---
title: "Different crystal systems with examples"
subject: "Engineering Geology I"
chapter: 3
key: "semester_3/engineering_geology_i:different-crystal-systems-with-examples"
source: https://www.bctengineer.com/q/semester_3/engineering_geology_i/different-crystal-systems-with-examples
site: BCT Engineering
---

# Different crystal systems with examples

Engineering Geology I · Chapter 3: Crystallography & Mineralogy

- Asked in: 2066 Jestha (old course), 6 marks; 2064 Jestha (old course), 3 marks; 2063 Baisakh (old course), 4 marks (asked 3 times)
- Video: [What gives crystals different shapes? | The 7 crystal systems](https://www.youtube.com/watch?v=ZJXe6QENzSg) — Becky Nesel
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/engineering_geology_i/different-crystal-systems-with-examples
- Whole chapter: https://www.bctengineer.com/md/semester_3/engineering_geology_i/chapter-3

## Question

Describe the different crystal systems with diagrams and examples.

## Short answer

The seven crystal systems, defined by axis lengths and angles, are: isometric (a=b=c, all 90°; e.g., galena), tetragonal (a=b≠c, 90°; zircon), orthorhombic (a≠b≠c, 90°; topaz), monoclinic (a≠b≠c, β≠90°; gypsum), triclinic (all ≠90°; kyanite), hexagonal (a1=a2=a3≠c, 120° & 90°; beryl), and trigonal (similar axes; quartz).

## Answer

Crystals are classified into **seven systems** by the length and mutual inclination of their three (or four) crystallographic axes a, b, c.

| System | Axes | Angles | Examples |
|---|---|---|---|
| Isometric (cubic) | a = b = c | α = β = γ = 90° | Galena, pyrite, halite, garnet |
| Tetragonal | a = b ≠ c | all 90° | Zircon, rutile, chalcopyrite |
| Orthorhombic | a ≠ b ≠ c | all 90° | Topaz, barite, olivine, sulphur |
| Monoclinic | a ≠ b ≠ c | α = γ = 90°, β ≠ 90° | Gypsum, orthoclase, mica, hornblende |
| Triclinic | a ≠ b ≠ c | none 90° | Plagioclase, kyanite, microcline |
| Hexagonal | a₁ = a₂ = a₃ ≠ c (4 axes) | three at 120°, c at 90° | Beryl, apatite, graphite |
| Trigonal (rhombohedral) | a₁ = a₂ = a₃ ≠ c, 3-fold axis | as hexagonal | Quartz, calcite, dolomite, hematite |

#### Sketches of axes
```text
 Isometric        Tetragonal       Orthorhombic
  c                c                 c
  |__b             |__b              |__b
 /a=b=c           /a=b<>c           /a<>b<>c
 all 90           all 90            all 90

 Monoclinic       Triclinic         Hexagonal
  c                c                  c
  |  /b            |  /b              | a2
 /|/               | /                 |/__a1
 a  beta<>90       a  none 90        a3 (120 deg)
```

Some books group the trigonal system under hexagonal, giving six systems.

## Check yourself

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

1. Crystals are classified into how many systems by axes length and inclination?
   A. Three
   B. Seven
   C. Five
   D. Nine
   Answer: B. Seven systems, though some books merge trigonal into hexagonal to give six. (Key point: Number of systems)

2. The tetragonal system has axes:
   A. a = b = c, all at 90 degrees
   B. a = b not equal to c, all at 90 degrees
   C. a, b, c all unequal, all at 90 degrees
   D. a, b, c unequal, none at 90 degrees
   Answer: B. Two equal horizontal axes and a different vertical one. (Key point: Tetragonal axes)

3. Which describes the monoclinic system and an example?
   A. a = b = c, all 90; gypsum
   B. Unequal axes, all 90; gypsum
   C. Unequal axes, none 90; gypsum
   D. a, b, c unequal; alpha = gamma = 90 degrees, beta not 90; gypsum
   Answer: D. Gypsum, orthoclase and mica are monoclinic. (Key point: Monoclinic)

4. Which system has all three axes unequal and none at 90 degrees?
   A. Triclinic (e.g. plagioclase, kyanite)
   B. Orthorhombic
   C. Monoclinic
   D. Isometric
   Answer: A. Triclinic is the least symmetrical system. (Key point: Triclinic)

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