---|---|
| E1 | V1 V2 | S1 |
| E2 | V2 V3 | S2 |
| E3 | V3 V6 | S2 |
| E4 | V6 V5 | S3 |
| E5 | V5 V4 | S1 |
| E6 | V4 V1 | S1 |
| E7 | V2 V5 | S1, S3 |
| E8 | V2 V6 | S2, S3 |

**Surface table**

| Surface | Edges |
|---|---|
| S1 | E1 E7 E5 E6 |
| S2 | E2 E3 E8 |
| S3 | E8 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A geometric (polygon) table consists of:
   A. Vertex, edge and surface tables
   B. Only colour tables
   C. Pixel buffers
   D. Transformation matrices
   Answer: A. They store the shape. (Key point: Geometric table)

2. For 6 vertices, 8 edges and 3 faces V - E + F equals:
   A. 2
   B. 1
   C. 0
   D. 3
   Answer: B. 6 - 8 + 3 = 1, valid for an open planar patch. (Key point: Euler check)

3. In the constructed table, E7 (V2 V5) belongs to:
   A. S2 only
   B. S1 and S3
   C. S1 only
   D. No surface
   Answer: B. It separates the quadrilateral S1 from triangle S3. (Key point: Shared edge)

4. The triangle S2 = V2 V3 V6 uses edges:
   A. E2 E3 E8
   B. E1 E7 E5
   C. E4 E7 E8
   D. E2 E4 E6
   Answer: A. V2V3 = E2, V3V6 = E3, V2V6 = E8. (Key point: Surface S2)

## Related in Computer Graphics

- [Geometric tables for 3D object](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ageometric-tables-3d-error-free) — Computer Graphics, chapter 6
- [Storing geometric and attribute information](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ageometric-attribute-info-storage) — Computer Graphics, chapter 6, asked 8×
- [Polygon table and normal of S1](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Apolygon-table-surface-normal-s1) — Computer Graphics, chapter 6
- [Conditions for error-free polygon table](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aerror-free-polygon-table-conditions) — Computer Graphics, chapter 6, asked 3×

## Related in other subjects

- [Geometric properties from channel offsets](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aopen-channel-cross-section-from-table-properties) — Hydraulics, chapter 6
- [Two-adjacent-edges discontinuous slab, 3.5x4.5 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Atwo-adjacent-edges-discontinuous-slab-3) — Design of RCC Structure, chapter 9
- [Principal points, object for infinity image](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Atwo-identical-lenses-infinity-object) — Engineering Physics, chapter 5
- [Demand 2074 BS, geometric and decreasing rate](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-a75) — Water Supply Engineering, chapter 3