---
title: "Symmetry elements, crystal systems, rock-forming minerals"
subject: "Engineering Geology I"
chapter: 3
key: "semester_3/engineering_geology_i:symmetry-elements-crystal-systems-rockforming"
source: https://www.bctengineer.com/q/semester_3/engineering_geology_i/symmetry-elements-crystal-systems-rockforming
site: BCT Engineering
---

# Symmetry elements, crystal systems, rock-forming minerals

Engineering Geology I · Chapter 3: Crystallography & Mineralogy

- Asked in: 2061 Baisakh (old course), 2+3+3 marks
- Video: [Crystal Systems Explained](https://www.youtube.com/watch?v=MqC_0OaPHHw) — SALT SHACK - EDUCATION
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/engineering_geology_i/symmetry-elements-crystal-systems-rockforming
- Whole chapter: https://www.bctengineer.com/md/semester_3/engineering_geology_i/chapter-3

## Question

Describe the symmetry elements and crystal systems with figures. Explain the engineering significance of rock-forming minerals.

## Short answer

Symmetry elements are planes, axes, and centre of symmetry. The six crystal systems are isometric, tetragonal, orthorhombic, monoclinic, triclinic, and hexagonal/trigonal. Rock-forming minerals like quartz, feldspar, and mica influence rock strength and durability.

## Answer

#### Elements of symmetry
Symmetry is the repetition of faces and edges in a crystal. There are three elements.
1. **Plane of symmetry**: a plane dividing the crystal into two mirror-image halves. Axial planes pass through two axes; diagonal planes pass through one axis and bisect the angle between the other two.
2. **Axis of symmetry**: a line about which rotation by 360° repeats the form 2 (diad, 180°), 3 (triad, 120°), 4 (tetrad, 90°) or 6 (hexad, 60°) times.
3. **Centre of symmetry**: a point at which any line through it meets similar faces at equal distance on both sides.

A cube has 9 planes, 13 axes and 1 centre.

#### Crystal systems
| System | Axes | Angles | Symmetry (normal class) | Example |
|---|---|---|---|---|
| Isometric | a = b = c | 90°, 90°, 90° | 9 P, 13 A, 1 C | Galena, garnet |
| Tetragonal | a = b ≠ c | all 90° | 5 P, 5 A, 1 C | Zircon |
| Orthorhombic | a ≠ b ≠ c | all 90° | 3 P, 3 A, 1 C | Topaz, barite |
| Monoclinic | a ≠ b ≠ c | β ≠ 90° | 1 P, 1 A, 1 C | Gypsum, orthoclase |
| Triclinic | a ≠ b ≠ c | none 90° | 1 C only | Plagioclase |
| Hexagonal | a₁ = a₂ = a₃ ≠ c | 120° and 90° | 7 P, 7 A, 1 C | Beryl, apatite |
| Trigonal | as hexagonal, 3-fold axis | as hexagonal | 3 P, 4 A, 1 C | Calcite, quartz |

```text
 Isometric     Tetragonal    Orthorhombic   Monoclinic
   c             c              c              c  /
   |_b           |_b            |_b            |_/b
  /a=b=c        /a=b<>c       /a<>b<>c        /a   beta<>90
```

#### Engineering significance of rock-forming minerals
- **Quartz**: hard, stable, no cleavage; gives strong, durable rocks; may react with cement alkalis if amorphous.
- **Feldspar**: common, hardness 6, but weathers to clay and weakens rock.
- **Mica**: perfect cleavage; mica-rich rocks (schist, phyllite) are weak and cause slope and tunnel failures.
- **Calcite**: soft and soluble; limestone makes cement but has cavities that cause leakage.
- **Amphibole, pyroxene and olivine**: dense and strong, found in dark rocks such as basalt and gabbro, but they weather faster than quartz.

## Check yourself

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

1. A centre of symmetry is a point where any line through it:
   A. Meets only the corners
   B. Meets one face only
   C. Divides the crystal into unequal halves
   D. Meets similar faces at equal distances on both sides
   Answer: D. It is an inversion point. (Key point: Centre of symmetry)

2. Which system has only a centre of symmetry in its normal class?
   A. Triclinic
   B. Isometric
   C. Orthorhombic
   D. Hexagonal
   Answer: A. Triclinic has 1 C only. (Key point: Triclinic)

3. The isometric normal class has:
   A. 3 planes, 3 axes and 1 centre
   B. 9 planes, 13 axes and 1 centre
   C. 7 planes, 7 axes and 1 centre
   D. 1 plane, 1 axis and 1 centre
   Answer: B. Isometric is the most symmetrical. (Key point: Isometric count)

4. Which mineral gives strong durable rocks but may react with cement alkalis if amorphous?
   A. Mica
   B. Calcite
   C. Quartz
   D. Feldspar
   Answer: C. Hard stable quartz is good, except reactive silica in concrete. (Key point: Engineering significance)

## Related in Engineering Geology I

- [Engineering significance of rock-forming minerals](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aengineering-significance-of-rockforming-minerals) — Engineering Geology I, chapter 3, asked 3×
- [Isometric crystal system with symmetry elements](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aisometric-crystal-system-with-symmetry) — Engineering Geology I, chapter 3, asked 5×
- [Engineering significance of three rock types](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aengineering-significance-of-three-rock) — Engineering Geology I, chapter 4, asked 5×
- [Petrology; engineering significance of rock classes](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Apetrology-engineering-significance-of-rock) — Engineering Geology I, chapter 4
- [Physical properties; orthorhombic symmetry elements](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aphysical-properties-orthorhombic-symmetry-elements) — Engineering Geology I, chapter 3
- [Symmetry elements of crystals](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Asymmetry-elements-of-crystals) — Engineering Geology I, chapter 3, asked 13×

## Related in other subjects

- [Rock forming minerals and significance](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Arock-forming-minerals) — Engineering Geology II, chapter 1, asked 6×